Entanglement detection via mutually unbiased bases

Abstract

We investigate correlations among complementary observables. In particular, we show how to take advantage of mutually unbiased bases (MUBs) for the efficient detection of entanglement in arbitrarily high-dimensional, multipartite and continuous variable quantum systems. The introduced entanglement criteria are relatively easy to implement experimentally since they require only a few local measurement settings. In addition, we establish a link between the separability problem and the maximum number of mutually unbiased bases -- opening a new avenue in this long-standing open problem.

8 pages, 2 figure

References in corpus (18)

• Entanglement detection
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Bloch vectors for qudits
• Taming multiparticle entanglement
• Entropic uncertainty relation for mutually unbiased bases
• Multipartite entanglement detection from correlation tensors
• On experimental procedures for entanglement verification
• Maximal Sets of Mutually Unbiased Quantum States in Dimension Six
• Numerical evidence for the maximum number of mutually unbiased bases in dimension six
• Quantum process reconstruction based on mutually unbiased basis
• Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models
• Correlation tensor criteria for genuine multiqubit entanglement
• Mutually Unbiased Bases for Continuous Variables
• A composite parameterization of unitary groups, density matrices and subspaces
• Mutually unbiased bases: tomography of spin states and star-product scheme
• Mutually Unbiased Bases and Semi-definite Programming
• Construction of mutually unbiased bases with cyclic symmetry for qubit systems
• Examining the dimensionality of genuine multipartite entanglement

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