Multipartite correlations in mutually unbiased bases

Abstract

We introduce new measures of multipartite quantum correlations based on classical correlations in mutually unbiased bases. These classical correlations are measured in terms of the classical mutual information, which has a clear operational meaning. We present sufficient conditions under which these measures are maximized. States that have previously been shown to be particularily important in the context of LOCC transformations fulfill these conditions and therefore maximize the correlation measures. In addition, we show how the new measures can be used to detect high-dimensional tripartite entanglement by using only a few local measurements.

arXiv comment18 pages (including appendix), 5 figures, 1 table

References in corpus (35)

• Quantum entanglement
• Advances in Quantum Metrology
• Three qubits can be entangled in two inequivalent ways
• Quantum secret sharing
• Distributed Entanglement
• Conditions for a class of entanglement transformations
• On mutually unbiased bases
• Four qubits can be entangled in nine different ways
• On the Theory of Quantum Secret Sharing
• A new proof for the existence of mutually unbiased bases
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• Entropic uncertainty relations - A survey
• Entanglement detection via mutually unbiased bases
• Improved entropic uncertainty relations and information exclusion relations
• Quantifying entanglement resources
• Entanglement Theory and the Second Law of Thermodynamics
• Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices
• The maximally entangled set of multipartite quantum states
• Experimental detection of entanglement via witness operators and local measurements
• N-particle N-level singlet states: Some properties and applications
• Mutually unbiased measurements in finite dimensions
• Operational multipartite entanglement measures
• Investigating three qubit entanglement with local measurements
• Entanglement detection using mutually unbiased measurements
• Entangled pure state transformations via local operations assisted by finitely many rounds of classical communication
• Entanglement manipulation of multipartite pure states with finite rounds of classical communication
• Complementarity and correlations
• The moduli space of three qutrit states
• Tight entropic uncertainty relations for systems with dimension three to five
• Deterministic Transformations of Multipartite Entangled States with Tensor Rank 2
• The maximally entangled set of 4-qubit states
• The MES of tripartite qutrit states and pure state separable transformations which are not possible via LOCC
• Graph-state formalism for mutually unbiased bases
• High-dimensional entanglement certification
• The source and accessible entanglement of few-body systems

Cited by in corpus (11)

• Measurements in two bases are sufficient for certifying high-dimensional entanglement
• Quantifying measurement incompatibility of mutually unbiased bases
• Entanglement witnesses from mutually unbiased bases
• Mutual Unbiasedness in Coarse-grained Continuous Variables
• A finite geometric toy model of space-time as an error correcting code
• Mutually Unbiased Coarse-Grained Measurements of Two or More Phase-Space Variables
• Tight bounds from multiple-observable entropic uncertainty relations
• Complementary properties of multiphoton quantum states in linear optics networks
• Constructing mutually unbiased bases from unextendible maximally entangled bases
• Generation and evaluation of multipartite entanglement with multi-rail encoding in linear optics networks
• Choice of mutually unbiased bases and outcome labelling affects measurement outcome secrecy