Entanglement and Designs

Abstract

We describe a connection between entanglement and designs. It involves the conical 2-designs introduced in a previous paper. These are a generalization of projective 2-designs which includes full sets of arbitrary rank mutually unbiased measurements (MUMs) and arbitrary rank symmetric informationally complete measurements (SIMs), as well as the more familiar MUBs and SICs. We show that a POVM is a conical 2-design if and only if there exists what we call a regular entanglement monotone whose restriction to the pure states is a function of the norm of the probability vector. In that case the concurrence is such a monotone. We also generalize and develop previous work on designs and entanglement detection.

5 pages. v2: references updated

References in corpus (7)

• Entanglement detection
• Tight informationally complete quantum measurements
• Symmetric Informationally Complete Measurements of Arbitrary Rank
• Entanglement detection using mutually unbiased measurements
• Quantum Conical Designs
• Separability criteria via sets of mutually unbiased measurements
• Entanglement detection via some classes of measurements

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• The SIC Question: History and State of Play
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• Generalization of Pauli channels through mutually unbiased measurements
• Conical Designs and Categorical Jordan Algebraic Post-Quantum Theories