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.

Highlights

  • Introduction and preliminariesIn the recent work [1] it was proved that arbitrary quantum measurement (POVM) can be simulated by projective measurements if one allows for standard classical operations, followed by postselection

  • In this work we present new result concerning the applications of general scheme of simulation for the task of Unambiguous State Discrimination (USD)

  • If quantum states are measured by POVM M, probability of success in this task is given by psucc (E, M) = ∑in=1 pi tr

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Summary

Introduction and preliminaries

In the recent work [1] it was proved that arbitrary quantum measurement (POVM) can be simulated by projective measurements if one allows for standard classical operations (randomization and post-processing), followed by postselection. The concrete algorithm of simulation was presented, with probability of success equal to the 1d for d-dimensional quantum system It has been studied what advantage POVMs offer over PMs for the task of Unambiguous State Discrimination (USD). In [2] the notion of simulability of POVMs by PMs was introduced—the POVM M is said to be PM-simulable if sampling from statistics that it would generate for arbitrary quantum state can n o be achieved by classical randomization of some projective measurements P(α) (not necessarily on the same space as M), followed by classical post-processing. If quantum states are measured by POVM M, probability of success in this task is given by psucc (E , M) = ∑in=1 pi tr (ρi Mi ).

The Best PM-Simulable POVM for USD
Better Strategy of Simulation for USD
Optimal Strategy for Simulation with Postselection for a Given Measurement
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