Abstract

The quantised nature of the electromagnetic field sets the classical limit to the sensitivity of position measurements. However, techniques based on the properties of quantum states can be exploited to accurately measure the relative displacement of a physical object beyond this classical limit. In this work, we use a simple scheme based on the split-detection of quantum correlations to measure the position of a shadow at the single-photon light level, with a precision that exceeds the shot-noise limit. This result is obtained by analysing the correlated signals of bi-photon pairs, created in parametric downconversion and detected by an electron multiplying CCD (EMCCD) camera employed as a split-detector. By comparing the measured statistics of spatially anticorrelated and uncorrelated photons we were able to observe a significant noise reduction corresponding to an improvement in position sensitivity of up to 17% (0.8dB). Our straightforward approach to sub-shot-noise position measurement is compatible with conventional shadow-sensing techniques based on the split-detection of light-fields, and yields an improvement that scales favourably with the detector’s quantum efficiency.

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References

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    [Crossref] [PubMed]

2016 (4)

R. P. Middlemiss, A. Samarelli, D. J. Paul, J. Hough, S. Rowan, and G. D. Hammond, “Measurement of the Earth tides with a MEMS gravimeter,” Nature 531, 614–617 (2016).
[Crossref] [PubMed]

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

K. Lyons, S. Pang, P. G. Kwiat, and A. N. Jordan, “Precision optical displacement measurements using biphotons,” Phys. Rev. A 93, 043841 (2016).
[Crossref]

A. Avella, I. Ruo-Berchera, I. P. Degiovanni, G. Brida, and M. Genovese, “Absolute calibration of an EMCCD camera by quantum correlation, linking photon counting to the analog regime,” Opt. Lett. 41, 1841–1844 (2016).
[Crossref] [PubMed]

2014 (2)

E. Lantz, P.-A. Moreau, and F. Devaux, “Optimizing the signal-to-noise ratio in the measurement of photon pairs with detector arrays,” Physical Review A 90, 063811 (2014).
[Crossref]

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

2013 (2)

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution Microscopy with Quantum Emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref] [PubMed]

D. S. Tasca, M. P. Edgar, F. Izdebski, G. S. Buller, and M. J. Padgett, “Optimizing the use of detector arrays for measuring intensity correlations of photon pairs,” Phys. Rev. A 88013816 (2013).
[Crossref]

2012 (2)

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

O. Schwartz and D. Oron, “Improved resolution in fluorescence microscopy using quantum correlations,” Phys. Rev. A 85, 033812 (2012).
[Crossref]

2010 (2)

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[Crossref]

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Purely spatial coincidences of twin photons in parametric spontaneous down-conversion,” Phys. Rev. A 81, 043825 (2010).
[Crossref]

2008 (3)

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of Sub-Shot-Noise Correlations of Spatial Fluctuations in the Photon-Counting Regime,” Phys. Rev. Lett. 101, 233604 (2008).
[Crossref] [PubMed]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. 386, 2262–2270 (2008).
[Crossref]

2004 (2)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-Enhanced Measurements: Beating the Standard Quantum Limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of Sub-Shot-Noise Spatial Correlation in High-Gain Parametric Down Conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[Crossref]

2003 (3)

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A Quantum Laser Pointer,” Science 301, 940–943 (2003).
[Crossref] [PubMed]

M. Robbins and B. Hadwen, “The noise performance of electron multiplying charge-coupled devices,” IEEE T. Electron Dev. 50, 1227–1232 (2003).
[Crossref]

A. G. Basden, C. A. Haniff, and C. D. Mackay, “Photon counting strategies with low-light-level CCDs,” Mon. Not. R. Astron. Soc. 345, 985 (2003).
[Crossref]

1995 (2)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Physical Review Letters 74, 3600–3603 (1995).
[Crossref]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Physical Review A 52, R3429–R3432 (1995).
[Crossref]

1990 (2)

1988 (1)

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[Crossref]

1987 (1)

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light - Enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[Crossref] [PubMed]

1985 (1)

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Agnew, M.

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Avella, A.

Aytür, O.

O. Aytür and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. 65, 1551–1554 (1990).
[Crossref] [PubMed]

Bache, M.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of Sub-Shot-Noise Spatial Correlation in High-Gain Parametric Down Conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[Crossref]

Bachor, H.-A.

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A Quantum Laser Pointer,” Science 301, 940–943 (2003).
[Crossref] [PubMed]

Basden, A. G.

A. G. Basden, C. A. Haniff, and C. D. Mackay, “Photon counting strategies with low-light-level CCDs,” Mon. Not. R. Astron. Soc. 345, 985 (2003).
[Crossref]

Blanchet, J.-L.

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Purely spatial coincidences of twin photons in parametric spontaneous down-conversion,” Phys. Rev. A 81, 043825 (2010).
[Crossref]

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of Sub-Shot-Noise Correlations of Spatial Fluctuations in the Photon-Counting Regime,” Phys. Rev. Lett. 101, 233604 (2008).
[Crossref] [PubMed]

E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. 386, 2262–2270 (2008).
[Crossref]

Bowen, W. P.

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A Quantum Laser Pointer,” Science 301, 940–943 (2003).
[Crossref] [PubMed]

Boyd, R.

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Brambilla, E.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of Sub-Shot-Noise Spatial Correlation in High-Gain Parametric Down Conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[Crossref]

Brida, G.

A. Avella, I. Ruo-Berchera, I. P. Degiovanni, G. Brida, and M. Genovese, “Absolute calibration of an EMCCD camera by quantum correlation, linking photon counting to the analog regime,” Opt. Lett. 41, 1841–1844 (2016).
[Crossref] [PubMed]

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[Crossref]

Buller, G.

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Buller, G. S.

D. S. Tasca, M. P. Edgar, F. Izdebski, G. S. Buller, and M. J. Padgett, “Optimizing the use of detector arrays for measuring intensity correlations of photon pairs,” Phys. Rev. A 88013816 (2013).
[Crossref]

Chelkowski, S.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Danzmann, K.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Degiovanni, I. P.

A. Avella, I. Ruo-Berchera, I. P. Degiovanni, G. Brida, and M. Genovese, “Absolute calibration of an EMCCD camera by quantum correlation, linking photon counting to the analog regime,” Opt. Lett. 41, 1841–1844 (2016).
[Crossref] [PubMed]

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

Deutsch, Z.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution Microscopy with Quantum Emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref] [PubMed]

Devaux, F.

E. Lantz, P.-A. Moreau, and F. Devaux, “Optimizing the signal-to-noise ratio in the measurement of photon pairs with detector arrays,” Physical Review A 90, 063811 (2014).
[Crossref]

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Purely spatial coincidences of twin photons in parametric spontaneous down-conversion,” Phys. Rev. A 81, 043825 (2010).
[Crossref]

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of Sub-Shot-Noise Correlations of Spatial Fluctuations in the Photon-Counting Regime,” Phys. Rev. Lett. 101, 233604 (2008).
[Crossref] [PubMed]

E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. 386, 2262–2270 (2008).
[Crossref]

Edgar, M.

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Edgar, M. P.

D. S. Tasca, M. P. Edgar, F. Izdebski, G. S. Buller, and M. J. Padgett, “Optimizing the use of detector arrays for measuring intensity correlations of photon pairs,” Phys. Rev. A 88013816 (2013).
[Crossref]

Fabre, C.

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A Quantum Laser Pointer,” Science 301, 940–943 (2003).
[Crossref] [PubMed]

Forneris, J.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

Franzen, A.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Furfaro, L.

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Purely spatial coincidences of twin photons in parametric spontaneous down-conversion,” Phys. Rev. A 81, 043825 (2010).
[Crossref]

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of Sub-Shot-Noise Correlations of Spatial Fluctuations in the Photon-Counting Regime,” Phys. Rev. Lett. 101, 233604 (2008).
[Crossref] [PubMed]

E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. 386, 2262–2270 (2008).
[Crossref]

Gatti, A.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of Sub-Shot-Noise Spatial Correlation in High-Gain Parametric Down Conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[Crossref]

Gatto Monticone, D.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

Genovese, M.

A. Avella, I. Ruo-Berchera, I. P. Degiovanni, G. Brida, and M. Genovese, “Absolute calibration of an EMCCD camera by quantum correlation, linking photon counting to the analog regime,” Opt. Lett. 41, 1841–1844 (2016).
[Crossref] [PubMed]

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[Crossref]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-Enhanced Measurements: Beating the Standard Quantum Limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

Goßler, S.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Grangier, P.

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light - Enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[Crossref] [PubMed]

Grosse, N.

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A Quantum Laser Pointer,” Science 301, 940–943 (2003).
[Crossref] [PubMed]

Hadwen, B.

M. Robbins and B. Hadwen, “The noise performance of electron multiplying charge-coupled devices,” IEEE T. Electron Dev. 50, 1227–1232 (2003).
[Crossref]

Hage, B.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Hall, J. L.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[Crossref]

Hammond, G. D.

R. P. Middlemiss, A. Samarelli, D. J. Paul, J. Hough, S. Rowan, and G. D. Hammond, “Measurement of the Earth tides with a MEMS gravimeter,” Nature 531, 614–617 (2016).
[Crossref] [PubMed]

Haniff, C. A.

A. G. Basden, C. A. Haniff, and C. D. Mackay, “Photon counting strategies with low-light-level CCDs,” Mon. Not. R. Astron. Soc. 345, 985 (2003).
[Crossref]

Hollberg, L. W.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Hough, J.

R. P. Middlemiss, A. Samarelli, D. J. Paul, J. Hough, S. Rowan, and G. D. Hammond, “Measurement of the Earth tides with a MEMS gravimeter,” Nature 531, 614–617 (2016).
[Crossref] [PubMed]

Itzhakov, S.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution Microscopy with Quantum Emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref] [PubMed]

Izdebski, F.

D. S. Tasca, M. P. Edgar, F. Izdebski, G. S. Buller, and M. J. Padgett, “Optimizing the use of detector arrays for measuring intensity correlations of photon pairs,” Phys. Rev. A 88013816 (2013).
[Crossref]

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Jedrkiewicz, O.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of Sub-Shot-Noise Spatial Correlation in High-Gain Parametric Down Conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[Crossref]

Jiang, Y.-K.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of Sub-Shot-Noise Spatial Correlation in High-Gain Parametric Down Conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[Crossref]

Jordan, A. N.

K. Lyons, S. Pang, P. G. Kwiat, and A. N. Jordan, “Precision optical displacement measurements using biphotons,” Phys. Rev. A 93, 043841 (2016).
[Crossref]

Katamadze, K.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

Kimble, H. J.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[Crossref]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Physical Review Letters 74, 3600–3603 (1995).
[Crossref]

Kumar, P.

O. Aytür and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. 65, 1551–1554 (1990).
[Crossref] [PubMed]

Kwiat, P. G.

K. Lyons, S. Pang, P. G. Kwiat, and A. N. Jordan, “Precision optical displacement measurements using biphotons,” Phys. Rev. A 93, 043841 (2016).
[Crossref]

Lam, P. K.

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A Quantum Laser Pointer,” Science 301, 940–943 (2003).
[Crossref] [PubMed]

Lantz, E.

E. Lantz, P.-A. Moreau, and F. Devaux, “Optimizing the signal-to-noise ratio in the measurement of photon pairs with detector arrays,” Physical Review A 90, 063811 (2014).
[Crossref]

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Purely spatial coincidences of twin photons in parametric spontaneous down-conversion,” Phys. Rev. A 81, 043825 (2010).
[Crossref]

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of Sub-Shot-Noise Correlations of Spatial Fluctuations in the Photon-Counting Regime,” Phys. Rev. Lett. 101, 233604 (2008).
[Crossref] [PubMed]

E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. 386, 2262–2270 (2008).
[Crossref]

LaPorta, A.

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light - Enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[Crossref] [PubMed]

Lastzka, N.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Leach, J.

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Leong, K. W.

Levitt, J. M.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution Microscopy with Quantum Emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref] [PubMed]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-Enhanced Measurements: Beating the Standard Quantum Limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

Lugiato, L. A.

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of Sub-Shot-Noise Spatial Correlation in High-Gain Parametric Down Conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[Crossref]

Lyons, K.

K. Lyons, S. Pang, P. G. Kwiat, and A. N. Jordan, “Precision optical displacement measurements using biphotons,” Phys. Rev. A 93, 043841 (2016).
[Crossref]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-Enhanced Measurements: Beating the Standard Quantum Limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

Mackay, C. D.

A. G. Basden, C. A. Haniff, and C. D. Mackay, “Photon counting strategies with low-light-level CCDs,” Mon. Not. R. Astron. Soc. 345, 985 (2003).
[Crossref]

Mehmet, M.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Mertz, J. C.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Middlemiss, R. P.

R. P. Middlemiss, A. Samarelli, D. J. Paul, J. Hough, S. Rowan, and G. D. Hammond, “Measurement of the Earth tides with a MEMS gravimeter,” Nature 531, 614–617 (2016).
[Crossref] [PubMed]

Moreau, P.-A.

E. Lantz, P.-A. Moreau, and F. Devaux, “Optimizing the signal-to-noise ratio in the measurement of photon pairs with detector arrays,” Physical Review A 90, 063811 (2014).
[Crossref]

Moreva, E.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

Olivero, P.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

Oron, D.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution Microscopy with Quantum Emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref] [PubMed]

O. Schwartz and D. Oron, “Improved resolution in fluorescence microscopy using quantum correlations,” Phys. Rev. A 85, 033812 (2012).
[Crossref]

Padgett, M.

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Padgett, M. J.

D. S. Tasca, M. P. Edgar, F. Izdebski, G. S. Buller, and M. J. Padgett, “Optimizing the use of detector arrays for measuring intensity correlations of photon pairs,” Phys. Rev. A 88013816 (2013).
[Crossref]

Pang, S.

K. Lyons, S. Pang, P. G. Kwiat, and A. N. Jordan, “Precision optical displacement measurements using biphotons,” Phys. Rev. A 93, 043841 (2016).
[Crossref]

Paul, D. J.

R. P. Middlemiss, A. Samarelli, D. J. Paul, J. Hough, S. Rowan, and G. D. Hammond, “Measurement of the Earth tides with a MEMS gravimeter,” Nature 531, 614–617 (2016).
[Crossref] [PubMed]

Pereira, S. F.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[Crossref]

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Physical Review A 52, R3429–R3432 (1995).
[Crossref]

Robbins, M.

M. Robbins and B. Hadwen, “The noise performance of electron multiplying charge-coupled devices,” IEEE T. Electron Dev. 50, 1227–1232 (2003).
[Crossref]

Rowan, S.

R. P. Middlemiss, A. Samarelli, D. J. Paul, J. Hough, S. Rowan, and G. D. Hammond, “Measurement of the Earth tides with a MEMS gravimeter,” Nature 531, 614–617 (2016).
[Crossref] [PubMed]

Ruo Berchera, I.

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[Crossref]

Ruo-Berchera, I.

A. Avella, I. Ruo-Berchera, I. P. Degiovanni, G. Brida, and M. Genovese, “Absolute calibration of an EMCCD camera by quantum correlation, linking photon counting to the analog regime,” Opt. Lett. 41, 1841–1844 (2016).
[Crossref] [PubMed]

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

Samarelli, A.

R. P. Middlemiss, A. Samarelli, D. J. Paul, J. Hough, S. Rowan, and G. D. Hammond, “Measurement of the Earth tides with a MEMS gravimeter,” Nature 531, 614–617 (2016).
[Crossref] [PubMed]

Schnabel, R.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Schwartz, O.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution Microscopy with Quantum Emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref] [PubMed]

O. Schwartz and D. Oron, “Improved resolution in fluorescence microscopy using quantum correlations,” Phys. Rev. A 85, 033812 (2012).
[Crossref]

Sergienko, A. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Physical Review Letters 74, 3600–3603 (1995).
[Crossref]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Physical Review A 52, R3429–R3432 (1995).
[Crossref]

Shapiro, J. H.

Shih, Y. H.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Physical Review A 52, R3429–R3432 (1995).
[Crossref]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Physical Review Letters 74, 3600–3603 (1995).
[Crossref]

Slusher, R. E.

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light - Enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[Crossref] [PubMed]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Strekalov, D. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Physical Review A 52, R3429–R3432 (1995).
[Crossref]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Physical Review Letters 74, 3600–3603 (1995).
[Crossref]

Tasca, D.

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Tasca, D. S.

D. S. Tasca, M. P. Edgar, F. Izdebski, G. S. Buller, and M. J. Padgett, “Optimizing the use of detector arrays for measuring intensity correlations of photon pairs,” Phys. Rev. A 88013816 (2013).
[Crossref]

Tenne, R.

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution Microscopy with Quantum Emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref] [PubMed]

Traina, P.

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

Trapani, P. Di

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of Sub-Shot-Noise Spatial Correlation in High-Gain Parametric Down Conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[Crossref]

Treps, N.

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A Quantum Laser Pointer,” Science 301, 940–943 (2003).
[Crossref] [PubMed]

Vahlbruch, H.

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

Valley, J. F.

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

Warburton, R.

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Wong, N. C.

Xiao, M.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[Crossref]

Yurke, B.

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light - Enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[Crossref] [PubMed]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

IEEE T. Electron Dev. (1)

M. Robbins and B. Hadwen, “The noise performance of electron multiplying charge-coupled devices,” IEEE T. Electron Dev. 50, 1227–1232 (2003).
[Crossref]

Mon. Not. R. Astron. Soc. (2)

A. G. Basden, C. A. Haniff, and C. D. Mackay, “Photon counting strategies with low-light-level CCDs,” Mon. Not. R. Astron. Soc. 345, 985 (2003).
[Crossref]

E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. 386, 2262–2270 (2008).
[Crossref]

Nano Lett. (1)

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution Microscopy with Quantum Emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref] [PubMed]

Nat. Commun. (1)

M. Edgar, D. Tasca, F. Izdebski, R. Warburton, J. Leach, M. Agnew, G. Buller, R. Boyd, and M. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref] [PubMed]

Nat. Photonics (1)

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[Crossref]

Nature (1)

R. P. Middlemiss, A. Samarelli, D. J. Paul, J. Hough, S. Rowan, and G. D. Hammond, “Measurement of the Earth tides with a MEMS gravimeter,” Nature 531, 614–617 (2016).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (5)

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[Crossref]

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Purely spatial coincidences of twin photons in parametric spontaneous down-conversion,” Phys. Rev. A 81, 043825 (2010).
[Crossref]

D. S. Tasca, M. P. Edgar, F. Izdebski, G. S. Buller, and M. J. Padgett, “Optimizing the use of detector arrays for measuring intensity correlations of photon pairs,” Phys. Rev. A 88013816 (2013).
[Crossref]

O. Schwartz and D. Oron, “Improved resolution in fluorescence microscopy using quantum correlations,” Phys. Rev. A 85, 033812 (2012).
[Crossref]

K. Lyons, S. Pang, P. G. Kwiat, and A. N. Jordan, “Precision optical displacement measurements using biphotons,” Phys. Rev. A 93, 043841 (2016).
[Crossref]

Phys. Rev. Lett. (8)

O. Aytür and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. 65, 1551–1554 (1990).
[Crossref] [PubMed]

O. Jedrkiewicz, Y.-K. Jiang, E. Brambilla, A. Gatti, M. Bache, L. A. Lugiato, and P. Di Trapani, “Detection of Sub-Shot-Noise Spatial Correlation in High-Gain Parametric Down Conversion,” Phys. Rev. Lett. 93, 243601 (2004).
[Crossref]

J.-L. Blanchet, F. Devaux, L. Furfaro, and E. Lantz, “Measurement of Sub-Shot-Noise Correlations of Spatial Fluctuations in the Photon-Counting Regime,” Phys. Rev. Lett. 101, 233604 (2008).
[Crossref] [PubMed]

D. Gatto Monticone, K. Katamadze, P. Traina, E. Moreva, J. Forneris, I. Ruo-Berchera, P. Olivero, I. P. Degiovanni, G. Brida, and M. Genovese, “Beating the Abbe Diffraction Limit in Confocal Microscopy via Nonclassical Photon Statistics,” Phys. Rev. Lett. 113, 143602 (2014).
[Crossref] [PubMed]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, “Observation of Squeezed Light with 10-dB Quantum-Noise Reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[Crossref] [PubMed]

H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, “Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency,” Phys. Rev. Lett. 117, 110801 (2016).
[Crossref]

R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, “Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity,” Phys. Rev. Lett. 55, 2409–2412 (1985).
[Crossref] [PubMed]

P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light - Enhanced polarization interferometer,” Phys. Rev. Lett. 59, 2153–2156 (1987).
[Crossref] [PubMed]

Physical Review A (2)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Physical Review A 52, R3429–R3432 (1995).
[Crossref]

E. Lantz, P.-A. Moreau, and F. Devaux, “Optimizing the signal-to-noise ratio in the measurement of photon pairs with detector arrays,” Physical Review A 90, 063811 (2014).
[Crossref]

Physical Review Letters (1)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Physical Review Letters 74, 3600–3603 (1995).
[Crossref]

Science (2)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-Enhanced Measurements: Beating the Standard Quantum Limit,” Science 306, 1330–1336 (2004).
[Crossref] [PubMed]

N. Treps, N. Grosse, W. P. Bowen, C. Fabre, H.-A. Bachor, and P. K. Lam, “A Quantum Laser Pointer,” Science 301, 940–943 (2003).
[Crossref] [PubMed]

Other (1)

E. Toninelli, “Sub-shot-noise shadow sensing with quantum correlations: EMCCD camera raw frames,” Enlighten (2017) [retrieved 15/08/2017], http://dx.doi.org/10.5525/gla.researchdata.393 .

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Figures (8)

Fig. 1
Fig. 1 Experimental setup used to measure noise reduction in the estimation of the position of a shadow. (a) The imaging system used to measure the position of the shadow cast by a scanning wire, consists of a 200 mm Fourier lens (L1) placed one focal length away from the crystal and the scanning wire; and a 50 mm relay lens (L2) placed two focal lengths away from the scanning wire and the plane of the EMCCD. A 10 nm band-pass interference filter (IF) centred at 710 nm was placed in front of the EMCCD. In order to compare the noise performance of uncorrelated and anticorrelated light, a neutral density filter (not shown in the figure) was introduced either before or after the crystal, allowing to switch respectively between position anticorrelated and uncorrelated light, while keeping a constant number of detected events. (b) The summed binary events, detected over the left and right halves of a square region of interest (A and B), were used to estimate the relative displacement of the shadow (Δx), for a certain width of the ROI (wROI) and width of the shadow (wshadow).
Fig. 2
Fig. 2 Characterisation of the degree of correlation for the anticorrelated and uncorrelated light sources. The anticorrelated data shows a clear noise reduction with respect to both the uncorrelated data and the shot-noise limit. Each point of the variance of (AB) normalised to the shot-noise was calculated over 50 frames. The x-axis shows the average number of detected events (i.e. photons + dark-counts).
Fig. 3
Fig. 3 Characterisation of the position estimator. The mean of the normalised residual difference is plotted as a function of the position of the scanning wire. The values of A and B allow to estimate the position of the wire within the position range delimited by the dotted lines, as described by Eq. (1). Four times the standard deviation (SD) was chosen to highlight the precision of the measurements. The yellow-shaded interval is used in Fig. 5 to show the frame to frame fluctuations of the position estimator.
Fig. 4
Fig. 4 Noise performance for anticorrelated and uncorrelated light as a function of wire position. The wire is scanned at increments of 10 pixels across the field of view for both position anticorrelated and uncorrelated light, as shown in the upper part of the figure. Each point in the graph corresponds to the estimation of the normalised variance of AB (i.e. the degree of correlation σ) each averaged over 2500 frames. The shaded areas indicate the confidence intervals at two SDs. The anticorrelated data shows noise suppression below both the uncorrelated counterpart and the shot-noise limit. The top-row shows five key positions of the scanning wire as detected by the EMCCD camera, and the red-dashed squares highlight the chosen ROI. A discussion of these positions of the scanning wire in terms of achievable noise suppression is provided in Appendix 4.5.
Fig. 5
Fig. 5 Fluctuations of the position estimator from frame to frame. The frame to frame normalised residual difference between A and B is plotted for the central position range highlighted in Fig. 3. Anticorrelated data shows a precision improvement in the position estimation of the wire compared to uncorrelated data.
Fig. 6
Fig. 6 Light-tight enclosure. The experiment enclosure is divided into two light-tight compartments by a blackened metal sheet partition: UV pump laser side (blue) and downconverted-light side with the EMCCD detector (red). The enclosure is constructed from metal frame clad with blackened wooden panels. Care was taken to eliminate stray light by employing custom light-tight I/O ports and designing an isolated air-cooling system for the laser.
Fig. 7
Fig. 7 Experimental evidence of strong anticorrelation of photon-pairs as detected in the far-field of the downconversion crystal. The correlation of a single frame detected by our EMCCD camera is shown. The whole optical channel was optimised to minimise losses, resulting in a strong single-frame correlation peak (SNR = 4.34) at 0.15 events per pixel per frame. The SNR is computed considering the height of the correlation peak with respect to the noise of the Gaussian pedestal.
Fig. 8
Fig. 8 Five key positions of the scanning wire as detected by the EMCCD camera. The amount of noise suppression depends on the number of jointly detected photon-pairs, which in turn depends on the position of the scanning wire. The red-dashed squares highlight the chosen region of interest. The numbers at the bottom indicate the positions of the scanning wire from the central white-dotted line.

Equations (7)

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Δ x = A B A + B l = A B N l ,
Δ ( A B ) 2 = A + B .
σ V a r ( A B ) A + B < 1 ,
Q E t o t a l = 1 σ u n . = 1 0.73 = 26 %
= 1 S D Δ x A C S D Δ x U C = 1 S D ( A B ) A C S D ( A B ) U C = 1 σ A C σ U C ,
0 = 1 0.79 1.14 = 16.8 % ( ± 2 % ) ( i . e . 0.80 d B )
S N L = 1 0.79 1.00 = 11.1 % ( ± 1 % ) ( i . e . 0.51 d B )

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