Reliable optimization of arbitrary functions over quantum measurements
arXiv:2302.07534 · doi:10.3390/e25020358
Abstract
As the connection between classical and quantum worlds, quantum measurements play a unique role in the era of quantum information processing. Given an arbitrary function of quantum measurements, how to obtain its optimal value is often considered as a basic yet important problem in various applications. Typical examples include but not limited to optimizing the likelihood functions in quantum measurement tomography, searching the Bell parameters in Bell-test experiments, and calculating the capacities of quantum channels. In this work, we propose reliable algorithms for optimizing arbitrary functions over the space of quantum measurements by combining the so-called Gilbert's algorithm for convex optimization with certain gradient algorithms. With extensive applications, we demonstrate the efficacy of our algorithms with both convex and nonconvex functions.
arXiv comment11 pages, 5 figures, 30 references
References in corpus (18)
- Entanglement detection
- Quantum state tomography via compressed sensing
- Efficient quantum state tomography
- Templates for Convex Cone Problems with Applications to Sparse Signal Recovery
- Quantum process tomography of a controlled-NOT gate
- Quantum Process Tomography: Resource Analysis of Different Strategies
- Ancilla-assisted quantum process tomography
- Maximum-likelihood estimation of quantum measurement
- Superfast maximum likelihood reconstruction for quantum tomography
- Deterministic realization of collective measurements via photonic quantum walks
- A proposed testbed for detector tomography
- Convex optimization over classes of multiparticle entanglement
- Quantum correlations are stronger than all nonsignaling correlations produced by n-outcome measurements
- Experimental self-characterization of quantum measurements
- Convex separation from convex optimization for large-scale problems
- Observation of stronger-than-binary correlations with entangled photonic qutrits
- Proposed experiment to test fundamentally binary theories
- Can non-local correlations be discriminated in polynomial time?