Markovianization with approximate unitary designs

Abstract

Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the environment forgetful. Here we prove that there are physical non-Markovian processes that with high probability look highly Markovian for all orders of correlations; we call this phenomenon Markovianization. Formally, we show that when a quantum process has dynamics given by an approximate unitary design, a large deviation bound on the size of non-Markovian memory is implied. We exemplify our result employing an efficient construction of an approximate unitary circuit design using two-qubit interactions only, showing how seemingly simple systems can speedily become forgetful. Conversely, since the process is closed, it should be possible to detect the underlying non-Markovian effects. However, for these processes, observing non-Markovian signatures would require highly entangling resources and hence be a difficult task.

6+9 pages, 5 figures. Published version, only presentation changes

References in corpus (9)

• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Evenly distributed unitaries: on the structure of unitary designs
• Operational Markov condition for quantum processes
• Quantum regression theorem and non-Markovianity of quantum dynamics
• An introduction to operational quantum dynamics
• Characterizing quantum dynamics with initial system-environment correlations
• Modern Concepts of Quantum Equilibration Do Not Rule Out Strange Relaxation Dynamics
• Phenomenological measure of quantum non-Markovianity

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