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12
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85038272251
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There exist upper bounds to the distillable entanglement and entanglement of formation. See, for example, Refs
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There exist upper bounds to the distillable entanglement and entanglement of formation. See, for example, Refs.
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13
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85038270342
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quant-ph/9707002
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E. Rains, quant-ph/9707002.
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Rains, E.1
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14
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85038344775
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quant-ph/0008047
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E. Rains, quant-ph/0008047;
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Rains, E.1
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15
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17
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0002548162
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For a review, see W. K. Wootters, P. Horodecki, and R. Horodecki, Quantum Inf. Comput. 1, 27 (2001).
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Wootters, W.K.1
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Horodecki, R.3
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18
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85038288966
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Equation 4 is the distillation ratio obtained through the hashing protocol
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Equation 4 is the distillation ratio obtained through the hashing protocol
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19
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4243684526
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The entanglement of formation of two qubits has been obtained in W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998);
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Wootters, W.K.1
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20
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18144442709
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the entanglement of formation of a class of states in higher dimensions has been obtained by B. M. Terhal and K. G. H. Vollbrecht, Phys. Rev. Lett. 85, 2625 (2000).
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21
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85038315651
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Throughout this paper we will omit tensor products if there is no danger of confusion
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Throughout this paper we will omit tensor products if there is no danger of confusion.
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22
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85038320920
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quant-ph/0201149
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P. Shor, quant-ph/0201149.
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Shor, P.1
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23
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85038327134
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As discussed in
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As discussed in
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24
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85038348188
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More precisely, inequality of Eq. 21 follows from applying the strong superadditivity of the von Neumann entropy, in the form (Formula presented), to the state (Formula presented), where (Formula presented) is an orthonormal set of vectors
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More precisely, inequality of Eq. 21 follows from applying the strong superadditivity of the von Neumann entropy, in the form (Formula presented), to the state (Formula presented), where (Formula presented) is an orthonormal set of vectors.
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-
-
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25
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85038283269
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Recall that for any mixed state (Formula presented) and any of its realizations (Formula presented), the concavity of the von Neumann entropy implies that (Formula presented)
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Recall that for any mixed state (Formula presented) and any of its realizations (Formula presented), the concavity of the von Neumann entropy implies that (Formula presented)
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26
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85038274345
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An alternative characterization of an entanglement-breaking channel (Formula presented): (Formula presented) is that it maps a maximally entangled state (Formula presented), where (Formula presented) is an auxiliary system and (Formula presented), into a separable state, following the ideas of
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An alternative characterization of an entanglement-breaking channel (Formula presented): (Formula presented) is that it maps a maximally entangled state (Formula presented), where (Formula presented) is an auxiliary system and (Formula presented), into a separable state, following the ideas of
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28
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0038721037
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J. I. Cirac, W. Dür, B. Kraus, and M. Lewenstein, Phys. Rev. Lett. 86, 544 (2001).
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0037788957
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W. Dür, J. I. Cirac, M. Lewenstein, and D. Bruss, Phys. Rev. A 61, 062313 (2000).
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