We show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally. The number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement. A similar, general condition is also shown for pure and mixed states. These results offer a rare operational interpretation for three abstractly defined distance like measures of multipartite entanglement.The problem of defining and understanding multiparty entanglement is a major open question in the field of quantum information. As entanglement theory becomes more useful in other areas of many body physics, multiparty entanglement becomes increasingly relevant to general physics, too. Hence, understanding the meaning of entanglement has become and interesting and important question.In the bipartite case, entanglement is fairly well understood [1]. There are many entanglement measures defined both operationally (in terms of the usefulness of states for quantum information tasks) and abstractly (such that they obey certain axioms and may be called entanglement monotones). One of the most celebrated results in bipartite entanglement theory is that for pure states essentially all measures coincide and have clear operational relevance. For more than two parties however, the operational approach quickly becomes very difficult. There are no clear "units of usefulness" and we have the possibility of inequivalent types of entanglement [2]. Some abstract measures do persist by their simplicity. In particular those measures that define "proximity" to the set of separable states [3,4,5] have natural multiparty analogues. However, due to their abstract definition, their operational meaning is not clear and remains an open question.In this Letter, we consider the connection between distance-like entanglement measures and the task of local operations and classical communication (LOCC) state discrimination with this question in mind. This task illustrates the restriction of only having local access to a system, fundamental to the use of entanglement in quantum information (and notions of locality). Indeed, LOCC measurement of quantum states is important for cryptographic protocols [6], channel capacities [7], and distributed quantum information processing [8].Intuitively we expect that entangled states are more difficult to discriminate locally, since inherently they possess properties that are non-local. Indeed it is known that entanglement can make LOCC discrimination more dif-perfectly under LOCC, the sum of the entanglement "distances" E(|ϕi ) must be less than the total dimension D (Theorem 1 and 2), thus N ≤ D/E(|ϕi ).ficult [9]. But the exact relation is thus far unclear, and there are no general quantitative results. The results that are known can be confusing. One of the earliest results on the subject reveals a set of non-entangled, product states that cannot be discriminated perfectly by LOCC [10]. Later it was shown that any two pure states ...

A quantum memory for light is a key element for the realization of future quantum information networks 1-3. Requirements for a good quantum memory are versatility (allowing a wide range of inputs) and preservation of quantum information in a way unattainable with any classical memory device. Here we demonstrate such a quantum memory for continuousvariable entangled states, which play a fundamental role in quantum information processing 4-6. We store an extensive alphabet of two-mode 6.0 dB squeezed states obtained by varying the orientation of squeezing and the displacement of the states. The two components of the entangled state are stored in two room-temperature cells separated by 0.5 m, one for each mode, with a memory time of 1 ms. The true quantum character of the memory is rigorously proved by showing that the experimental memory fidelity 0.52 ± 0.02 significantly exceeds the benchmark of 0.45 for the best possible classical memory for a range of displacements. The continuous-variable regime represents one of the principal avenues towards the realization of quantum information processing and communication 4-6. In the optical domain it operates with well-known optical modulation and detection techniques and allows for deterministic quantum operations. In the atomic domain it has been developed on the platform of atomic ensembles 2,3,7. Advances in the realization of continuous-variable quantum protocols include unconditional quantum teleportation involving light 8 and atoms 9 , a number of results on memory 2,3,10,11 and quantum key distribution 12. Hybrid continuous/discrete-variable operations 13-15 paving the road towards continuous-variable quantum computation 16,17 have also been reported. However, the ability to store non-classical continuous-variable states of light is crucial to enable further progress, in particular, for continuous-variable linear optics quantum computing with offline resources 17 , continuous-variable quantum repeaters 18,19 , entanglement-enhanced quantum metrology, iterative continuousvariable entanglement distillation 20 , continuous-variable clusterstate quantum computation 21 , communication/cryptography protocols involving several rounds 22 and quantum illumination 23. Compared with a number of impressive results reporting discrete-variable quantum memories at the single-photon level (see reviews 1-3 and references therein), there have been very few experiments towards quantum memory for continuousvariable non-classical states. A fractional, 20 nsec, delay of 50 nsec pulsed continuous-variable entangled states in the atomic

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We study various distance-like entanglement measures of multipartite states under certain symmetries. Using group averaging techniques we provide conditions under which the relative entropy of entanglement, the geometric measure of entanglement and the logarithmic robustness are equivalent. We consider important classes of multiparty states, and in particular show that these measures are equivalent for all stabilizer states, symmetric basis and antisymmetric basis states. We rigorously prove a conjecture that the closest product state of permutation symmetric states can always be chosen to be permutation symmetric. This allows us to calculate the explicit values of various entanglement measures for symmetric and antisymmetric basis states, observing that antisymmetric states are generally more entangled. We use these results to obtain a variety of interesting ensembles of quantum states for which the optimal LOCC discrimination probability may be explicitly determined and achieved. We also discuss applications to the construction of optimal entanglement witnesses