Detecting Consistency of Overlapping Quantum Marginals by Separability

Abstract

The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the $k$-symmetric extension problem in general, and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-known $k$-symmetric extension criterion for separability.

Important references added. 6 pages, 3 figures

References in corpus (12)

• General Monogamy Inequality for Bipartite Qubit Entanglement
• A complete family of separability criteria
• Is Entanglement Monogamous?
• N-representability is QMA-complete
• One-and-a-half quantum de Finetti theorems
• The Pauli principle revisited
• Detecting multipartite entanglement
• The structure of degradable quantum channels
• Pinning of Fermionic Occupation Numbers
• Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems
• On quantum estimation, quantum cloning and finite quantum de Finetti theorems
• Spectrum conditions for symmetric extendible states

Cited by in corpus (8)

• Resource theory of unextendibility and non-asymptotic quantum capacity
• Extendibility of bosonic Gaussian states
• Limitations of semidefinite programs for separable states and entangled games
• Some Ulam's reconstruction problems for quantum states
• Quantum Gauge Networks: A New Kind of Tensor Network
• Symmetric vs. bosonic extension for bipartite states
• Local density matrices of many-body states in the constant weight subspaces
• Construction of quantum states with special properties by projection methods