C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010), and references therein.

[CrossRef]

P. M. Anisimov, G. M. Raterman, S. 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]

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).

[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).

[CrossRef]

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

[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).

[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]

A. Luis, “Paradoxical evolution of the number of photons in the Jaynes-Cummings model,” J. Opt. Soc. Am. B 24, 2619 (2007). Subtracting photons can sometimes raise the average photon number. For the state |ψ〉=(|1〉+|11〉)/2 the average photon number is 6, but the state obtained by the action of the annihilation operator, a^|ψ〉, after renormalization, the average photon number has increased to 9.17.

[CrossRef]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).

[CrossRef]

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).

[CrossRef]

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).

[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (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, 06314 (2001).

[CrossRef]

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).

[CrossRef]

V. Bužek and M. Hillery, “Quantum disentanglement and phase measurement,” Czech. J. Phys. 45, 711–725 (1995).

[CrossRef]

B. Böhmer and U. Leonhardt, “Correlation interferometer for squeezed light,” Opt. Commun. 118, 181–185 (1995).

[CrossRef]

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).

[CrossRef]

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).

[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]

G. S. Agarwal, “Generation of pair coherent states and squeezing via the competition of four-wave mixing and amplified spontaneous emission,” Phys. Rev. Lett. 57, 827–830 (1986).

[CrossRef]

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).

[CrossRef]

P. M. Anisimov, G. M. Raterman, S. 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]

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]

B. Böhmer and U. Leonhardt, “Correlation interferometer for squeezed light,” Opt. Commun. 118, 181–185 (1995).

[CrossRef]

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).

[CrossRef]

V. Bužek and M. Hillery, “Quantum disentanglement and phase measurement,” Czech. J. Phys. 45, 711–725 (1995).

[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).

[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, 06314 (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]

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).

[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).

[CrossRef]

P. M. Anisimov, G. M. Raterman, S. 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]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).

[CrossRef]

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).

[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).

[CrossRef]

P. M. Anisimov, G. M. Raterman, S. 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]

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

[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).

[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).

[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).

[CrossRef]

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).

[CrossRef]

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010), and references therein.

[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, 06314 (2001).

[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]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).

[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).

[CrossRef]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).

[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).

[CrossRef]

V. Bužek and M. Hillery, “Quantum disentanglement and phase measurement,” Czech. J. Phys. 45, 711–725 (1995).

[CrossRef]

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).

[CrossRef]

P. M. Anisimov, G. M. Raterman, S. 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]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).

[CrossRef]

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).

[CrossRef]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).

[CrossRef]

P. M. Anisimov, G. M. Raterman, S. 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]

B. Böhmer and U. Leonhardt, “Correlation interferometer for squeezed light,” Opt. Commun. 118, 181–185 (1995).

[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).

[CrossRef]

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).

[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).

[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).

[CrossRef]

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).

[CrossRef]

C. C. Gerry and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).

[CrossRef]

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010), and references therein.

[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).

[CrossRef]

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).

[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).

[CrossRef]

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).

[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]

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).

[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).

[CrossRef]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).

[CrossRef]

P. M. Anisimov, G. M. Raterman, S. 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]

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]

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]

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]

P. M. Anisimov, G. M. Raterman, S. 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]

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]

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).

[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]

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).

[CrossRef]

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).

[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]

A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).

[CrossRef]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).

[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).

[CrossRef]

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).

[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).

[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]

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

[CrossRef]

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010), and references therein.

[CrossRef]

V. Bužek and M. Hillery, “Quantum disentanglement and phase measurement,” Czech. J. Phys. 45, 711–725 (1995).

[CrossRef]

D. Rosenberg, A. E. Lita, A. J. Miller, S. Nam, and R. E. Schwall, “Performance of photon-number resolving transition-edge sensors with integrated 1550 nm cavities,” IEEE Trans. Appl. Supercond. 15, 575–578 (2005).

[CrossRef]

G. S. Agarwal, “Nonclassical statistics of fields in pair coherent states,” J. Opt. Soc. Am. B 5, 1940–1947 (1988).

[CrossRef]

A. Luis, “Paradoxical evolution of the number of photons in the Jaynes-Cummings model,” J. Opt. Soc. Am. B 24, 2619 (2007). Subtracting photons can sometimes raise the average photon number. For the state |ψ〉=(|1〉+|11〉)/2 the average photon number is 6, but the state obtained by the action of the annihilation operator, a^|ψ〉, after renormalization, the average photon number has increased to 9.17.

[CrossRef]

B. Böhmer and U. Leonhardt, “Correlation interferometer for squeezed light,” Opt. Commun. 118, 181–185 (1995).

[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]

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).

[CrossRef]

M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D-G. Welsch, “Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).

[CrossRef]

T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdal, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A 82, 031802(R) (2010).

[CrossRef]

C. C. Gerry and R. A. Campos, “Generation of maximally entangled photonic states with a quantum optical Fredkin gate,” Phys. Rev. A 64, 06314 (2001).

[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]

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 and J. Mimih, “Heisenberg-limited interferometry with pair coherent states and parity measurements,” Phys. Rev. A 82, 013831 (2010).

[CrossRef]

G. S. Agarwal, “Generation of pair coherent states and squeezing via the competition of four-wave mixing and amplified spontaneous emission,” Phys. Rev. Lett. 57, 827–830 (1986).

[CrossRef]

P. M. Anisimov, G. M. Raterman, S. 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]

M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).

[CrossRef]

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).

[CrossRef]

R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, “Proposal for a loophole-free test using homodyne detection,” Phys. Rev. Lett. 93, 130409 (2004).

[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Bouri, and P. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).

[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]

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).

[CrossRef]