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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 : (14)

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    • Obviously, unique up to local unitary transformations.
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    • 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.
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    • This software package, which stands for POlyhedron Representation Transformation Algorithm, is available at http://www.zib.de/Optimization/ Software/Porta/
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    • 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″.
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    • 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.
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    • 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.
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    • 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.
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    • 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).
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    • 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.
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    • 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.


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