-
1
-
-
0141558835
-
-
note
-
s are separable. Physically, separable states are those that the different parties can prepare if they are allowed to use only local operations in each local system and to communicate classically. States that are not separable are called entangled.
-
-
-
-
2
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-
4243445702
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-
C. H. Bennett, H. J. Bernstein, S. Popescu and B. Schumacher, Phys. Rev. A 53 (1996), 2046.
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Phys. Rev. A
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, pp. 2046
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-
Bennett, C.H.1
Bernstein, H.J.2
Popescu, S.3
Schumacher, B.4
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3
-
-
4043132188
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C. H. Bennett, S. Popescu, D. Rohrlich, J. A. Smolin and A. V. Thapliyal, Phys. Rev. A 63 (2001), 012307.
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(2001)
Phys. Rev. A
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, pp. 012307
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-
Bennett, C.H.1
Popescu, S.2
Rohrlich, D.3
Smolin, J.A.4
Thapliyal, A.V.5
-
7
-
-
85111345823
-
-
note
-
3 to appear simultaneously and in arbitrary proportions on both sides of Eq. (4).
-
-
-
-
9
-
-
4444269235
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-
V. Vedral, M. B. Plenio, M. A. Rippin and P. L. Knight, Phys. Rev. Lett. 78 (1997), 2275; V. Vedral and M. B. Plenio, Phys. Rev. A 57 (1998), 1619.
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(1997)
Phys. Rev. Lett.
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, pp. 2275
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-
Vedral, V.1
Plenio, M.B.2
Rippin, M.A.3
Knight, P.L.4
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10
-
-
0032025985
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-
V. Vedral, M. B. Plenio, M. A. Rippin and P. L. Knight, Phys. Rev. Lett. 78 (1997), 2275; V. Vedral and M. B. Plenio, Phys. Rev. A 57 (1998), 1619.
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(1998)
Phys. Rev. A
, vol.57
, pp. 1619
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-
Vedral, V.1
Plenio, M.B.2
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11
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-
4243216277
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-
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin and W. K. Wootters, Phys. Rev. A 54 (1996), 3824.
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(1996)
Phys. Rev. A
, vol.54
, pp. 3824
-
-
Bennett, C.H.1
DiVincenzo, D.P.2
Smolin, J.A.3
Wootters, W.K.4
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13
-
-
85111345870
-
-
note
-
⊗N.
-
-
-
-
16
-
-
0032341219
-
-
An heuristic justification for the first of these inequalities can be found in M. Plenio and V. Vedral, Contemp. Phys. 39 (1998), 431.
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(1998)
Contemp. Phys.
, vol.39
, pp. 431
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Plenio, M.1
Vedral, V.2
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17
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0033611008
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-
Asymptotic transformations are only approximate reversible, in the sense that an o(1) error and o(N) inefficiency are allowed. Note that because of the continuity of the relative entropy of entanglement (see M. J. Donald and M. Horodecki, Phys. Lett. A 264 (1999), 257), an o(1) error in N copies of a state can reduce the relative entropy of entanglement by at most o(N). This term does not contribute to the regularized version of the relative entropy of entanglement.
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(1999)
Phys. Lett. A
, vol.264
, pp. 257
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-
Donald, M.J.1
Horodecki, M.2
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18
-
-
85111346988
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-
note
-
s as a result of its monotonicity under LOCC [9]. The only requirement is that Ω has to be invariant under LOCC, as it happens for Ω = Sep, PPT.
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-
-
-
20
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0141782139
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M. Lewenstein, B. Kraus, J. I. Cirac and P. Horodecki, Phys. Rev. A 62 (2000), 52310.
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(2000)
Phys. Rev. A
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, pp. 52310
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-
Lewenstein, M.1
Kraus, B.2
Cirac, J.I.3
Horodecki, P.4
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21
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0042542909
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-
P. Horodecki, Phys. Lett. A 232 (1997), 333; C. H. Bennett, D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin and B. M. Terhal, Phys. Rev. Lett. 82 (1999), 5385; D. Bruß and A. Peres, Phys. Rev. A 61 (2000), R30301.
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(1997)
Phys. Lett. A
, vol.232
, pp. 333
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-
Horodecki, P.1
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22
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4243962237
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P. Horodecki, Phys. Lett. A 232 (1997), 333; C. H. Bennett, D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin and B. M. Terhal, Phys. Rev. Lett. 82 (1999), 5385; D. Bruß and A. Peres, Phys. Rev. A 61 (2000), R30301.
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(1999)
Phys. Rev. Lett.
, vol.82
, pp. 5385
-
-
Bennett, C.H.1
DiVincenzo, D.P.2
Mor, T.3
Shor, P.W.4
Smolin, J.A.5
Terhal, B.M.6
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23
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-
0038816596
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-
P. Horodecki, Phys. Lett. A 232 (1997), 333; C. H. Bennett, D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin and B. M. Terhal, Phys. Rev. Lett. 82 (1999), 5385; D. Bruß and A. Peres, Phys. Rev. A 61 (2000), R30301.
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(2000)
Phys. Rev. A
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-
Bruß, D.1
Peres, A.2
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26
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-
0141558829
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-
note
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PPT(ρAB).
-
-
-
-
27
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-
0141558830
-
-
private communication, has pointed out to us this powerful generalization of a result of [8]
-
D. P. DiVincenzo, private communication, has pointed out to us this powerful generalization of a result of [8].
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DiVincenzo, D.P.1
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29
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0000727092
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K. Zyczkowski, P. Horodecki, A. Sanpera and M. Lewenstein, Phys. Rev. A 58 (1998), 883.
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(1998)
Phys. Rev. A
, vol.58
, pp. 883
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-
Zyczkowski, K.1
Horodecki, P.2
Sanpera, A.3
Lewenstein, M.4
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32
-
-
0141558834
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-
note
-
This can be checked by noticing that the bipartite reduced density matrices of the states discussed in [6] (which contain the Schmidt-decomposable states of [3] as a particular case) consist of a mixture of locally orthogonal pure states (either product or entangled). Thus, the entanglement of the mixed state can be distilled without losses by means of a projective local measurement that probabilistically picks up one of the pure states of the mixture.
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33
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0141447257
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quant-ph/0201079
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Yu Shi, quant-ph/0201079.
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Shi, Y.1
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