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Frontiers in Optics

Quantum Process Estimation with an Unknown Detector

Michał Karpiński, Merlin Cooper, Brian J. Smith

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We present an operational approach to quantum process estimation, where the detector response is characterized directly by a set of probe states. Numerical simulations are presented for both discrete and continuous-variable quantum optical processes, which demonstrate the utility of this technique.
DOI
10.1364/ls.2014.lth1i.5

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Quantum detector tomography is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, a novel quantum detector tomography method is proposed. First, a series of different probe states are used to generate measurement data. Then, using constrained linear regression estimation, a stage-1 estimation of the detector is obtained. Finally, the positive semidefinite requirement is added to guarantee a physical stage-2 estimation. This Two-stage Estimation (TSE) method has computational complexity O(nd2M), where n is the number of d-dimensional detector matrices and M is the number of different probe states. An error upper bound is established, and optimization on the coherent probe states is investigated. We perform simulation and a quantum optical experiment to testify the effectiveness of the TSE method.
We have developed an enhanced technique for characterizing quantum optical processes based on probing unknown quantum processes only with coherent states. Our method substantially improves the original proposal (Lobino et al 2008 Science 322 563), which uses a filtered Glauber–Sudarshan decomposition to determine the effect of the process on an arbitrary state. We introduce a new relation between the action of a general quantum process on coherent state inputs and its action on an arbitrary quantum state. This relation eliminates the need to invoke the Glauber–Sudarshan representation for states; hence, it dramatically simplifies the task of process identification and removes a potential source of error. The new relation also enables straightforward extensions of the method to multi-mode and non-trace-preserving processes. We illustrate our formalism with several examples, in which we derive analytic representations of several fundamental quantum optical processes in the Fock basis. In particular, we introduce photon-number cutoff as a reasonable physical resource limitation and address resource versus accuracy trade-off in practical applications. We show that the accuracy of process estimation scales inversely with the square root of photon-number cutoff.