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Italian Quantum Information Science Conference (IQIS)

Implementation of POVMs by Projective Measurements and Postselection:Optimal Strategies and Applications to Unambiguous State Discrimination

Filip B. Maciejewski, Michał Oszmaniec

Published Nov 19, 2019• 0 citations
Publisher

Abstract

We present new results concerning simulation of general quantum measurements (POVMs) by projective measurements (PMs) for the task of Unambiguous State Discrimination (USD). We formulate a problem of finding optimal strategy of simulation for given quantum measurement. The problem can be solved for qubit and qutrits measurements by Semi-Definite Programming (SDP) methods.

DOI
10.3390/proceedings2019012056

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We present new results concerning simulation of general quantum measurements (POVMs) by projective measurements (PMs) for the task of Unambiguous State Discrimination (USD). We formulate a problem of finding optimal strategy of simulation for given quantum measurement. The problem can be solved for qubit and qutrits measurements by Semi-Definite Programming (SDP) methods.
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We report an alternative scheme for implementing generalized quantum measurements that does not require the usage of an auxiliary system. Our method utilizes solely (a) classical randomness and postprocessing, (b) projective measurements on a relevant quantum system, and (c) postselection on nonobserving certain outcomes. The scheme implements arbitrary quantum measurement in dimension ddd with the optimal success probability 1/d1/d1/d. We apply our results to bound the relative power of projective and generalized measurements for unambiguous state discrimination. Finally, we test our scheme experimentally on an IBM quantum processor. Interestingly, due to noise involved in the implementation of entangling gates, the quality with which our scheme implements generalized qubit measurements outperforms the standard construction using an auxiliary system.
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Standard projective measurements (PMs) represent a subset of all possible measurements in quantum physics, defined by positive-operator-valued measures. We study what quantum measurements are projective simulable, that is, can be simulated by using projective measurements and classical randomness. We first prove that every measurement on a given quantum system can be realized by classical randomization of projective measurements on the system plus an ancilla of the same dimension. Then, given a general measurement in dimension two or three, we show that deciding whether it is PM simulable can be solved by means of semidefinite programming. We also establish conditions for the simulation of measurements using projective ones valid for any dimension. As an application of our formalism, we improve the range of visibilities for which two-qubit Werner states do not violate any Bell inequality for all measurements. From an implementation point of view, our work provides bounds on the amount of white noise a measurement tolerates before losing any advantage over projective ones.