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

Abstract

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.

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References in corpus (7)

• Entanglement detection
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Approaching Unit Visibility for Control of a Superconducting Qubit with Dispersive Readout
• Bounding the set of quantum correlations
• Direct Fidelity Estimation from Few Pauli Measurements
• Leggett-Garg Macrorealism and temporal correlations
• Fundamental accuracy-resolution trade-off for timekeeping devices

Cited by in corpus (2)

• Semidefinite programming relaxations for quantum correlations
• Entanglement-breaking channels are a quantum memory resource