Distillability of Inseparable Quantum Systems

We apply the inseparability criterion for $2 \times 2$ systems, local filtering and Bennett et al. purification protocol [Phys. Rev. Lett. {\bf 76}, 722 (1996)] to show how to distill {\it any} inseparable $2\times 2$ system. The extended protocol is illustrated geometrically by means of the state parameters in the Hilbert-Schmidt space.Comment: Revtex, 4 pages (in twocolumn format), introduction and conclusion are slightly modified; one postscript figure available at request from [email protected]

Entanglement and thermodynamical analogies

We provide some new properties of entanglement of formation. In particular, we obtain an additive lower bound for entanglement of formation. Subsequently we develop the concept of local orthogonality of ensembles which leads to the mixed states with distillable entanglement equal to entanglement of formation. Then we consider thermodynamical analogies within the entanglement processing domain. Especially, we exploit analogy entanglement -- energy. In this scheme the total entanglement i.e. the amount of singlet pairs needed for local preparation of a state corresponds to internal energy while the free entanglement defined as the number of pairs which can be recovered from the state (distillable entanglement) is the counterpart of free energy. In particular, it leads us to the question about ``temperature'' of entanglement. We also propose a scheme of the search of representative state for given entanglement which can be viewed as an analogue of the Jaynes maximum entropy principle.Comment: RevTeX, 11 page

Optimal compression of quantum information for one-qubit source at incomplete data: a new aspect of Jaynes principle

We consider the problem of optimal processing of quantum information at incomplete experimental data characterizing the quantum source. In particular, we then prove that for one-qubit quantum source the Jaynes principle offers a simple scheme for optimal compression of quantum information. According to the scheme one should process as if the density matrix of the source were actually equal to the matrix of the Jaynes state.Comment: RevTeX, 4 pages, a simpler version of the proof for compression at two-observable data has been provided, some minor changes has been mad

On balance of information in bipartite quantum communication systems: entanglement-energy analogy

We adopt the view according to which information is the primary physical entity that posseses objective meaning. Basing on two postulates that (i) entanglement is a form of quantum information corresponding to internal energy (ii) sending qubits corresponds to work, we show that in the closed bipartite quantum communication systems the information is conserved. We also discuss entanglement-energy analogy in context of the Gibbs-Hemholtz-like equation connecting the entanglement of formation, distillable entanglement and bound entanglement. Then we show that in the deterministic protocols of distillation the information is conserved. We also discuss the objectivity of quantum information in context of information interpretation of quantum states and alghoritmic complexity.Comment: 8 pages, Revtex, extended version including discussion on interpretation problems in particular objectivity of quantum informatio

Bound entanglement can be activated

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 single pair of free entangled particles. It allows for teleportation via the pair with the fidelity impossible to achieve without support of bound entanglement. The result also suggests that the distillable entanglement may be not additive.Comment: RevTeX, 4 page

General teleportation channel, singlet fraction and quasi-distillation

We prove a theorem on direct relation between the optimal fidelity $f_{max}$ of teleportation and the maximal singlet fraction $F_{max}$ attainable by means of trace-preserving LQCC action (local quantum and classical communication). For a given bipartite state acting on $C^d\otimes C^d$ we have $f_{max}= {F_{max}d+1\over d+1}$. We assume completely general teleportation scheme (trace preserving LQCC action over the pair and the third particle in unknown state). The proof involves the isomorphism between quantum channels and a class of bipartite states. We also exploit the technique of $U\otimes U^*$ twirling states (random application of unitary transformation of the above form) and the introduced analogous twirling of channels. We illustrate the power of the theorem by showing that {\it any} bound entangled state does not provide better fidelity of teleportation than for the purely classical channel. Subsequently, we apply our tools to the problem of the so-called conclusive teleportation, then reduced to the question of optimal conclusive increasing of singlet fraction. We provide an example of state for which Alice and Bob have no chance to obtain perfect singlet by LQCC action, but still singlet fraction arbitrarily close to unity can be obtained with nonzero probability. We show that a slight modification of the state has a threshold for singlet fraction which cannot be exceeded anymore.Comment: RevTeX, 14 pages, proposition in Sec. VI has been corrected, many minor correction

Erratum: Asymptotic entanglement manipulations can be genuinely irreversible. [Phys. Rev. Lett. {\bf 84}, 4260 (2000)]

This is erratum of the paper [Phys. Rev. Lett. {\bf 84}, 4260 (2000)]Comment: 1 page, added date of Werner's earlier proof of bound for distillable entanglement (Benasque, 1998

Reduction criterion of separability and limits for a class of protocols of entanglement distillation

We analyse the problem of distillation of entanglement of mixed states in higher dimensional compound systems. Employing the positive maps method [M. Horodecki et al., Phys. Lett. A 223 1 (1996)] we introduce and analyse a criterion of separability which relates the structures of the total density matrix and its reductions. We show that any state violating the criterion can be distilled by suitable generalization of the two-qubit protocol which distills any inseparable two-qubit state. Conversely, all the states which can be distilled by such a protocol must violate the criterion. The proof involves construction of the family of states which are invariant under transformation $\varrho\to U\otimes U^*\varrho U^\dagger\otimes U^{*\dagger}$ where $U$ is a unitary transformation and star denotes complex conjugation. The states are related to the depolarizing channel generalized to non-binary case.Comment: RevTeX, 13 pages, rewritten to more readable form, some details adde

Mixed-state entanglement and quantum communication

We present basics of mixed-state entanglement theory. The first part of the article is devoted to mathematical characterizations of entangled states. In second part we discuss the question of using mixed-state entanglement for quantum communication. In particular, a type of entanglement that is not directly useful for quantum communcation (called bound entanglement) is analysed in detail.Comment: 42 pages; the article is part of a book entitled {\it Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments} by G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rotteler, H. Weinfurter, R. Werner and A. Zeilinger, published in {\it Springer Tracts in Modern Physics}, July 200

Quantum information isomorphism: beyond the dillemma of Scylla of ontology and Charybdis of instrumentalism

In order to have the most safe way of dealing with unanalysable quantum whole the Copenhagen interpretation takes as a "frame of reference" the preparation parameters and outcomes of the measurements. It represents {\it passive} Ptolemean-like instrumentalism directly related to "what we see in the sky" i.e. to the "surface" of the things. However the notion of quantum information leads to {\it active} Copernican-like realism which involves (intrinsic) ordering principle and thinking about the whole as being analysable. One dares then to consider subsystems as localised in space, controlled individually, and communicated. This makes natural treating quantum information (quantum states) as by no means merely knowledge. Moreover it involves complementarity between local and nonlocal information. To avoid dilemma between Scylla of ontology and Charybdis of instrumentalism, the concept of {\it quantum information isomorphism} is proposed according to which quantum description of Nature and their mathematical representation. By definition it is not only just one-to-one mapping, but it preserves the structure. It allows, in particular, to treat the "wave function" as isomorphic image of what we are processing in laboratories implying that quantum information is indeed carried by the quantum systems.Comment: Preliminary version, to be submitted to special issue of the IBM Journal of Research and Development for Charles Bennett's 60th birthday To appear in special issue of the IBM Journal of Research and Development for Charles Bennett's 60th birthda