arXiv subjects

Michal Horodecki

Publications and source records attributed to Michal Horodecki.

At least 109 records · Page 6Linked to original sources

arXiv1999

Local environment can enhance fidelity of quantum teleportation

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.

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arXiv1999

Continuity of Relative Entropy of Entanglement

We show that an entanglement measure called relative entropy of entanglement satisfies a strong continuity condition. If two states are close to each other then so are their entanglements per particle pair in this measure. It follows in particular, that the measure is appropriate for the description of entanglement manipulations in the limit of an infinite number of pairs of particles.

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arXiv1999

MR spectroscopy with parabolic magnetic field: spin-oscillator coupling effect

The spectrum of the spin particle in oscillatory potential subjected to external parabolic magnetic field ${\bf B}=(B_0+Gx+\tilde G x^2){\bf \hat z}$ is obtained. The structure of energy levels of the considered system allows to identify the frequency of the oscillator via the spectrum of spin sublevels coming only from {\it one} oscillatory level. The effect is due to the gradient terms in the form of the field.

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arXiv1999

Binding entanglement channels

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 such class of channels. We also show that any bound entangled state can be used to construction of the map corresponding the binding entanglement channel.

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arXiv1999

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.

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arXiv1998

Einstein-Podolsky-Rosen paradox without 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''.

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arXiv1998

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.

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arXiv1998

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.

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arXiv1998

Universal Quantum Information Compression

Suppose that a quantum source is known to have von Neumann entropy less than or equal to S but is otherwise completely unspecified. We describe a method of universal quantum data compression which will faithfully compress the quantum information of any such source to S qubits per signal (in the limit of large block lengths).

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arXiv1998

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.

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arXiv1998

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.

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arXiv1998

Jaynes principle versus entanglement

We show, by explicit examples, that the Jaynes inference scheme based on maximization of entropy can produce inseparable states even if there exists a separable state compatible with the measured data. It can lead to problems with processing of entanglement. The difficulty vanishes when one uses inference scheme based on minimization of entanglement.

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arXiv1998

Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?

It is shown that if a mixed state can be distilled to the singlet form, it must violate partial transposition criterion [A. Peres, Phys. Rev. Lett. 76, 1413 (1996)]. It implies that there are two qualitatively different types of entanglement: ``free'' entanglement which is distillable, and ``bound'' entanglement which cannot be brought to the singlet form useful for quantum communication purposes. Possible physical meaning of the result is discussed.

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arXiv1997

Limits for compression of quantum information carried by ensembles of mixed states

We consider the problem of compression of the quantum information carried by ensemble of mixed states. We prove that for arbitrary coding schemes the least number of qubits needed to convey the signal states asymptotically faithfully is bounded from below by the Holevo function $S(\varrho)-\sum_ip_iS(\varrho_i)$. We also show that a compression protocol can be composed with another one, provided that the latter offers perfect transmission. Such a compound protocol is applied to the case of binary source. It is conjectured to reach the obtained bound. Finally, we point out that in the case of mixed signal states there could be a difference between the maximal compression rates at the coding schemes which are ``blind'' to the signal and the ones which assume the knowledge about the identities of the signal states.

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arXiv1997

Are there basic laws of quantum information processing?

We prove within the standard quantum formalism without reduction postulate that the no-cloning theorem and the principle of no-increasing of entanglement under local actions and one-way classical communication are equivalent. We argue that the result is a manifestation of more general principles governing quantum information processing analogous to the thermodynamical laws.

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arXiv1996

Generalized quantum measurements and local realism

The structure of a local hidden variable model for experiments involving sequences of measurements rigorously is analyzed. Constraints imposed by local realism on the conditional probabilities of the outcomes of such measurement schemes are explicitly derived. The violation of local realism in the case of ``hidden nonlocality'' is illustrated by an operational example.

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arXiv1996

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.

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arXiv1996

Information-theoretic aspects of quantum inseparability of mixed states

Information-theoretic aspects of quantum inseparability of mixed states are investigated in terms of the $α$-entropy inequalities and teleportation fidelity. Inseparability of mixed states is defined and a complete characterization of the inseparable $2\times2$ systems with maximally disordered subsystems is presented within the Hilbert-Schmidt space formalism. A connection between teleportation and negative conditional $α$-entropy is also emphasized.

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