P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).

[CrossRef]
[PubMed]

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, “Resolution and sensitivity of a Fabry–Perot interferometer with a photon-number-resolving detector,” Phys. Rev. A 80, 043822 (2009).

[CrossRef]

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).

[CrossRef]
[PubMed]

R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Quantum phase estimation with lossy interferometers,” Phys. Rev. A 80, 013825 (2009).

[CrossRef]

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).

[CrossRef]

J. P. Dowling, “Quantum optical metrology—the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).

[CrossRef]

G. Gilbert, M. Hamrick, and Y. S. Weinstein, “Use of maximally entangled N-photon states for practical quantum interferometry,” J. Opt. Soc. Am. B 25, 1336–1340 (2008).

[CrossRef]

S. D. Huver, C. F. Wildfeuer, and J. P. Dowling, “Entangled Fock states for robust quantum optical metrology, imaging, and sensing,” Phys. Rev. A 78, 063828 (2008).

[CrossRef]

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).

[CrossRef]
[PubMed]

Y. Gao and H. Lee, “Sub-shot-noise quantum optical interferometry: a comparison of entangled state performance within a unified measurement scheme,” J. Mod. Opt. 55, 3319–3327 (2008).

[CrossRef]

G. A. Durkin and J. P. Dowling, “Local and global distinguishability in quantum interferometry,” Phys. Rev. Lett. 99, 070801 (2007).

[CrossRef]
[PubMed]

M. A. Rubin and S. Kaushik, “Loss-induced limits to phase measurement precision with maximally entangled states,” Phys. Rev. A 75, 053805 (2007).

[CrossRef]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[CrossRef]
[PubMed]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).

[CrossRef]
[PubMed]

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).

[CrossRef]

G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, “Nonlinear interferometry via Fock-state projection,” Phys. Rev. Lett. 96, 203601 (2006).

[CrossRef]
[PubMed]

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803(R) (2005).

[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Quantum nondemolition measurement of parity and generation of parity eigenstates in optical fields,” Phys. Rev. A 72, 053818 (2005).

[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).

[CrossRef]
[PubMed]

P. Kok, S. L. Braunstein, and J. P. Dowling, “Quantum lithography, entanglement and Heisenberg-limited parameter estimation,” J. Opt. B: Quantum Semiclassical Opt. 6, S811–S815 (2004).

[CrossRef]

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).

[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Nonlinear interferometer as a resource for maximally entangled photonic states: application to interferometry,” Phys. Rev. A 66, 013804 (2002).

[CrossRef]

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum-optical Fredkin gate,” Phys. Rev. A 64, 063814 (2001).

[CrossRef]

C. C. Gerry, “Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime,” Phys. Rev. A 61, 043811 (2000).

[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).

[CrossRef]
[PubMed]

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).

[CrossRef]
[PubMed]

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).

[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).

[CrossRef]
[PubMed]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).

[CrossRef]
[PubMed]

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).

[CrossRef]
[PubMed]

R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Quantum phase estimation with lossy interferometers,” Phys. Rev. A 80, 013825 (2009).

[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Quantum nondemolition measurement of parity and generation of parity eigenstates in optical fields,” Phys. Rev. A 72, 053818 (2005).

[CrossRef]

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).

[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Nonlinear interferometer as a resource for maximally entangled photonic states: application to interferometry,” Phys. Rev. A 66, 013804 (2002).

[CrossRef]

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).

[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).

[CrossRef]
[PubMed]

G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, “Nonlinear interferometry via Fock-state projection,” Phys. Rev. Lett. 96, 203601 (2006).

[CrossRef]
[PubMed]

P. Kok, S. L. Braunstein, and J. P. Dowling, “Quantum lithography, entanglement and Heisenberg-limited parameter estimation,” J. Opt. B: Quantum Semiclassical Opt. 6, S811–S815 (2004).

[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).

[CrossRef]
[PubMed]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Quantum nondemolition measurement of parity and generation of parity eigenstates in optical fields,” Phys. Rev. A 72, 053818 (2005).

[CrossRef]

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).

[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Nonlinear interferometer as a resource for maximally entangled photonic states: application to interferometry,” Phys. Rev. A 66, 013804 (2002).

[CrossRef]

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum-optical Fredkin gate,” Phys. Rev. A 64, 063814 (2001).

[CrossRef]

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).

[CrossRef]
[PubMed]

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).

[CrossRef]

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, “Resolution and sensitivity of a Fabry–Perot interferometer with a photon-number-resolving detector,” Phys. Rev. A 80, 043822 (2009).

[CrossRef]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).

[CrossRef]
[PubMed]

A. Chiruvelli and H. Lee, “Parity measurements in quantum optical metrology,” arXiv:0901.4395.

R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Quantum phase estimation with lossy interferometers,” Phys. Rev. A 80, 013825 (2009).

[CrossRef]

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).

[CrossRef]
[PubMed]

R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Quantum phase estimation with lossy interferometers,” Phys. Rev. A 80, 013825 (2009).

[CrossRef]

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).

[CrossRef]
[PubMed]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).

[CrossRef]
[PubMed]

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, “Resolution and sensitivity of a Fabry–Perot interferometer with a photon-number-resolving detector,” Phys. Rev. A 80, 043822 (2009).

[CrossRef]

S. D. Huver, C. F. Wildfeuer, and J. P. Dowling, “Entangled Fock states for robust quantum optical metrology, imaging, and sensing,” Phys. Rev. A 78, 063828 (2008).

[CrossRef]

J. P. Dowling, “Quantum optical metrology—the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).

[CrossRef]

G. A. Durkin and J. P. Dowling, “Local and global distinguishability in quantum interferometry,” Phys. Rev. Lett. 99, 070801 (2007).

[CrossRef]
[PubMed]

P. Kok, S. L. Braunstein, and J. P. Dowling, “Quantum lithography, entanglement and Heisenberg-limited parameter estimation,” J. Opt. B: Quantum Semiclassical Opt. 6, S811–S815 (2004).

[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).

[CrossRef]
[PubMed]

G. A. Durkin and J. P. Dowling, “Local and global distinguishability in quantum interferometry,” Phys. Rev. Lett. 99, 070801 (2007).

[CrossRef]
[PubMed]

G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, “Nonlinear interferometry via Fock-state projection,” Phys. Rev. Lett. 96, 203601 (2006).

[CrossRef]
[PubMed]

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, “Resolution and sensitivity of a Fabry–Perot interferometer with a photon-number-resolving detector,” Phys. Rev. A 80, 043822 (2009).

[CrossRef]

G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, “Nonlinear interferometry via Fock-state projection,” Phys. Rev. Lett. 96, 203601 (2006).

[CrossRef]
[PubMed]

Y. Gao and H. Lee, “Sub-shot-noise quantum optical interferometry: a comparison of entangled state performance within a unified measurement scheme,” J. Mod. Opt. 55, 3319–3327 (2008).

[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Quantum nondemolition measurement of parity and generation of parity eigenstates in optical fields,” Phys. Rev. A 72, 053818 (2005).

[CrossRef]

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).

[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Nonlinear interferometer as a resource for maximally entangled photonic states: application to interferometry,” Phys. Rev. A 66, 013804 (2002).

[CrossRef]

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum-optical Fredkin gate,” Phys. Rev. A 64, 063814 (2001).

[CrossRef]

C. C. Gerry, “Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime,” Phys. Rev. A 61, 043811 (2000).

[CrossRef]

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge Univ. Press, 2005).

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).

[CrossRef]
[PubMed]

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).

[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).

[CrossRef]
[PubMed]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).

[CrossRef]
[PubMed]

S. D. Huver, C. F. Wildfeuer, and J. P. Dowling, “Entangled Fock states for robust quantum optical metrology, imaging, and sensing,” Phys. Rev. A 78, 063828 (2008).

[CrossRef]

M. A. Rubin and S. Kaushik, “Loss-induced limits to phase measurement precision with maximally entangled states,” Phys. Rev. A 75, 053805 (2007).

[CrossRef]

G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, “Nonlinear interferometry via Fock-state projection,” Phys. Rev. Lett. 96, 203601 (2006).

[CrossRef]
[PubMed]

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge Univ. Press, 2005).

P. Kok, S. L. Braunstein, and J. P. Dowling, “Quantum lithography, entanglement and Heisenberg-limited parameter estimation,” J. Opt. B: Quantum Semiclassical Opt. 6, S811–S815 (2004).

[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).

[CrossRef]
[PubMed]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).

[CrossRef]
[PubMed]

Y. Gao and H. Lee, “Sub-shot-noise quantum optical interferometry: a comparison of entangled state performance within a unified measurement scheme,” J. Mod. Opt. 55, 3319–3327 (2008).

[CrossRef]

A. Chiruvelli and H. Lee, “Parity measurements in quantum optical metrology,” arXiv:0901.4395.

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).

[CrossRef]
[PubMed]

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803(R) (2005).

[CrossRef]

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).

[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).

[CrossRef]
[PubMed]

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).

[CrossRef]
[PubMed]

R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Quantum phase estimation with lossy interferometers,” Phys. Rev. A 80, 013825 (2009).

[CrossRef]

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).

[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).

[CrossRef]
[PubMed]

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, “Resolution and sensitivity of a Fabry–Perot interferometer with a photon-number-resolving detector,” Phys. Rev. A 80, 043822 (2009).

[CrossRef]

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).

[CrossRef]
[PubMed]

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803(R) (2005).

[CrossRef]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[CrossRef]
[PubMed]

A. E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040 (2008).

[CrossRef]
[PubMed]

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803(R) (2005).

[CrossRef]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).

[CrossRef]
[PubMed]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[CrossRef]
[PubMed]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[CrossRef]
[PubMed]

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, “Resolution and sensitivity of a Fabry–Perot interferometer with a photon-number-resolving detector,” Phys. Rev. A 80, 043822 (2009).

[CrossRef]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).

[CrossRef]
[PubMed]

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).

[CrossRef]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).

[CrossRef]
[PubMed]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).

[CrossRef]
[PubMed]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).

[CrossRef]
[PubMed]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).

[CrossRef]
[PubMed]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).

[CrossRef]
[PubMed]

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803(R) (2005).

[CrossRef]

M. A. Rubin and S. Kaushik, “Loss-induced limits to phase measurement precision with maximally entangled states,” Phys. Rev. A 75, 053805 (2007).

[CrossRef]

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).

[CrossRef]
[PubMed]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[CrossRef]
[PubMed]

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).

[CrossRef]

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).

[CrossRef]
[PubMed]

R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Quantum phase estimation with lossy interferometers,” Phys. Rev. A 80, 013825 (2009).

[CrossRef]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[CrossRef]
[PubMed]

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).

[CrossRef]
[PubMed]

R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Quantum phase estimation with lossy interferometers,” Phys. Rev. A 80, 013825 (2009).

[CrossRef]

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).

[CrossRef]
[PubMed]

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).

[CrossRef]
[PubMed]

R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Quantum phase estimation with lossy interferometers,” Phys. Rev. A 80, 013825 (2009).

[CrossRef]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).

[CrossRef]
[PubMed]

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, “Resolution and sensitivity of a Fabry–Perot interferometer with a photon-number-resolving detector,” Phys. Rev. A 80, 043822 (2009).

[CrossRef]

S. D. Huver, C. F. Wildfeuer, and J. P. Dowling, “Entangled Fock states for robust quantum optical metrology, imaging, and sensing,” Phys. Rev. A 78, 063828 (2008).

[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).

[CrossRef]
[PubMed]

J. P. Dowling, “Quantum optical metrology—the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).

[CrossRef]

Y. Gao and H. Lee, “Sub-shot-noise quantum optical interferometry: a comparison of entangled state performance within a unified measurement scheme,” J. Mod. Opt. 55, 3319–3327 (2008).

[CrossRef]

P. Kok, S. L. Braunstein, and J. P. Dowling, “Quantum lithography, entanglement and Heisenberg-limited parameter estimation,” J. Opt. B: Quantum Semiclassical Opt. 6, S811–S815 (2004).

[CrossRef]

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).

[CrossRef]

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).

[CrossRef]
[PubMed]

C. F. Wildfeuer, A. J. Pearlman, J. Chen, J. Fan, A. Migdall, and J. P. Dowling, “Resolution and sensitivity of a Fabry–Perot interferometer with a photon-number-resolving detector,” Phys. Rev. A 80, 043822 (2009).

[CrossRef]

R. A. Campos, C. C. Gerry, and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).

[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Nonlinear interferometer as a resource for maximally entangled photonic states: application to interferometry,” Phys. Rev. A 66, 013804 (2002).

[CrossRef]

C. C. Gerry, A. Benmoussa, and R. A. Campos, “Quantum nondemolition measurement of parity and generation of parity eigenstates in optical fields,” Phys. Rev. A 72, 053818 (2005).

[CrossRef]

C. C. Gerry, “Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime,” Phys. Rev. A 61, 043811 (2000).

[CrossRef]

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum-optical Fredkin gate,” Phys. Rev. A 64, 063814 (2001).

[CrossRef]

D. Rosenberg, A. E. Lita, A. J. Miller, and S. W. Nam, “Noise-free high-efficiency photon-number-resolving detectors,” Phys. Rev. A 71, 061803(R) (2005).

[CrossRef]

R. Demkowicz-Dobrzanski, U. Dorner, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Quantum phase estimation with lossy interferometers,” Phys. Rev. A 80, 013825 (2009).

[CrossRef]

V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound quantum imaging,” Phys. Rev. A 79, 013827 (2009).

[CrossRef]

S. D. Huver, C. F. Wildfeuer, and J. P. Dowling, “Entangled Fock states for robust quantum optical metrology, imaging, and sensing,” Phys. Rev. A 78, 063828 (2008).

[CrossRef]

M. A. Rubin and S. Kaushik, “Loss-induced limits to phase measurement precision with maximally entangled states,” Phys. Rev. A 75, 053805 (2007).

[CrossRef]

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).

[CrossRef]

K. J. Resch, K. L. Pregnell, R. Prevedel, A. Gilchrist, G. J. Pryde, J. L. O’Brien, and A. G. White, “Time-reversal and super-resolving phase measurements,” Phys. Rev. Lett. 98, 223601 (2007).

[CrossRef]
[PubMed]

U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).

[CrossRef]
[PubMed]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).

[CrossRef]
[PubMed]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).

[CrossRef]
[PubMed]

G. A. Durkin and J. P. Dowling, “Local and global distinguishability in quantum interferometry,” Phys. Rev. Lett. 99, 070801 (2007).

[CrossRef]
[PubMed]

G. Khoury, H. S. Eisenberg, E. J. S. Fonseca, and D. Bouwmeester, “Nonlinear interferometry via Fock-state projection,” Phys. Rev. Lett. 96, 203601 (2006).

[CrossRef]
[PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science 306, 1330–1336 (2004).

[CrossRef]
[PubMed]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the standard quantum limit with four-entangled photons,” Science 316, 726–729 (2007).

[CrossRef]
[PubMed]

For example, two-photon microscopy is capable of resolving sub-wavelength features because it demonstrates amplitude super-resolution. There are many other primarily scanning techniques that are based on sharp amplitude dependence in order to produce high-resolution images pixel by pixel. Something similar could be implemented here given our phase super-resolution where one would have to scan a beam of light across a sample and measure phase shifts on a point-by-point basis. The finite size of the scanning laser beam would have to be deconvoluted out of the final image.

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge Univ. Press, 2005).

A. Chiruvelli and H. Lee, “Parity measurements in quantum optical metrology,” arXiv:0901.4395.

Perkin-Elmer SPCM-AQRH-xx APD operating manual.