Classical complexity and quantum entanglement
Journal of Computer and System Sciences - Special issue: STOC 2003
Combinatorial laplacians and positivity under partial transpose
Mathematical Structures in Computer Science
On independent permutation separability criteria
Quantum Information & Computation
An analytic approach to the problem of separability of quantum states based upon the theory of cones
Quantum Information Processing
Entanglement detection and distillation for arbitrary bipartite systems
Quantum Information Processing
Quantum Information Processing
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In the present paper we develop and investigate a novel approach that aims to characterize quantum entanglement by using cross norms. In the first part of the paper we further develop the mathematical theory by determining the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the second part we show that our techniques induce a novel powerful analytical and computable separability criterion for bipartite systems. This new criterion complements the well-known Peres positive partial transpose criterion in several aspects. It is a necessary but in general not a sufficient criterion for separability. We demonstrate the power of the new criterion by evaluating the criterion for a number of important examples. We also demonstrate that the new criterion is able to detect bound entangled states.