Characterizing quantum states via sector lengths

Abstract

Correlations in multiparticle systems are constrained by restrictions from quantum mechanics. A prominent example for these restrictions are monogamy relations, limiting the amount of entanglement between pairs of particles in a three-particle system. A powerful tool to study correlation constraints is the notion of sector lengths. These quantify, for different $k$, the amount of $k$-partite correlations in a quantum state in a basis-independent manner. We derive tight bounds on the sector lengths in multi-qubit states and highlight applications of these bounds to entanglement detection, monogamy relations and the $n$-representability problem. For the case of two- and three qubits we characterize the possible sector lengths completely and prove a symmetrized version of strong subadditivity for the linear entropy.

19 pages, 3 figures, 2 tables

References in corpus (15)

• Entanglement detection
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Spin squeezing and entanglement
• N-representability is QMA-complete
• Optimal entanglement criterion for mixed quantum states
• Duality for monogamy of entanglement
• Entanglement monotones and maximally entangled states in multipartite qubit systems
• Characterizing multipartite entanglement without shared reference frames
• Monogamy equalities for qubit entanglement from Lorentz invariance
• Higher entropic uncertainty relations for anti-commuting observables
• Detecting genuine multipartite entanglement of pure states with bipartite correlations
• Evaluable multipartite entanglement measures: are multipartite concurrences entanglement monotones?
• Some inequalities for quantum Tsallis entropy related to the strong subadditivity
• Higher dimensional entanglement without correlations
• Reply to Comment on "Regional Versus Global Entanglement in Resonating-Valence-Bond States"

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