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arXiv:quant-ph/9902056

Nonlocality without inequalities using unambiguous discrimination between non-orthogonal states

Adan Cabello, Jose Luis Cereceda

Published Feb 15, 1999• 0 citations
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Abstract

This paper has been withdrawn.
DOI
10.48550/arxiv.quant-ph/9902056

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We consider a general version of the phenomenon of more nonlocality with less entanglement within the framework of the unambiguous (i.e., conclusive) quantum state discrimination problem under local quantum operations and classical communication. We show that although the phenomenon was obtained before for two qutrits, it can also be observed for two qubits, whereas still being at the single-copy level. We establish that the phenomenon is intrinsically connected to the concept of unextendible entangled bases in the two-qubit case. In the process, we demonstrate a hierarchy of nonlocality among sets of two-qubit orthogonal pure states where the ``nonlocality'' is in the sense of a difference between global and local abilities of quantum state discrimination. We present a complete characterization of two-qubit pure orthogonal state sets of cardinality three with respect to their nonlocality in terms of unambiguous local distinguishability, the status for other cardinalities being already known. The results are potentially useful for secure quantum communication technologies with an optimal amount of resources.
Unambiguous quantum state discrimination (UQSD), assisted by an auxiliary system, generally requires quantum correlations as a resource. We find that quantum coherence can be utilized as a resource in an allied UQSD protocol that is devoid of quantum correlations. We propose a mechanism for quantum state discrimination where the non-orthogonality of the input states can be converted to quantum coherence of the auxiliary system. We quantify the required coherence generated during this and the optimal unambiguous quantum state discrimination strategy in some specific cases. In particular, our result introduces how to find the optimal strategy by measuring quantum coherence in protocols that discriminates between two non-orthogonal quantum states.
Unambiguous discrimination among non-orthogonal but linearly independent quantum states is possible with a certain probability of success. Here we consider a variant of that problem; rather than discriminating among all of the different states, we shall discriminate between two subsets of them. In particular, for the case of 3 states, we find the optimal strategy to distinguish one from the other two. This procedure has a higher probability of success than distinguishing all 3 states. We show how to construct generalized interferometers that provide an implementation of the optimal strategy.