Random repeated quantum interactions and random invariant states

Abstract

We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems ${\mathcal{K}}_n,n\ge 1$. Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between $\mathcal{H}$ and ${\mathcal{K}}_n$. The other involves random quantum states describing each copy ${\mathcal{K}}_n$. In the limit of a large number of interactions, we present convergence results for the asymptotic state of $\mathcal{H}$. This is achieved by studying spectral properties of (random) quantum channels which guarantee the existence of unique invariant states. Finally this allows to introduce a new physically motivated ensemble of random density matrices called the \emph{asymptotic induced ensemble}.

References in corpus (9)

• Aspects of generic entanglement
• Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1
• Random Quantum Operations
• On the dimension of subspaces with bounded Schmidt rank
• Existence, uniqueness and approximation of a stochastic Schrödinger equation: the diffusive case
• Generic local distinguishability and completely entangled subspaces
• Asymptotics of random density matrices
• Random repeated interaction quantum systems
• The probability of entanglement

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• Multipartite correlations in quantum collision models
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• Linear response theory and entropic fluctuations in repeated interaction quantum systems
• Markovian Repeated Interaction Quantum Systems
• On the spectral gap of random quantum channels
• Application of Shemesh theorem to quantum channels
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• Classical restrictions of generic matrix product states are quasi-locally Gibbsian
• A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement