메뉴 건너뛰기




Volumn 77, Issue 1, 2008, Pages

Convertibility between two-qubit states using stochastic local quantum operations assisted by classical communication

Author keywords

[No Author keywords available]

Indexed keywords

NETWORK PROTOCOLS; QUANTUM THEORY; RANDOM PROCESSES; SET THEORY;

EID: 38549132379     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.012332     Document Type: Article
Times cited : (15)

References (51)
  • 3
    • 0037574296 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413
    • A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413 77, 1413 (1996)
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 1413
    • Peres, A.1
  • 5
    • 0039624459 scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.40.4277
    • R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.4277 40, 4277 (1989).
    • (1989) Phys. Rev. A , vol.40 , pp. 4277
    • Werner, R.F.1
  • 6
    • 0000525266 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.59.4206
    • M. Horodecki and P. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.4206 59, 4206 (1999).
    • (1999) Phys. Rev. A , vol.59 , pp. 4206
    • Horodecki, M.1    Horodecki, P.2
  • 7
    • 0035679286 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.64.062307
    • K. G. H. Vollbrecht and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.062307 64, 062307 (2001).
    • (2001) Phys. Rev. A , vol.64 , pp. 062307
    • Vollbrecht, K.G.H.1    Werner, R.F.2
  • 8
    • 18344383219 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.63.042111
    • T. Eggeling and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.042111 63, 042111 (2001).
    • (2001) Phys. Rev. A , vol.63 , pp. 042111
    • Eggeling, T.1    Werner, R.F.2
  • 9
    • 0000620953 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.83.436
    • M. A. Nielsen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83. 436 83, 436 (1999).
    • (1999) Phys. Rev. Lett. , vol.83 , pp. 436
    • Nielsen, M.A.1
  • 10
    • 0034652055 scopus 로고    scopus 로고
    • JMOPEW 0950-0340 10.1080/095003400148268
    • G. Vidal, J. Mod. Opt. JMOPEW 0950-0340 10.1080/095003400148268 47, 355 (2000).
    • (2000) J. Mod. Opt. , vol.47 , pp. 355
    • Vidal, G.1
  • 11
    • 0000953494 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.62.062314
    • W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.062314 62, 062314 (2000).
    • (2000) Phys. Rev. A , vol.62 , pp. 062314
    • Dür, W.1    Vidal, G.2    Cirac, J.I.3
  • 12
    • 0000303412 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.83.1046
    • G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1046 83, 1046 (1999).
    • (1999) Phys. Rev. Lett. , vol.83 , pp. 1046
    • Vidal, G.1
  • 14
    • 4143072819 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.83.2656
    • A. Kent, N. Linden, and S. Massar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.2656 83, 2656 (1999).
    • (1999) Phys. Rev. Lett. , vol.83 , pp. 2656
    • Kent, A.1    Linden, N.2    Massar, S.3
  • 15
    • 0034706481 scopus 로고    scopus 로고
    • PYLAAG 0375-9601 10.1016/S0375-9601(00)00611-3
    • L.-X. Cen, F.-L. Li, and S.-Y. Zhu, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00611-3 275, 368 (2000)
    • (2000) Phys. Lett. A , vol.275 , pp. 368
    • Cen, L.-X.1    Li, F.-L.2    Zhu, S.-Y.3
  • 16
    • 0036577433 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.65.052318
    • L.-X. Cen, N.-J. Wu, F.-H. Yang, and J.-H. An, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.052318 65, 052318 (2002).
    • (2002) Phys. Rev. A , vol.65 , pp. 052318
    • Cen, L.-X.1    Wu, N.-J.2    Yang, F.-H.3    An, J.-H.4
  • 17
    • 4644359625 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.78.5022
    • S. Hill and W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.5022 78, 5022 (1997).
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 5022
    • Hill, S.1    Wootters, W.K.2
  • 18
    • 0035396243 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.64.010101
    • F. Verstraete, J. Dehaene, and B. DeMoor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.010101 64, 010101 (R) (2001).
    • (2001) Phys. Rev. A , vol.64 , pp. 010101
    • Verstraete, F.1    Dehaene, J.2    Demoor, B.3
  • 19
    • 38549141303 scopus 로고    scopus 로고
    • Obviously, unique up to local unitary transformations.
    • Obviously, unique up to local unitary transformations.
  • 20
    • 38549182559 scopus 로고    scopus 로고
    • Maximal, in the sense that no SLOCC transformations can bring the state to another one with higher entanglement of formation.
    • Maximal, in the sense that no SLOCC transformations can bring the state to another one with higher entanglement of formation.
  • 21
    • 0036508820 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.65.032308
    • F. Verstraete, J. Dehaene, and B. DeMoor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032308 65, 032308 (2002).
    • (2002) Phys. Rev. A , vol.65 , pp. 032308
    • Verstraete, F.1    Dehaene, J.2    Demoor, B.3
  • 23
    • 4243656245 scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.74.2619
    • S. Popescu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.2619 74, 2619 (1995)
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 2619
    • Popescu, S.1
  • 24
    • 0000296001 scopus 로고    scopus 로고
    • PYLAAG 0375-9601 10.1016/S0375-9601(96)80001-6
    • N. Gisin, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(96)80001-6 210, 151 (1996).
    • (1996) Phys. Lett. A , vol.210 , pp. 151
    • Gisin, N.1
  • 27
    • 38549129901 scopus 로고    scopus 로고
    • Their separability can be veirfied, for example, by writing these operators in full in the product basis via Eq. 4 and showing that they admit convex decomposition in terms of separable states. Alternatively, via the Choi-Jamiołkowski isomorphism that will be discussed later in Sec. 3 and the remarks made towards the end of Sec. 3, one can also see that these matrices correspond to separable states.
    • Their separability can be veirfied, for example, by writing these operators in full in the product basis via Eq. 4 and showing that they admit convex decomposition in terms of separable states. Alternatively, via the Choi-Jamiołkowski isomorphism that will be discussed later in Sec. 3 and the remarks made towards the end of Sec. 3, one can also see that these matrices correspond to separable states.
  • 29
    • 38549180705 scopus 로고    scopus 로고
    • This software package, which stands for POlyhedron Representation Transformation Algorithm, is available at
    • This software package, which stands for POlyhedron Representation Transformation Algorithm, is available at http://www.zib.de/Optimization/ Software/Porta/
  • 32
    • 0030106462 scopus 로고    scopus 로고
    • SIREAD 0036-1445 10.1137/1038003
    • L. Vandenberghe and S. Boyd, SIAM Rev. SIREAD 0036-1445 10.1137/1038003 38, 49 (1996)
    • (1996) SIAM Rev. , vol.38 , pp. 49
    • Vandenberghe, L.1    Boyd, S.2
  • 34
    • 38549084308 scopus 로고    scopus 로고
    • http://www.physics.uq.edu.au/qisci/yerng/
  • 35
    • 38549114192 scopus 로고    scopus 로고
    • Note that to verify Z2 against Eq. 9, one should also rewrite Zw,2 obtained in Eq. 8 in the appropriate tensor-product basis such that Zw,2 acts on H A′ H A″ H B′ H B″.
    • Note that to verify Z2 against Eq. 9, one should also rewrite Zw,2 obtained in Eq. 8 in the appropriate tensor-product basis such that Zw,2 acts on H A′ H A″ H B′ H B″.
  • 36
    • 35448975107 scopus 로고
    • RMHPBE 0034-4877 10.1016/0034-4877(72)90011-0
    • A. Jamiołkowski, Rep. Math. Phys. RMHPBE 0034-4877 10.1016/0034-4877(72)90011-0 3, 275 (1972)
    • (1972) Rep. Math. Phys. , vol.3 , pp. 275
    • Jamiołkowski, A.1
  • 37
    • 0016522050 scopus 로고
    • LAAPAW 0024-3795 10.1016/0024-3795(75)90075-0
    • M. D. Choi, Linear Algebr. Appl. LAAPAW 0024-3795 10.1016/0024-3795(75) 90075-0 10, 285 (1975)
    • (1975) Linear Algebr. Appl. , vol.10 , pp. 285
    • Choi, M.D.1
  • 38
    • 0008689297 scopus 로고
    • RMHPBE 0034-4877 10.1016/0034-4877(86)90039-X
    • V. P. Belavkin and P. Staszewski, Rep. Math. Phys. RMHPBE 0034-4877 10.1016/0034-4877(86)90039-X 24, 49 (1986).
    • (1986) Rep. Math. Phys. , vol.24 , pp. 49
    • Belavkin, V.P.1    Staszewski, P.2
  • 39
    • 38549136967 scopus 로고    scopus 로고
    • arXiv:quant-ph/9707002.
    • E. M. Rains, e-print arXiv:quant-ph/9707002.
    • Rains, E.M.1
  • 40
    • 0032025985 scopus 로고    scopus 로고
    • PLRAAN 1050-2947 10.1103/PhysRevA.57.1619
    • V. Vedral and M. B. Plenio, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.1619 57, 1619 (1998).
    • (1998) Phys. Rev. A , vol.57 , pp. 1619
    • Vedral, V.1    Plenio, M.B.2
  • 41
    • 38549110746 scopus 로고    scopus 로고
    • Following Kraus' work on CPM, this specific form of the CPM is also known as a Kraus decomposition of the CPM, with each Ai Bi in the sum conventionally called the Kraus operator associated with the CPM.
    • Following Kraus' work on CPM, this specific form of the CPM is also known as a Kraus decomposition of the CPM, with each Ai Bi in the sum conventionally called the Kraus operator associated with the CPM.
  • 43
    • 0003007332 scopus 로고
    • APNYA6 0003-4916 10.1016/0003-4916(71)90108-4
    • K. Kraus, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(71)90108-4 64, 311 (1971).
    • (1971) Ann. Phys. (N.Y.) , vol.64 , pp. 311
    • Kraus, K.1
  • 46
    • 38549163380 scopus 로고    scopus 로고
    • The ρE derived from G0 in Eq. 6 is an example of this sort. In fact, in this case, if the input state has no support on Π1 nor Π2, the map always outputs the zero matrix.
    • The ρE derived from G0 in Eq. 6 is an example of this sort. In fact, in this case, if the input state has no support on Π1 nor Π2, the map always outputs the zero matrix.
  • 47
    • 38549102739 scopus 로고    scopus 로고
    • Since the mapping from any ρ Ps to a separable CPM via Eq. 13 is only defined up to a positive constant, for the subsequent discussion, we might as well consider the cone generated by Ps.
    • Since the mapping from any ρ Ps to a separable CPM via Eq. 13 is only defined up to a positive constant, for the subsequent discussion, we might as well consider the cone generated by Ps.
  • 49
    • 38549098713 scopus 로고    scopus 로고
    • Strictly, the inequality 23 is only valid when λ3 λ4. When λ3 = λ4, F2 degenerates into an edge of the polytope Pλ. If λ1 = λ2, F2 collapses into a single point λ= λ 12 = λ (34).
    • Strictly, the inequality 23 is only valid when λ3 λ4. When λ3 = λ4, F2 degenerates into an edge of the polytope Pλ. If λ1 = λ2, F2 collapses into a single point λ = λ 12 = λ (34).
  • 50
    • 38549111527 scopus 로고    scopus 로고
    • Within TE, 1-2 λ2 -2 λ3 =0 only when λ = λ 12 and λ (23) = λ 13. In this case, F3 degenerates into the line joining λ 12 and λ 13.
    • Within TE, 1-2 λ2 -2 λ3 =0 only when λ = λ 12 and λ (23) = λ 13. In this case, F3 degenerates into the line joining λ 12 and λ 13.
  • 51
    • 38549148924 scopus 로고    scopus 로고
    • By this, of course, we are referring only to the states given in Eq. 31 that are originally of rank 3, and which becomes rank 2 upon quasidistillation. The states given in Eq. 31 that are of rank 2 get quasidistilled to the singlet state and so the process is clearly reversible in this case.
    • By this, of course, we are referring only to the states given in Eq. 31 that are originally of rank 3, and which becomes rank 2 upon quasidistillation. The states given in Eq. 31 that are of rank 2 get quasidistilled to the singlet state and so the process is clearly reversible in this case.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.