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- Title
Markovianization with approximate unitary designs.
- Authors
Figueroa–Romero, Pedro; Pollock, Felix A.; Modi, Kavan
- 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. A question of foundational importance is 'why is nature forgetful?', playing an important role in our understanding of thermodynamics. Here, the authors study a class of quantum processes, called approximate unitary designs, to show that these processes are highly forgetful - i.e. Markovian.
- Subjects
MEMORYLESS systems; MATHEMATICS; OPEN systems (Physics); THERMODYNAMICS; PROBABILITY theory
- Publication
Communications Physics, 2021, Vol 4, Issue 1, p1
- ISSN
2399-3650
- Publication type
Article
- DOI
10.1038/s42005-021-00629-w