Abstract
AbstractWe derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains, which provide constraints on finite-time fluctuations of time-additive quantities around their averages. We employ spectral, perturbation and martingale techniques, together with non-commutative $$L_2$$
L
2
theory, to derive: (i) a Bernstein-type concentration bound for time averages of the measurement outcomes of a quantum Markov chain, (ii) a Hoeffding-type concentration bound for the same process, (iii) a generalization of the Bernstein-type concentration bound for counting processes of continuous-time quantum Markov processes, (iv) new concentration bounds for empirical fluxes of classical Markov chains which broaden the range of applicability of the corresponding classical bounds beyond empirical averages. We also suggest potential application of our results to parameter estimation and consider extensions to reducible quantum channels, multi-time statistics and time-dependent measurements, and comment on the connection to so-called thermodynamic uncertainty relations.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics
Reference71 articles.
1. Accardi, L., Frigerio, A., Lewis, J.T.: Quantum stochastic processes. Publications of the R.I.M.S 18, 97–133 (1982)
2. Amini, N.H., Bompais, M., Pellegrini, C.: On asymptotic stability of quantum trajectories and their Cesaro mean. J. Phys. A 54(38), 385304 (2021). (21)
3. Amorim, É., Carlen, E.A.: Complete positivity and self-adjointness. Linear Algebra Appl. 611, 389–439 (2021)
4. Attal, S., Guillotin-Plantard, N., Sabot, C.: Central limit theorems for open quantum random walks and quantum measurement records. Ann. Henri Poincaré 16(1), 15–43 (2015)
5. Attal, S., Pautrat, Y.: From repeated to continuous quantum interactions. Ann. Henri Poincaré 7(1), 59–104 (2006)
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