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arXiv:quant-ph/0009123

Measurement of quantum devices

Jaromı́r Fiurášek, Z. Hradil

Published Sep 29, 2000• 1 citation
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Abstract

Maximum-likelihood estimation is applied to identification of an unknown quantum mechanical process represented by a ``black box''. In contrast to linear reconstruction schemes the proposed approach always yields physically sensible results. Its feasibility is demonstrated using the Monte Carlo simulations for the two-level system (single qubit).

DOI
10.48550/arxiv.quant-ph/0009123

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Maximum-likelihood estimation is applied to identification of an unknown quantum mechanical process represented by a ``black box''. In contrast to linear reconstruction schemes the proposed approach always yields physically sensible results. Its feasibility is demonstrated using the Monte Carlo simulations for the two-level system (single qubit).
Maximum-likelihood estimation is applied to the determination of an unknown quantum measurement. The calibrated measuring apparatus carries out measurements on many different quantum states and the positive operator-valued measure governing the measurement statistics is then inferred from the collected data via the maximum-likelihood principle. In contrast to the procedures based on linear inversion, our approach always provides a physically sensible result. We illustrate the method on the case of the Stern-Gerlach apparatus.
Any quantum dynamics, i.e., the process that is described by a completely positive (CP) map of a quantum-mechanical system, can be probed in two different ways. Either we use a single entangled state of a bipartite system, or we use a collection of linearly independent single-particle test states (forming a basis of the vector space of all Hermitian operators). Given the fragility of entangled states, in this chapter we will focus our attention on the process reconstruction using only single-particle states.