We investigate the physically allowed probabilities for transforming one N-partite W-class state to another by means of local operations assisted with classical communication. Recently, S. Kintas, and S. Turgut [J. Math. Phys. 51, 092202 (2010)] obtained an upper bound for the maximum probability of transforming two such states. Here, we provide a simple sufficient and necessary condition for when this upper bound can be satisfied and, thus, when optimality of state transformation can be achieved. Our discussion involves obtaining lower bounds for the transformation of arbitrary W-class states and showing precisely when this bound saturates the bound of Kintas, and Turgut. Finally, we consider the question of transforming symmetric W-class states and find that, in general, the optimal one-shot procedure for converting two symmetric states requires a nonsymmetric filter by all the parties.

We investigate absolutely maximally entangled (AME) states, which are multipartite quantum states that are maximally entangled with respect to any possible bipartition. These strong entanglement properties make them a powerful resource for a variety of quantum information protocols. In this paper, we show the existence of AME states for any number of parties, given that the dimension of the involved systems is chosen appropriately. We prove the equivalence of AME states shared between an even number of parties and pure state threshold quantum secret sharing (QSS) schemes, and prove necessary and sufficient entanglement properties for a wider class of ramp QSS schemes. We further show how AME states can be used as a valuable resource for open-destination teleportation protocols and to what extend entanglement swapping generalizes to AME states.

We study the existence of absolutely maximally entangled (AME) states in quantum mechanics and its applications to quantum information. AME states are characterized by being maximally entangled for all bipartitions of the system and exhibit genuine multipartite entanglement. With such states, we present a parallel teleportation protocol which teleports multiple quantum states between groups of senders and receivers. The notable features of this protocol are that (i) the partition into senders and receivers can be chosen after the state has been distributed, and (ii) one group has to perform joint quantum operations while the parties of the other group only have to act locally on their system. We also prove the equivalence between pure state quantum secret sharing schemes and AME states with an even number of parties.

Quantum entanglement is fundamentally related to the operational setting of local quantum operations and classical communication (LOCC). A more general class of operations known as separable operations (SEP) is often employed to approximate LOCC, but the exact difference between LOCC and SEP is unknown. In this letter, we compare the two classes in performing particular tripartite to bipartite entanglement conversions and report a gap as large as 12.5% between SEP and LOCC, which is the first known appreciable gap between the classes. Our results rely on constructing a computable entanglement monotone with a clear operational meaning that, unlike all other such monotones previously studied, is not monotonic under SEP. Finally, we prove the curious fact that convergent sequences of LOCC protocols need not be LOCC feasible in the limit.

In this article, we extend recent results concerning random-pair Einstein-Podolsky-Rosen distillation and the operational gap between separable operations (SEPs) and local operations with classical communication (LOCC). In particular, we consider the problem of obtaining bipartite maximal entanglement from an N-qubit W-class state (i.e., that of the form root x(0)|00 ... 0 > + root x(1)|10 ... 0 > + ... + root x(n)|00 ... 1 >) when the target pairs are a priori unspecified. We show that when x(0) = 0, the optimal probabilities for SEPs can be computed using semidefinite programming. On the other hand, to bound the optimal probabilities achievable by LOCC, we introduce entanglement monotones defined on the N-qubit W class of states. The LOCC monotones we construct can be increased by SEPs, and in terms of transformation success probability, we are able to quantify a gap as large as 37% between the two classes. Additionally, we demonstrate transformations rho(circle times n) -> sigma(circle times n) that are feasible by SEP for any n but impossible by LOCC.

In this article we obtain results for the task of converting a single N-qubit W-class state (of the form root x(0)vertical bar 00 ... 0 > + root x(1)vertical bar 10 ... 0 > + ... + root x(N)vertical bar 00 ... 1 >) into maximum entanglement shared between two random parties. Previous studies in random distillation have not considered how the particular choice of target pairs affects the transformation, and here we develop a strategy for distilling into general configurations of target pairs. We completely solve the problem of determining the optimal distillation probability for all three-qubit configurations and most four-qubit configurations when x(0) = 0. Our proof involves deriving new entanglement monotones defined on the set of four-qubit W-class states. As an additional application of our results, we present new upper bounds for converting a generic W-class state into the standard W state vertical bar W-N > = root 1/N (vertical bar 10 ... 0 > + ... + vertical bar 00 ... 1 >).

Received 7 November 2011DOI:https://doi.org/10.1103/PhysRevA.84.059902©2011 American Physical Society

For a tripartite pure state of three qubits, it is well known that there are two inequivalent classes of genuine tripartite entanglement, namely the Greenberger-Horne-Zeilinger (GHZ) class and the W class. Any two states within the same class can be transformed into each other with stochastic local operations and classical communication with a nonzero probability. The optimal conversion probability, however, is only known for special cases. Here, lower and upper bounds are derived for the optimal probability of transformation from a GHZ state to other states of the GHZ class. A key idea in the derivation of the upper bounds is to consider the action of the local operations and classical communications (LOCC) protocol on a different input state, namely 1/root 2[vertical bar 000 > - vertical bar 111 >], and to demand that the probability of an outcome remains bounded by 1. We also find an upper bound for more general cases by using the constraints of the so-called interference term and 3-tangle. Moreover, some of the results are generalized to the case in which each party holds a higher dimensional system. In particular, the GHZ state generalized to three qutrits; that is, vertical bar GHZ3 > = 1/root 3[vertical bar 000 > + vertical bar 111 > + vertical bar 222 >] shared among three parties can be transformed to any tripartite three-qubit pure state with probability 1 via LOCC. Some of our results can also be generalized to the case of a multipartite state shared by more than three parties.