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

TL;DR

This paper investigates how quantum conditional mutual information (QCMI) decays exponentially in finitely correlated states of quantum spin chains, showing that such states are approximate quantum Markov chains with implications for quantum recovery.

Contribution

It demonstrates that purely generated finitely correlated states are approximate quantum Markov chains with exponentially small QCMI, providing bounds and recovery channels.

Findings

QCMI decays exponentially with buffer size

States can be approximately recovered via quantum channels

Explicit bounds on decay rate and recovery channels are provided

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.