Some Properties of the Computable Cross Norm Criterion for Separability

Abstract

The computable cross norm (CCN) criterion is a new powerful analytical and computable separability criterion for bipartite quantum states, that is also known to systematically detect bound entanglement. In certain aspects this criterion complements the well-known Peres positive partial transpose (PPT) criterion. In the present paper we study important analytical properties of the CCN criterion. We show that in contrast to the PPT criterion it is not sufficient in dimension 2 x 2. In higher dimensions we prove theorems connecting the fidelity of a quantum state with the CCN criterion. We also analyze the behaviour of the CCN criterion under local operations and identify the operations that leave it invariant. It turns out that the CCN criterion is in general not invariant under local operations.

7 pages; accepted by Physical Review A; error in Appendix B corrected

References in corpus (14)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Bell Inequalities and the Separability Criterion
• Information-theoretic aspects of quantum inseparability of mixed states
• Characterizing Entanglement
• Distinguishing separable and entangled states
• Further results on the cross norm criterion for separability
• The Uniqueness Theorem for Entanglement Measures
• Local filtering operations on two qubits
• Universal teleportation with a twist
• A separability criterion for density operators
• Separability and Fourier representations of density matrices
• Complete Separability and Fourier representations of n-qubit states
• Separability of mixed quantum states: linear contractions approach

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