Paweł Horodecki

We pose the fundamental question of communication properties of primitives irrespectively of their implementation. To illustrate the idea we introduce the concept of entanglement-swapping boxes, i.e. we consider any quantum operations which perform entanglement swapping, not necessarily via simple quantum teleportation. We ask a question about the properties of such boxes., i.e. what local operations and how much classical communication are needed to perform them. We also ask if any box which performs entanglement swapping can be used to establish classical communication. We show that each box needs at least two bits of classical communication to perform it. It is also shown that each box can be used for classical communication and, most importantly, that there exist boxes which allow to communicate at most one bit. Surprisingly we find basic irreversibility in the process of entanglement swapping with respect to its communication properties.Comment: Accepted for publication in Phys. Rev. A as a Rapid Communicatio

We argue that a complete characterization of quantum correlations in bipartite systems of many dimensions may require a quantity which, even for pure states, does not reduce to a single number. Subsequently, we introduce multidimensional generalizations of concurrence and find evidence that they may provide useful tools for the analysis of quantum correlations in mixed bipartite states. We also introduce biconcurrence that leads to a necessary and sufficient condition for separability.

We argue that a complete characterisation of quantum correlations in bipartite systems of many dimensions may require a quantity which, even for pure states, does not reduce to a single number. Subsequently, we introduce multi-dimensional generalizations of concurrence and find evidence that they may provide useful tools for the analysis of quantum correlations in mixed bipartite states. We also introudce {\it biconcurrence} that leads to a necessary and sufficient condition for separability.

We show how an interaction with the environment can enhance fidelity of quantum teleportation. To this end, we present examples of states which cannot be made useful for teleportation by any local unitary transformations; nevertheless, after being subjected to a dissipative interaction with the local environment, the states allow for teleportation with genuinely quantum fidelity. The surprising fact here is that the necessary interaction does not require any intelligent action from the parties sharing the states. In passing, we produce some general results regarding optimization of teleportation fidelity by local action. We show that bistochastic processes cannot improve fidelity of two-qubit states. We also show that in order to have their fidelity improvable by a local process, the bipartite states must violate the so-called reduction criterion of separability.

We define the binding entanglement channel as the quantum channel through which quantum information cannot be reliably transmitted, but which can be used to share bound entanglement. We provide a characterization of this class of channels. We also show that any bound entangled state can be used for the construction of a map corresponding to the binding entanglement channel.

We show how an interaction with the environment can enhance fidelity of quantum teleportation. To this end, we present examples of states which cannot be made useful for teleportation by any local unitary transformations; nevertheless, after being subjected to a dissipative interaction with the local environment, the states allow for teleportation with genuinely quantum fidelity. The surprising fact here is that the necessary interaction does not require any intelligent action from the parties sharing the states. In passing, we produce some general results regarding optimization of teleportation fidelity by local action. We show that bistochastic processes cannot improve fidelity of two-qubit states. We also show that in order to have their fidelity improvable by a local process, the bipartite states must violate the so-called reduction criterion of separability.

It is argued that the nonlocality without entanglement discovered quite recently by Bennett et al. [Phys. Rev. A 59, 1070 (1999)] should rather be interpreted as the Einstein-Podolsky-Rosen paradox without entanglement. It would be a true demonstration of nonlocality without entanglement if one knew that quantum mechanics provides the best possible means for extracting information from a physical system, i.e., that it is “informationally complete.”

Bound entanglement is the noisy entanglement which cannot be distilled to a singlet form. Thus it cannot be used alone for quantum communication purposes. Here we show that, nevertheless, the bound entanglement can be, in a sense, pumped into a single pair of free entangled particles. It allows for teleportation via the pair with the fidelity impossible to achieve without support of bound entanglement.

We claim that the nonlocality without entanglement revealed quite recently by Bennett {\it et al.} [quant-ph/9804053] should be rather interpreted as {\it Einstein-Podolsky-Rosen paradox without entanglement}. It would be true nonlocality without entanglement if one knew that quantum mechnics provides the best possible means for extracting information from physical system i.e. that it is ``operationally complete''.