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Volumn 79, Issue 5, 2009, Pages

Correlation matrices of two-mode bosonic systems

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC CONDITIONS; ARBITRARY MATRICES; BOSONIC SYSTEMS; CORRELATION MATRIX; GAUSSIAN STATE; SYMMETRIC MATRICES; SYMPLECTIC;

EID: 66149098104     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.79.052327     Document Type: Article
Times cited : (154)

References (58)
  • 1
    • 66149097077 scopus 로고    scopus 로고
    • This is actually true only when a denumerable number of bosonic degrees of freedom is considered (usually the case in quantum optics) and Stone-von Neumann theorem applies.
    • This is actually true only when a denumerable number of bosonic degrees of freedom is considered (usually the case in quantum optics) and Stone-von Neumann theorem applies.
  • 5
    • 4243688364 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.80.4084;
    • S. L. Braunstein, Phys. Rev. Lett. 80, 4084 (1998) 10.1103/PhysRevLett. 80.4084
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 4084
    • Braunstein, S.L.1
  • 10
    • 8644223169 scopus 로고    scopus 로고
    • 10.1209/epl/i2004-10203-9;
    • S. Pirandola, Europhys. Lett. 68, 323 (2004) 10.1209/epl/i2004-10203-9
    • (2004) Europhys. Lett. , vol.68 , pp. 323
    • Pirandola, S.1
  • 12
    • 0032561423 scopus 로고    scopus 로고
    • 10.1126/science.282.5389.706;
    • A. Furusawa, Science 282, 706 (1998) 10.1126/science.282.5389.706
    • (1998) Science , vol.282 , pp. 706
    • Furusawa, A.1
  • 18
    • 33750595092 scopus 로고    scopus 로고
    • 10.1134/S1054660X06100057;
    • S. Pirandola and S. Mancini, Laser Phys. 16, 1418 (2006) 10.1134/S1054660X06100057
    • (2006) Laser Phys. , vol.16 , pp. 1418
    • Pirandola, S.1    Mancini, S.2
  • 20
    • 26944437410 scopus 로고    scopus 로고
    • 10.1142/S0219749905000815
    • S. Pirandola, Int. J. Quant. Inf. 3, 239 (2005). 10.1142/ S0219749905000815
    • (2005) Int. J. Quant. Inf. , vol.3 , pp. 239
    • Pirandola, S.1
  • 21
    • 4243332662 scopus 로고    scopus 로고
    • 10.1103/PhysRevA.61.022309;
    • M. Hillery, Phys. Rev. A 61, 022309 (2000) 10.1103/PhysRevA.61.022309
    • (2000) Phys. Rev. A , vol.61 , pp. 022309
    • Hillery, M.1
  • 22
    • 0346688181 scopus 로고    scopus 로고
    • 10.1103/PhysRevA.61.010303;
    • T. C. Ralph, Phys. Rev. A 61, 010303 (R) (1999) 10.1103/PhysRevA.61. 010303
    • (1999) Phys. Rev. A , vol.61 , pp. 010303
    • Ralph, T.C.1
  • 23
    • 4243774239 scopus 로고    scopus 로고
    • 10.1103/PhysRevA.62.062306;
    • T. C. Ralph, Phys. Rev. A 62, 062306 (2000) 10.1103/PhysRevA.62.062306
    • (2000) Phys. Rev. A , vol.62 , pp. 062306
    • Ralph, T.C.1
  • 24
  • 31
    • 0000588867 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.84.2726
    • R. Simon, Phys. Rev. Lett. 84, 2726 (2000). 10.1103/PhysRevLett.84.2726
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 2726
    • Simon, R.1
  • 33
    • 0035896862 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.86.3658
    • R. F. Werner and M. M. Wolf, Phys. Rev. Lett. 86, 3658 (2001). 10.1103/PhysRevLett.86.3658
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 3658
    • Werner, R.F.1    Wolf, M.M.2
  • 34
    • 33645068164 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.96.110402
    • A. Serafini, Phys. Rev. Lett. 96, 110402 (2006). 10.1103/PhysRevLett.96. 110402
    • (2006) Phys. Rev. Lett. , vol.96 , pp. 110402
    • Serafini, A.1
  • 37
    • 66149132753 scopus 로고    scopus 로고
    • Often, in the theoretical practice, the second moments of a bosonic or canonical quantum system are grouped together in a matrix called "correlation" or "covariance" matrix.
    • Often, in the theoretical practice, the second moments of a bosonic or canonical quantum system are grouped together in a matrix called "correlation" or "covariance" matrix.
  • 40
    • 26944493827 scopus 로고    scopus 로고
    • 10.1103/PhysRevA.71.055801
    • S. L. Braunstein, Phys. Rev. A 71, 055801 (2005). 10.1103/PhysRevA.71. 055801
    • (2005) Phys. Rev. A , vol.71 , pp. 055801
    • Braunstein, S.L.1
  • 41
    • 66149084940 scopus 로고    scopus 로고
    • It is trivial to say that a global invariant is also a local invariant.
    • It is trivial to say that a global invariant is also a local invariant.
  • 42
    • 0001316020 scopus 로고
    • 10.2307/2371062
    • J. Williamson, Am. J. Math. 58, 141 (1936). 10.2307/2371062
    • (1936) Am. J. Math. , vol.58 , pp. 141
    • Williamson, J.1
  • 43
    • 66149129271 scopus 로고    scopus 로고
    • In fact, the matrix iΩV is Hermitian and, therefore, diagonalizable by a unitary transformation. Then, by taking the modulus of its 2n real eigenvalues, one gets the n symplectic eigenvalues of V.
    • In fact, the matrix iΩV is Hermitian and, therefore, diagonalizable by a unitary transformation. Then, by taking the modulus of its 2n real eigenvalues, one gets the n symplectic eigenvalues of V.
  • 45
    • 47749125433 scopus 로고    scopus 로고
    • 10.1103/PhysRevA.78.012331;
    • S. Pirandola and S. Lloyd, Phys. Rev. A 78, 012331 (2008) 10.1103/PhysRevA.78.012331
    • (2008) Phys. Rev. A , vol.78 , pp. 012331
    • Pirandola, S.1    Lloyd, S.2
  • 51
    • 66149119459 scopus 로고    scopus 로고
    • For every M M (n,R) there always exists a pair of proper rotations R1, R2 SO (n) such that M= R1 D R2T with D diagonal and real.
    • For every M M (n,R) there always exists a pair of proper rotations R1, R2 SO (n) such that M= R1 D R2T with D diagonal and real.
  • 52
    • 66149087395 scopus 로고    scopus 로고
    • For the possibility of symplectically diagonalizing quadratic forms under different positivity conditions, see Appendix 6 of Ref..
    • For the possibility of symplectically diagonalizing quadratic forms under different positivity conditions, see Appendix 6 of Ref..
  • 53
    • 66149093929 scopus 로고    scopus 로고
    • According to the Sylvester's law of inertia, congruence transformations preserve the signs of the eigenvalues.
    • According to the Sylvester's law of inertia, congruence transformations preserve the signs of the eigenvalues.
  • 54
    • 0037574296 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.77.1413
    • A. Peres, Phys. Rev. Lett. 77, 1413 (1996). 10.1103/PhysRevLett.77.1413
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 1413
    • Peres, A.1
  • 55
    • 64149111850 scopus 로고    scopus 로고
    • 10.1103/PhysRevA.79.032334
    • K. Fujikawa, Phys. Rev. A 79, 032334 (2009). 10.1103/PhysRevA.79.032334
    • (2009) Phys. Rev. A , vol.79 , pp. 032334
    • Fujikawa, K.1
  • 56
    • 66149119068 scopus 로고    scopus 로고
    • Notice that Ref. adopts the commutation relations [x l, x m] =i Ωlm, so that the variance of the vacuum noise is equal to 1/2. In this notation, our Eq. 85 becomes detAdetB+ [(1/4) -detC] 2 - I4 (detA+detB) /4, which is exactly the Eq. (17) of Ref..
    • Notice that Ref. adopts the commutation relations [x l, x m] =i Ωlm, so that the variance of the vacuum noise is equal to 1/2. In this notation, our Eq. 85 becomes detAdetB+ [(1/4) -detC] 2 - I4 (detA+detB) /4, which is exactly the Eq. (17) of Ref..
  • 57
    • 0004151494 scopus 로고    scopus 로고
    • This theorem is a specialization of the orthogonal block diagonalization which is valid for all the normal matrices [see, e.g., Cambridge University Press, New York
    • This theorem is a specialization of the orthogonal block diagonalization which is valid for all the normal matrices [see, e.g., R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University Press, New York, 2006), Chap.]. Clearly, the uniqueness of A and O holds up to permutation in the spectrum.
    • (2006) Matrix Analysis
    • Horn, R.A.1    Johnson, C.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.