Optimisation of time-ordered processes in the finite and asymptotic regime

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Hauptverfasser: Weilenmann, Mirjam, Budroni, Costantino, Navascues, Miguel
Format: Preprint
Veröffentlicht: 2023
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author Weilenmann, Mirjam
Budroni, Costantino
Navascues, Miguel
author_facet Weilenmann, Mirjam
Budroni, Costantino
Navascues, Miguel
contents Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through adaptive measurements, computing the maximum average score of a preparation game over a continuous set of target states and limiting the behavior of a (quantum) finite-state automaton. In this work, we introduce tractable relaxations of this class of optimization problems. To illustrate their performance, we use them to: (a) compute the probability that a finite-state automaton outputs a given sequence of bits; (b) develop a new many-body entanglement detection protocol; (c) let the computer invent an adaptive protocol for magic state detection. As we further show, the maximum score of a sequential problem in the limit of infinitely many time steps is in general incomputable. Nonetheless, we provide general heuristics to bound this quantity and show that they provide useful estimates in relevant scenarios.
format Preprint
id arxiv_https___arxiv_org_abs_2302_02918
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Optimisation of time-ordered processes in the finite and asymptotic regime
Weilenmann, Mirjam
Budroni, Costantino
Navascues, Miguel
Quantum Physics
Optimization and Control
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through adaptive measurements, computing the maximum average score of a preparation game over a continuous set of target states and limiting the behavior of a (quantum) finite-state automaton. In this work, we introduce tractable relaxations of this class of optimization problems. To illustrate their performance, we use them to: (a) compute the probability that a finite-state automaton outputs a given sequence of bits; (b) develop a new many-body entanglement detection protocol; (c) let the computer invent an adaptive protocol for magic state detection. As we further show, the maximum score of a sequential problem in the limit of infinitely many time steps is in general incomputable. Nonetheless, we provide general heuristics to bound this quantity and show that they provide useful estimates in relevant scenarios.
title Optimisation of time-ordered processes in the finite and asymptotic regime
topic Quantum Physics
Optimization and Control
url https://arxiv.org/abs/2302.02918