Markovianization with approximate unitary designs

• URL: http://arxiv.org/abs/2004.07620v2
• Date: Wed, 9 Jun 2021 10:32:36 GMT
• Title: Markovianization with approximate unitary designs
• Authors: Pedro Figueroa-Romero, Felix A. Pollock, Kavan Modi
• Abstract summary: We prove that there are physical non-Markovian processes that look highly Markovian for all orders of correlations. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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