H. Mikami, Y. Li, and T. Kobayashi, "Generation of the four-photon W state and other multiphoton entangled states using parametric down-conversion," Phys. Rev. A 70, 052308 (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]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuous-variable polarization entanglement," Phys. Rev. A 65, 052306 (2002).

[Crossref]

P. Usachev, J. Söderholm, G. Björk, and A. Trifonov, "Experimental verification of differences between classical and quantum polarization properties," Opt. Commun. 193, 161-173 (2001).

[Crossref]

T. Tsegaye, J. Söderholm, M. Atatüre, A. Trifonov, G. Björk, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Experimental demonstration of three mutuary orthogonal polarization states of entangled photons," Phys. Rev. Lett. 85, 5013-5017 (2000).

[Crossref]
[PubMed]

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, "Observation of four-photon interference with a beam splitter by pulsed parametric down-conversion," Phys. Rev. Lett. 83, 959-962 (1999).

[Crossref]

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, D. N. Klyshko, and S. P. Kulik, "Polarization state of a biphoton: quantum ternary logic," Phys. Rev. A 60, R4209-R4212 (1999).

[Crossref]

A. Kuzmich and L. Mandel, "Sub-shot-noise interferometric measurements with two-photon states," Quantum Semiclassic. Opt. 10, 493-500 (1998).

[Crossref]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).

[Crossref]
[PubMed]

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

[Crossref]
[PubMed]

A. Luis and L. L. Sánchez-Soto, "Phase-difference operator," Phys. Rev. A 48, 4702-4708 (1993).

[Crossref]
[PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).

[Crossref]
[PubMed]

B. Yurke, S. L. McCall, and J. R. Klauder, "SU(2) and SU(1,1) interferometers," Phys. Rev. A 33, 4033-4054 (1986).

[Crossref]
[PubMed]

B. Yurke, "Input states for enhancement of Fermion interferometer sensitivity," Phys. Rev. Lett. 56, 1515-1517 (1986).

[Crossref]
[PubMed]

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

[Crossref]

E. Collett, "Stokes parameters for quantum systems," Am. J. Phys. 38, 563-574 (1970).

[Crossref]

T. Tsegaye, J. Söderholm, M. Atatüre, A. Trifonov, G. Björk, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Experimental demonstration of three mutuary orthogonal polarization states of entangled photons," Phys. Rev. Lett. 85, 5013-5017 (2000).

[Crossref]
[PubMed]

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]

P. Usachev, J. Söderholm, G. Björk, and A. Trifonov, "Experimental verification of differences between classical and quantum polarization properties," Opt. Commun. 193, 161-173 (2001).

[Crossref]

T. Tsegaye, J. Söderholm, M. Atatüre, A. Trifonov, G. Björk, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Experimental demonstration of three mutuary orthogonal polarization states of entangled photons," Phys. Rev. Lett. 85, 5013-5017 (2000).

[Crossref]
[PubMed]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).

[Crossref]
[PubMed]

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, D. N. Klyshko, and S. P. Kulik, "Polarization state of a biphoton: quantum ternary logic," Phys. Rev. A 60, R4209-R4212 (1999).

[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]
[PubMed]

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

[Crossref]

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, D. N. Klyshko, and S. P. Kulik, "Polarization state of a biphoton: quantum ternary logic," Phys. Rev. A 60, R4209-R4212 (1999).

[Crossref]

E. Collett, "Stokes parameters for quantum systems," Am. J. Phys. 38, 563-574 (1970).

[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]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).

[Crossref]
[PubMed]

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

[Crossref]
[PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).

[Crossref]
[PubMed]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).

[Crossref]
[PubMed]

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, D. N. Klyshko, and S. P. Kulik, "Polarization state of a biphoton: quantum ternary logic," Phys. Rev. A 60, R4209-R4212 (1999).

[Crossref]

B. Yurke, S. L. McCall, and J. R. Klauder, "SU(2) and SU(1,1) interferometers," Phys. Rev. A 33, 4033-4054 (1986).

[Crossref]
[PubMed]

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, D. N. Klyshko, and S. P. Kulik, "Polarization state of a biphoton: quantum ternary logic," Phys. Rev. A 60, R4209-R4212 (1999).

[Crossref]

H. Mikami, Y. Li, and T. Kobayashi, "Generation of the four-photon W state and other multiphoton entangled states using parametric down-conversion," Phys. Rev. A 70, 052308 (2004).

[Crossref]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuous-variable polarization entanglement," Phys. Rev. A 65, 052306 (2002).

[Crossref]

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, D. N. Klyshko, and S. P. Kulik, "Polarization state of a biphoton: quantum ternary logic," Phys. Rev. A 60, R4209-R4212 (1999).

[Crossref]

A. Kuzmich and L. Mandel, "Sub-shot-noise interferometric measurements with two-photon states," Quantum Semiclassic. Opt. 10, 493-500 (1998).

[Crossref]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuous-variable polarization entanglement," Phys. Rev. A 65, 052306 (2002).

[Crossref]

H. Mikami, Y. Li, and T. Kobayashi, "Generation of the four-photon W state and other multiphoton entangled states using parametric down-conversion," Phys. Rev. A 70, 052308 (2004).

[Crossref]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuous-variable polarization entanglement," Phys. Rev. A 65, 052306 (2002).

[Crossref]

A. Luis and L. L. Sánchez-Soto, "Phase-difference operator," Phys. Rev. A 48, 4702-4708 (1993).

[Crossref]
[PubMed]

A. Kuzmich and L. Mandel, "Sub-shot-noise interferometric measurements with two-photon states," Quantum Semiclassic. Opt. 10, 493-500 (1998).

[Crossref]

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).

[Crossref]
[PubMed]

B. Yurke, S. L. McCall, and J. R. Klauder, "SU(2) and SU(1,1) interferometers," Phys. Rev. A 33, 4033-4054 (1986).

[Crossref]
[PubMed]

H. Mikami, Y. Li, and T. Kobayashi, "Generation of the four-photon W state and other multiphoton entangled states using parametric down-conversion," Phys. Rev. A 70, 052308 (2004).

[Crossref]

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, "Observation of four-photon interference with a beam splitter by pulsed parametric down-conversion," Phys. Rev. Lett. 83, 959-962 (1999).

[Crossref]

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).

[Crossref]
[PubMed]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuous-variable polarization entanglement," Phys. Rev. A 65, 052306 (2002).

[Crossref]

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, "Observation of four-photon interference with a beam splitter by pulsed parametric down-conversion," Phys. Rev. Lett. 83, 959-962 (1999).

[Crossref]

T. Tsegaye, J. Söderholm, M. Atatüre, A. Trifonov, G. Björk, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Experimental demonstration of three mutuary orthogonal polarization states of entangled photons," Phys. Rev. Lett. 85, 5013-5017 (2000).

[Crossref]
[PubMed]

A. Luis and L. L. Sánchez-Soto, "Phase-difference operator," Phys. Rev. A 48, 4702-4708 (1993).

[Crossref]
[PubMed]

T. Tsegaye, J. Söderholm, M. Atatüre, A. Trifonov, G. Björk, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Experimental demonstration of three mutuary orthogonal polarization states of entangled photons," Phys. Rev. Lett. 85, 5013-5017 (2000).

[Crossref]
[PubMed]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuous-variable polarization entanglement," Phys. Rev. A 65, 052306 (2002).

[Crossref]

P. Usachev, J. Söderholm, G. Björk, and A. Trifonov, "Experimental verification of differences between classical and quantum polarization properties," Opt. Commun. 193, 161-173 (2001).

[Crossref]

T. Tsegaye, J. Söderholm, M. Atatüre, A. Trifonov, G. Björk, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Experimental demonstration of three mutuary orthogonal polarization states of entangled photons," Phys. Rev. Lett. 85, 5013-5017 (2000).

[Crossref]
[PubMed]

T. Tsegaye, J. Söderholm, M. Atatüre, A. Trifonov, G. Björk, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Experimental demonstration of three mutuary orthogonal polarization states of entangled photons," Phys. Rev. Lett. 85, 5013-5017 (2000).

[Crossref]
[PubMed]

P. Usachev, J. Söderholm, G. Björk, and A. Trifonov, "Experimental verification of differences between classical and quantum polarization properties," Opt. Commun. 193, 161-173 (2001).

[Crossref]

T. Tsegaye, J. Söderholm, M. Atatüre, A. Trifonov, G. Björk, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Experimental demonstration of three mutuary orthogonal polarization states of entangled photons," Phys. Rev. Lett. 85, 5013-5017 (2000).

[Crossref]
[PubMed]

T. Tsegaye, J. Söderholm, M. Atatüre, A. Trifonov, G. Björk, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Experimental demonstration of three mutuary orthogonal polarization states of entangled photons," Phys. Rev. Lett. 85, 5013-5017 (2000).

[Crossref]
[PubMed]

P. Usachev, J. Söderholm, G. Björk, and A. Trifonov, "Experimental verification of differences between classical and quantum polarization properties," Opt. Commun. 193, 161-173 (2001).

[Crossref]

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, "Observation of four-photon interference with a beam splitter by pulsed parametric down-conversion," Phys. Rev. Lett. 83, 959-962 (1999).

[Crossref]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).

[Crossref]
[PubMed]

B. Yurke, "Input states for enhancement of Fermion interferometer sensitivity," Phys. Rev. Lett. 56, 1515-1517 (1986).

[Crossref]
[PubMed]

B. Yurke, S. L. McCall, and J. R. Klauder, "SU(2) and SU(1,1) interferometers," Phys. Rev. A 33, 4033-4054 (1986).

[Crossref]
[PubMed]

E. Collett, "Stokes parameters for quantum systems," Am. J. Phys. 38, 563-574 (1970).

[Crossref]

P. Usachev, J. Söderholm, G. Björk, and A. Trifonov, "Experimental verification of differences between classical and quantum polarization properties," Opt. Commun. 193, 161-173 (2001).

[Crossref]

H. Mikami, Y. Li, and T. Kobayashi, "Generation of the four-photon W state and other multiphoton entangled states using parametric down-conversion," Phys. Rev. A 70, 052308 (2004).

[Crossref]

A. Luis and L. L. Sánchez-Soto, "Phase-difference operator," Phys. Rev. A 48, 4702-4708 (1993).

[Crossref]
[PubMed]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuous-variable polarization entanglement," Phys. Rev. A 65, 052306 (2002).

[Crossref]

B. Yurke, S. L. McCall, and J. R. Klauder, "SU(2) and SU(1,1) interferometers," Phys. Rev. A 33, 4033-4054 (1986).

[Crossref]
[PubMed]

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, D. N. Klyshko, and S. P. Kulik, "Polarization state of a biphoton: quantum ternary logic," Phys. Rev. A 60, R4209-R4212 (1999).

[Crossref]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).

[Crossref]
[PubMed]

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

[Crossref]

T. Tsegaye, J. Söderholm, M. Atatüre, A. Trifonov, G. Björk, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Experimental demonstration of three mutuary orthogonal polarization states of entangled photons," Phys. Rev. Lett. 85, 5013-5017 (2000).

[Crossref]
[PubMed]

Z. Y. Ou, J.-K. Rhee, and L. J. Wang, "Observation of four-photon interference with a beam splitter by pulsed parametric down-conversion," Phys. Rev. Lett. 83, 959-962 (1999).

[Crossref]

B. Yurke, "Input states for enhancement of Fermion interferometer sensitivity," Phys. Rev. Lett. 56, 1515-1517 (1986).

[Crossref]
[PubMed]

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

[Crossref]
[PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).

[Crossref]
[PubMed]

A. Kuzmich and L. Mandel, "Sub-shot-noise interferometric measurements with two-photon states," Quantum Semiclassic. Opt. 10, 493-500 (1998).

[Crossref]

In case of birefringence, the operator Â2 can also be expressed by a real matrix. The operator Â=−i(âxdaggerây+âydaggerâx) has pure imaginary elements in the matrix representation. The matrix representation of Â is then written by the form, i× (a real matrix). This shows that all the elements of Â2 are real.

In case of birefringence, all elements of the vector Âe are pure imaginary. Hence in the following discussion, the notation Âe should read Âe/i.