Spectrum conditions for symmetric extendible states

Abstract

We analyze bipartite quantum states that admit a symmetric extension. Any such state can be decomposed into a convex combination of states that allow a _pure_ symmetric extension. A necessary condition for a state to admit a pure symmetric extension is that the spectra of the local and global density matrices are equal. This condition is also sufficient for two qubits, but not for any larger systems. Using this condition we present a conjectured necessary and sufficient condition for a two qubit state to admit symmetric extension, which we prove in some special cases. The results from symmetric extension carry over to degradable and anti-degradable channels and we use this to prove that all degradable channels with qubit output have a qubit environment.

14 pages, 2 figures

References in corpus (18)

• Mixed State Entanglement and Quantum Error Correction
• Distributed Entanglement
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Distillation of secret key and entanglement from quantum states
• Monogamy of entanglement and other correlations
• Information-theoretic aspects of quantum inseparability of mixed states
• Distinguishing separable and entangled states
• Entanglement as precondition for secure quantum key distribution
• Separable states are more disordered globally than locally
• Monogamy of nonlocal quantum correlations
• Degenerate Quantum Codes for Pauli Channels
• The structure of degradable quantum channels
• Quantum Capacities of Channels with small Environment
• Compatibility of subsystem states and convex geometry
• Symmetric extension in two-way quantum key distribution
• Compatibility of subsystem states
• Simple test for quantum channel capacity
• Compatibility Relations between the Reduced and Global Density Matrixes

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• Quantum Channel Capacities with Passive Environment Assistance
• Compatible quantum correlations: on extension problems for Werner and isotropic states
• Symmetric extension in two-way quantum key distribution
• Error Thresholds for Arbitrary Pauli Noise
• Quantum communication on the bosonic loss-dephasing channel
• Norms and Cones in the Theory of Quantum Entanglement
• Symmetric extension of bipartite quantum states and its use in quantum key distribution with two-way postprocessing
• Detecting Consistency of Overlapping Quantum Marginals by Separability
• Symmetric extendibility for qudits and tolerable error rates in quantum cryptography
• Symmetric extendibility for a class of qudit states
• Symmetric extendibility of quantum states
• Hybrid Zero-capacity Channels
• Information-theoretic aspects of the generalized amplitude damping channel
• Sufficient condition for nonexistence of symmetric extension of qudits using Bell inequalities
• Entanglement of temporal sections as quantum histories and their quantum correlation bounds
• Distributing bipartite quantum systems under timing constraints
• Efficient bounds on quantum communication rates via their reduced variants