Beating noise with abstention in state estimation
Gendra Casalí, Bernat (Universitat Autònoma de Barcelona. Departament de Física)
Ronco Bonvehi, Elio (Universitat Autònoma de Barcelona. Departament de Física)
Calsamiglia Costa, John (Universitat Autònoma de Barcelona. Departament de Física)
Muñoz Tapia, Ramon (Universitat Autònoma de Barcelona. Departament de Física)
Bagán Capella, Emili (Universitat Autònoma de Barcelona. Departament de Física)

Date:	2012
Abstract:	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.
Grants:	Ministerio de Ciencia e Innovación FIS2008-01236 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-0985
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra, i la creació d'obres derivades, sempre que no sigui amb finalitats comercials i que es distribueixin sota la mateixa llicència que regula l'obra original. Cal que es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Analytical expressions ; Asymptotic expressions ; Beating noise ; Exponential rates ; Fixed fidelity ; Large N ; N qubits ; Nonideal ; Optimal protocols ; Qubit state ; Standard estimation
Published in:	New journal of physics, Vol. 14 (October 2012) , art. 105015, ISSN 1367-2630

DOI: 10.1088/1367-2630/14/10/105015

17 p, 934.7 KB

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