TY - JOUR

T1 - Unambiguous comparison of the states of multiple quantum systems

AU - Chefles, A.

AU - Andersson, E.

AU - Jex, I.

PY - 2004/7/23

Y1 - 2004/7/23

N2 - We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all N systems are in the same state. Alternatively, one may ask whether or not the states of all N systems are different. We investigate the possibility of unambiguously obtaining this kind of information. It is found that some unambiguous comparison tasks are possible only when certain linear independence conditions are satisfied. We also obtain measurement strategies for certain comparison tasks which are optimal under a broad range of circumstances, in particular when the states are completely unknown. Such strategies, which we call universal comparison strategies, are found to have intriguing connections with the problem of quantifying the distinguishability of a set of quantum states and also with unresolved conjectures in linear algebra. We finally investigate a potential generalization of unambiguous state comparison, which we term unambiguous overlap filtering.

AB - We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all N systems are in the same state. Alternatively, one may ask whether or not the states of all N systems are different. We investigate the possibility of unambiguously obtaining this kind of information. It is found that some unambiguous comparison tasks are possible only when certain linear independence conditions are satisfied. We also obtain measurement strategies for certain comparison tasks which are optimal under a broad range of circumstances, in particular when the states are completely unknown. Such strategies, which we call universal comparison strategies, are found to have intriguing connections with the problem of quantifying the distinguishability of a set of quantum states and also with unresolved conjectures in linear algebra. We finally investigate a potential generalization of unambiguous state comparison, which we term unambiguous overlap filtering.

KW - quantum

KW - quantum systems

KW - measurement strategies

KW - linear algebra

KW - quantum states

UR - http://arxiv.org/PS_cache/quant-ph/pdf/0402/0402125v4.pdf

UR - http://dx.doi.org/10.1088/0305-4470/37/29/009

U2 - 10.1088/0305-4470/37/29/009

DO - 10.1088/0305-4470/37/29/009

M3 - Article

SN - 0305-4470

VL - 37

SP - 7315

EP - 7340

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 29

ER -