Local Distinguishability of Multipartite Orthogonal Quantum States

We consider one copy of a quantum system prepared in one of two orthogonal pure states, entangled or otherwise, and distributed between any number of parties. We demonstrate that it is possible to identify which of these two states the system is in by means of local operations and classical communication alone. The protocol we outline is both completely reliable and completely general - it will correctly distinguish any two orthogonal states 100% of the time.Comment: 5 pages, revte

Distinguishing two-qubit states using local measurements and restricted classical communication

The problem of unambiguous state discrimination consists of determining which of a set of known quantum states a particular system is in. One is allowed to fail, but not to make a mistake. The optimal procedure is the one with the lowest failure probability. This procedure has been extended to bipartite states where the two parties, Alice and Bob, are allowed to manipulate their particles locally and communicate classically in order to determine which of two possible two-particle states they have been given. The failure probability of this local procedure has been shown to be the same as if the particles were together in the same location. Here we examine the effect of restricting the classical communication between the parties, either allowing none or eliminating the possibility that one party's measurement depends on the result of the other party's. These issues are studied for two-qubit states, and optimal procedures are found. In some cases the restrictions cause increases in the failure probability, but in other cases they do not. Applications of these procedures, in particular to secret sharing, are discussed.Comment: 18 pages, two figure

Generic local distinguishability and completely entangled subspaces

A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, S, approaching the full dimension of the system, D. We show that almost all subspaces with dimension less than or equal to S are completely entangled, and then use this fact to prove that n random pure quantum states are unambiguously locally distinguishable if and only if n does not exceed D-S. This condition holds for almost all sets of states of all multipartite systems, and reveals something surprising. The criterion is identical for separable and for nonseparable states: entanglement makes no difference.Comment: 12 page

A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces

Entanglement witnesses (EWs) constitute one of the most important entanglement detectors in quantum systems. Nevertheless, their complete characterization, in particular with respect to the notion of optimality, is still missing, even in the decomposable case. Here we show that for any qubit-qunit decomposable EW (DEW) W the three statements are equivalent: (i) the set of product vectors obeying \bra{e,f}W\ket{e,f}=0 spans the corresponding Hilbert space, (ii) W is optimal, (iii) W=Q^{\Gamma} with Q denoting a positive operator supported on a completely entangled subspace (CES) and \Gamma standing for the partial transposition. While, implications $(i)\Rightarrow(ii)$ and $(ii)\Rightarrow(iii)$ are known, here we prove that (iii) implies (i). This is a consequence of a more general fact saying that product vectors orthogonal to any CES in C^{2}\otimes C^{n} span after partial conjugation the whole space. On the other hand, already in the case of C^{3}\otimes C^{3} Hilbert space, there exist DEWs for which (iii) does not imply (i). Consequently, either (i) does not imply (ii), or (ii) does not imply (iii), and the above transparent characterization obeyed by qubit-qunit DEWs, does not hold in general.Comment: 13 pages, proof of lemma 4 corrected, theorem 3 removed, some parts improve

Classical and quantum fingerprinting with shared randomness and one-sided error

Within the simultaneous message passing model of communication complexity, under a public-coin assumption, we derive the minimum achievable worst-case error probability of a classical fingerprinting protocol with one-sided error. We then present entanglement-assisted quantum fingerprinting protocols attaining worst-case error probabilities that breach this bound.Comment: 10 pages, 1 figur

Optimal Conclusive Discrimination of Two Non-orthogonal Pure Product Multipartite States Locally

We consider one copy of a quantum system prepared in one of two non-orthogonal pure product states of multipartite distributed among separated parties. We show that there exist protocols which obtain optimal probability in the sense of conclusive discrimination by means of local operations and classical communications(LOCC) as good as by global operations. Also, we show a protocol which minimezes the average number of local operations. Our result implies that two product pure multipartite states might not have the non-local property though more than two can have.Comment: revtex, 3 pages, no figur

Distillable entanglement in d⊗dd\otimes d dimension

Distillable entanglement ($E_d$) is one of the acceptable measures of entanglement of mixed states. Based on discrimination through local operation and classical communication, this paper gives $E_d$ for two classes of orthogonal multipartite maximally entangled states.Comment: 6 page

Mixture of multiple copies of maximally entangled states is quasi-pure

Employing the general BXOR operation and local state discrimination, the mixed state of the form \rho^{(k)}_{d}=\frac{1}{d^{2}}\sum_{m,n=0}^{d-1}(|\phi_{mn}><\phi_{mn}|)^{\otim es k} is proved to be quasi-pure, where $\{|\phi_{mn}>\}$ is the canonical set of mutually orthogonal maximally entangled states in $d\times d$. Therefore irreversibility does not occur in the process of distillation for this family of states. Also, the distillable entanglement is calculated explicitly.Comment: 6 pages, 1 figure. The paper is subtantially revised and the general proof is give

The distillable entanglement of multiple copies of Bell states

It is impossible to discriminate four Bell states through local operations and classical communication (LOCC), if only one copy is provided. To complete this task, two copies will suffice and be necessary. When $n$ copies are provided, we show that the distillable entanglement is exactly $n-2$.Comment: An argument in the original paper is replaced by a procedure of strict proo