Decay of quantum conditional mutual information for purely generated finitely correlated states

Abstract

The connection between quantum state recovery and quantum conditional mutual information (QCMI) is studied for the class of purely generated finitely correlated states (pgFCS) of one-dimensional quantum spin chains. For a tripartition of the chain into two subsystems separated by a buffer region, it is shown that a pgFCS is an approximate quantum Markov chain, and stronger, may be approximated by a quantum Markov chain in trace distance, with an error exponentially small in the buffer size. This implies that, (1) a locally corrupted state can be approximately recovered by action of a quantum channel on the buffer system, and (2) QCMI is exponentially small in the size of the buffer region. Bounds on the exponential decay rate of QCMI and examples of quantum recovery channels are presented.

arXiv comment24 pages, 1 figure

References in corpus (25)

• Efficient classical simulation of slightly entangled quantum computations
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Area laws in quantum systems: mutual information and correlations
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• Matrix-product-groundstates for one-dimensional spin-1 quantum antiferromagnets
• Quantum conditional mutual information and approximate Markov chains
• Continuity of quantum conditional information
• Exponential Decay of Correlations Implies Area Law
• Sequential Generation of Matrix-Product States in Cavity QED
• Universal recovery maps and approximate sufficiency of quantum relative entropy
• Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
• Robustness of quantum Markov chains
• Quantum SDP-Solvers: Better upper and lower bounds
• Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature
• Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states
• Universal recovery map for approximate Markov chains
• Entanglement of the Antisymmetric State
• Quantum Approximate Markov Chains are Thermal
• Spectral convergence bounds for classical and quantum Markov processes
• Efficient description of many-body systems with Matrix Product Density Operators
• Mixed s-sourcery: Building many-body states using bubbles of Nothing
• Limits on the storage of quantum information in a volume of space
• Symmetry-protected dissipative preparation of matrix product states
• Matrix Product Density Operators: when do they have a local parent Hamiltonian?

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