Understanding entanglement as resource: locally distinguishing unextendible product bases

It is known that the states in an unextendible product basis (UPB) cannot be distinguished perfectly when the parties are restricted to local operations and classical communication (LOCC). Previous discussions of such bases have left open the following question: What entanglement resources are necessary and/or sufficient for this task to be possible with LOCC? In this paper, I present protocols which use entanglement more efficiently than teleportation to distinguish certain classes of UPB's. The ideas underlying my approach to this problem offer rather general insight into why entanglement is useful for such tasks.Comment: Final, published version. Many revisions following very useful suggestions of the referee have been added. In particular, Appendix A has been completely rewritte

Testing for a pure state with local operations and classical communication

We examine the problem of using local operations and classical communication (LOCC) to distinguish a known pure state from an unknown (possibly mixed) state, bounding the error probability from above and below. We study the asymptotic rate of detecting multiple copies of the pure state and show that, if the overlap of the two states is great enough, then they can be distinguished asymptotically as well with LOCC as with global measurements; otherwise, the maximal Schmidt coefficient of the pure state is sufficient to determine the asymptotic error rate.Comment: 11 pages, 2 figures. Published version with small revisions and expanded title

Local indistinguishability: more nonlocality with less entanglement

We provide a first operational method for checking indistinguishability of orthogonal states by local operations and classical communication (LOCC). This method originates from the one introduced by Ghosh et al. (Phys. Rev. Lett. 87, 5807 (2001) (quant-ph/0106148)), though we deal with pure states. We apply our method to show that an arbitrary complete multipartite orthogonal basis is indistinguishable by LOCC, if it contains at least one entangled state. We also show that probabilistic local distinguishing is possible for full basis if and only if all vectors are product. We employ our method to prove local indistinguishability in an example with sets of pure states of 3X3, which shows that one can have ``more nonlocality with less entanglement'', where ``more nonlocality'' is in the sense of ``increased local indistinguishability of orthogonal states''. This example also provides, to our knowledge, the only known example where d orthogonal states in dXd are locally indistinguishable.Comment: 4 pages, no figures, RevTeX4, partially supersedes quant-ph/0204116, to appear in Phys. Rev. Let

Tight bounds on the distinguishability of quantum states under separable measurements

One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this work, we characterize the distinguishability of sets of multipartite quantum states when restricted to separable measurements -- those which contain the class of local measurements but nevertheless are free of entanglement between the component systems. We consider two quantities: The separable fidelity -- a truly quantum quantity -- which measures how well we can "clone" the input state, and the classical probability of success, which simply gives the optimal probability of identifying the state correctly. We obtain lower and upper bounds on the separable fidelity and give several examples in the bipartite and multipartite settings where these bounds are optimal. Moreover the optimal values in these cases can be attained by local measurements. We further show that for distinguishing orthogonal states under separable measurements, a strategy that maximizes the probability of success is also optimal for separable fidelity. We point out that the equality of fidelity and success probability does not depend on an using optimal strategy, only on the orthogonality of the states. To illustrate this, we present an example where two sets (one consisting of orthogonal states, and the other non-orthogonal states) are shown to have the same separable fidelity even though the success probabilities are different.Comment: 19 pages; published versio

Quantum Data Hiding

We expand on our work on Quantum Data Hiding -- hiding classical data among parties who are restricted to performing only local quantum operations and classical communication (LOCC). We review our scheme that hides one bit between two parties using Bell states, and we derive upper and lower bounds on the secrecy of the hiding scheme. We provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme. We give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement. A candidate data hiding scheme that does not use entanglement is presented. We show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme.Comment: 19 pages, IEEE style, 8 figures, submitted to IEEE Transactions on Information Theor

Faithful Squashed Entanglement

Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states. This implies that squashed entanglement is faithful, that is, strictly positive if and only if the state is entangled. We derive the bound on squashed entanglement from a bound on quantum conditional mutual information, which is used to define squashed entanglement and corresponds to the amount by which strong subadditivity of von Neumann entropy fails to be saturated. Our result therefore sheds light on the structure of states that almost satisfy strong subadditivity with equality. The proof is based on two recent results from quantum information theory: the operational interpretation of the quantum mutual information as the optimal rate for state redistribution and the interpretation of the regularised relative entropy of entanglement as an error exponent in hypothesis testing. The distance to the set of separable states is measured by the one-way LOCC norm, an operationally-motivated norm giving the optimal probability of distinguishing two bipartite quantum states, each shared by two parties, using any protocol formed by local quantum operations and one-directional classical communication between the parties. A similar result for the Frobenius or Euclidean norm follows immediately. The result has two applications in complexity theory. The first is a quasipolynomial-time algorithm solving the weak membership problem for the set of separable states in one-way LOCC or Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show that multiple provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations thereby providing a new characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published version, claims have been weakened from the LOCC norm to the one-way LOCC nor

Why should we care about quantum discord?

Entanglement is a central feature of quantum theory. Mathematical properties and physical applications of pure state entanglement make it a template to study quantum correlations. However, an extension of entanglement measures to mixed states in terms of separability does not always correspond to all the operational aspects. Quantum discord measures allow an alternative way to extend the idea of quantum correlations to mixed states. In many cases these extensions are motivated by physical scenarios and quantum information protocols. In this chapter we discuss several settings involving correlated quantum systems, ranging from distributed gates to detectors testing quantum fields. In each setting we show how entanglement fails to capture the relevant features of the correlated system, and discuss the role of discord as a possible alternative.Comment: Written for "Lectures on general quantum correlations and their applications