TY - JOUR

T1 - Beating noise with abstention in state estimation

AU - Gendra, Bernat

AU - Ronco-Bonvehi, Elio

AU - Calsamiglia, John

AU - Muñoz-Tapia, Ramon

AU - Bagan, Emilio

PY - 2012/10/1

Y1 - 2012/10/1

N2 - We address the problem of estimating pure qubit states with nonideal (noisy) measurements in the multiple-copy scenario, where the data consist of a number N of identically prepared qubits. We show that the average fidelity of the estimates can increase significantly if the estimation protocol allows for inconclusive answers, or abstentions. We present the optimal protocol and compute its fidelity for a given probability of abstention. The improvement over standard estimation, without abstention, can be viewed as an effective noise reduction. These and other results are illustrated for small values of N. For asymptotically large N, we derive analytical expressions of the fidelity and the probability of abstention and show that for a fixed fidelity gain the latter decreases with N at an exponential rate given by a Kulback-Leibler (relative) entropy. As a byproduct, we give an asymptotic expression in terms of this very entropy of the probability that a system of N qubits, all prepared in the same state, has a given total angular momentum. We also discuss an extreme situation where noise increases with N and where estimation with abstention provides the most significant improvement as compared to the standard approach. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

AB - We address the problem of estimating pure qubit states with nonideal (noisy) measurements in the multiple-copy scenario, where the data consist of a number N of identically prepared qubits. We show that the average fidelity of the estimates can increase significantly if the estimation protocol allows for inconclusive answers, or abstentions. We present the optimal protocol and compute its fidelity for a given probability of abstention. The improvement over standard estimation, without abstention, can be viewed as an effective noise reduction. These and other results are illustrated for small values of N. For asymptotically large N, we derive analytical expressions of the fidelity and the probability of abstention and show that for a fixed fidelity gain the latter decreases with N at an exponential rate given by a Kulback-Leibler (relative) entropy. As a byproduct, we give an asymptotic expression in terms of this very entropy of the probability that a system of N qubits, all prepared in the same state, has a given total angular momentum. We also discuss an extreme situation where noise increases with N and where estimation with abstention provides the most significant improvement as compared to the standard approach. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

U2 - https://doi.org/10.1088/1367-2630/14/10/105015

DO - https://doi.org/10.1088/1367-2630/14/10/105015

M3 - Article

VL - 14

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

M1 - 105015

ER -