Stochastic Matrix Product States

Abstract

The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a new measure for correlations which is analogous to the entanglement entropy, the entropy cost $S_C$, and show that this measure quantifies the bond dimension needed to represent a steady state as a matrix product state. We illustrate these concepts on the hand of the asymmetric exclusion process.

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• Measures of distinguishability between stochastic processes
• Tensor-network algorithm for nonequilibrium relaxation in the thermodynamic limit
• Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System
• Exact epidemic models from a tensor product formulation
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• Border Ranks of Positive and Invariant Tensor Decompositions: Applications to Correlations
• Matrix Product States approach to non-Markovian processes
• Steady state representations for the harmonic process