How many mutually unbiased bases are needed to detect bound entangled states?

Abstract

From a practical perspective it is advantageous to develop methods that verify entanglement in quantum states with as few measurements as possible. In this paper we investigate the minimal number of mutually unbiased bases (MUBs) needed to detect bound entanglement in bipartite $(d\times d)$-dimensional states, i.e. entangled states that are positive under partial transposition. In particular, we show that a class of entanglement witnesses composed of mutually unbiased bases can detect bound entanglement if the number of measurements is greater than $d/2+1$. This is a substantial improvement over other detection methods, requiring significantly fewer resources than either full quantum state tomography or measuring a complete set of $d+1$ MUBs. Our approach is based on a partial characterisation of the (non-)decomposability of entanglement witnesses. We show that non-decomposability is a universal property of MUBs, which holds regardless of the choice of complementary observables, and we find that both the number of measurements and the structure of the witness play an important role in the detection of bound entanglement.

11 pages, identical to published version

References in corpus (15)

• Entanglement detection
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Quantum theory based on real numbers can be experimentally falsified
• Experimental multiparticle entanglement dynamics induced by decoherence
• Measurement-Device-Independent Entanglement Witnesses for All Entangled Quantum States
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
• Characterization of high-dimensional entangled systems via mutually unbiased measurements
• Experimental bound entanglement in a four-photon state
• Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements
• Entanglement witnesses and geometry of entanglement of two--qutrit states
• Separability of diagonal symmetric states: a quadratic conic optimization problem
• Optimality for indecomposable entanglement witnesses
• Generalized Circulant Densities and a Sufficient Condition for Separability
• Entangled symmetric states and copositive matrices
• Small sets of complementary observables

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