Non-Markovian quantum processes: Complete framework and efficient characterization
By F. A. Pollock, C'esar A. Rodr'iguez-Rosario, T. Frauenheim, Mauro Paternostro, Kavan Modi. 2015
326 citations recorded by the source corpus.
Currently, there is no systematic way to describe a quantum process with memory solely in terms of experimentally accessible quantities. However, recent technological advances mean we have control over systems at scales where memory effects are non-negligible. The lack of such an operational description has hindered advances in understanding physical, chemical and biological processes, where often unjustified theoretical assumptions are made to render a dynamical description tractable. This has led to theories plagued with unphysical results and no consensus on what a quantum Markov (memoryless) process is. Here, we develop a universal framework to characterise arbitrary non-Markovian quantum processes. We show how a multi-time non-Markovian process can be reconstructed experimentally, and that it has a natural representation as a many body quantum state, where temporal correlations are mapped to spatial ones. Moreover, this state is expected to have an efficient matrix product operator form in many cases. Our framework constitutes a systematic tool for the effective description of memory-bearing open-system evolutions.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/8860a12b55da21c05de91d737a68bbb8bfbb4265
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
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Citations in the corpus
- Experimental photonic quantum memristor (2021, methodology): “For a full description one could compute the process tensor [58] over the time series length, however it is sufficient for us to consider a list of completely positive trace preserving maps that take the input quantum state and update the next map (dependent on the quantum memristor’s state).”
- Concepts of quantum non-Markovianity: A hierarchy (2017, unknown): “[84, 85], based on “causal interventions” (see also Ref.”