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Michal Horodecki

Publications and source records attributed to Michal Horodecki.

At least 91 records · Page 5Linked to original sources
arXiv2002

Dynamics of quantum entanglement

A model of discrete dynamics of entanglement of bipartite quantum state is considered. It involves a global unitary dynamics of the system and periodic actions of local bistochastic or decaying channel. For initially pure states the decay of entanglement is accompanied with an increase of von Neumann entropy of the system. We observe and discuss revivals of entanglement due to unitary interaction of both subsystems. For some mixed states having different marginal entropies of both subsystems (one of them larger than the global entropy and the other one one smaller) we find an asymmetry in speed of entanglement decay. The entanglement of these states decreases faster, if the depolarizing channel acts on the "classical" subsystem, characterized by smaller marginal entropy.

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arXiv2002

A Thermodynamical Approach to Quantifying Quantum Correlations

We consider the amount of work which can be extracted from a heat bath using a bipartite state shared by two parties. In general it is less then the amount of work extractable when one party is in possession of the entire state. We derive bounds for this "work deficit" and calculate it explicitly for a number of different cases. For pure states the work deficit is exactly equal to the distillable entanglement of the state, and this is also achievable for maximally correlated states. In these cases a form of complementarity exists between physical work which can be extracted and distillable entanglement. The work deficit is a good measure of the quantum correlations in a state and provides a new paradigm for understanding quantum non-locality.

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arXiv2002

Local indistinguishability and LOCC monotones

We provide a method for checking indistinguishability of a set of multipartite orthogonal states by local operations and classical communication (LOCC). It bases on the principle of nonincreasing of entanglement under LOCC. This method originates from the one introduced by Ghosh \emph{et al.} (Phys. Rev. Lett. \textbf{87}, 5807 (2001) (quant-ph/0106148)), though we deal with {\emph pure} states. In the bipartite case, our method is operational, although we do not know whether it can always detect local indistinguishability. We apply our method to show that an arbitrary complete multipartite orthogonal basis is indistinguishable if it contains at least one entangled state. We also show that probabilistic distinguishing is possible for full basis if and only if all vectors are product. We employ our method to prove local indistinguishability in a very interesting example akin to "nonlocality without entanglement".

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arXiv2002

Separability of mixed quantum states: linear contractions approach

Recently, a new and powerful separability criterion was introduced in [O. Rudolph, quant-ph/0202121] and [Chen {\it et al.}, quant-ph/0205017]. Composing the main idea behind the above criterion and the necessary and sufficient condition in terms of positive maps, we provide a characterization of separable states by means of linear contractions. The latter need not be positive maps. We extend the idea to multipartite systems, and find that, somewhat suprisingly, partial realigment (unlike partial transposition) can detect genuinely triparite entanglement. We also show that for multipartite system any permutation of indices of density matrix leads to separability criterion.

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arXiv2002

The entanglement of purification

We introduce a measure of both quantum as well as classical correlations in a quantum state, the entanglement of purification. We show that the (regularized) entanglement of purification is equal to the entanglement cost of creating a state $ρ$ asymptotically from maximally entangled states, with negligible communication. We prove that the classical mutual information and the quantum mutual information divided by two are lower bounds for the regularized entanglement of purification. We present numerical results of the entanglement of purification for Werner states in ${\cal H}_2 \otimes {\cal H}_2$.

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arXiv2002

The Uniqueness Theorem for Entanglement Measures

We explore and develop the mathematics of the theory of entanglement measures. After a careful review and analysis of definitions, of preliminary results, and of connections between conditions on entanglement measures, we prove a sharpened version of a uniqueness theorem which gives necessary and sufficient conditions for an entanglement measure to coincide with the reduced von Neumann entropy on pure states. We also prove several versions of a theorem on extreme entanglement measures in the case of mixed states. We analyse properties of the asymptotic regularization of entanglement measures proving, for example, convexity for the entanglement cost and for the regularized relative entropy of entanglement.

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arXiv2001

Universal Quantum Estimator

We present a simple device based on the controlled-SWAP gate that performs quantum state tomography. It can also be used to determine maximum and minimum eigenvalues, expectation values of arbitrary observables, purity estimation as well as characterizing quantum channels. The advantage of this scheme is that the architecture is fixed and the task performed is determined by the input data.

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arXiv2001

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.

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arXiv2001

Classical capacity of a noiseless quantum channel assisted by noisy entanglement

We derive the general formula for the capacity of a noiseless quantum channel assisted by an arbitrary amount of noisy entanglement. In this capacity formula, the ratio of the quantum mutual information and the von Neumann entropy of the sender's share of the noisy entanglement plays the role of mutual information in the completely classical case. A consequence of our results is that bound entangled states cannot increase the capacity of a noiseless quantum channel.

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arXiv2001

Concurrence in arbitrary dimensions

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.

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arXiv2001

Dynamical description of quantum computing: generic nonlocality of quantum noise

We develop dynamical non-Markovian description of quantum computing in weak coupling limit, in lowest order approximation. We show that long range memory of quantum reservoir produces strong interrelation between structure of noise and quantum algorithm, implying nonlocal attacks of noise. We then argue that the quantum error correction method fails to protect quantum computation against electromagnetic or phonon vacuum which exhibit $1/t^4$ memory. This shows that the implicit assumption of quantum error correction theory -- independence of noise and self-dynamics -- fails in long time regimes. We also use our approach to present {\it pure} decoherence and decoherence accompanied by dissipation in terms of spectral density of reservoir. The so-called {\it dynamical decoupling} method is discussed in this context. Finally, we propose {\it minimal decoherence model}, in which the only source of decoherence is vacuum. We optimize fidelity of quantum information processing under the trade-off between speed of gate and strength of decoherence.

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arXiv2000

Optimal compression for mixed signal states

We consider the problem of the optimal compression rate in the case of the source producing mixed signal states within the {\it visible} scheme (where Alice, who is to compress the signal, can know the identities of the produced states). We show that a simple strategy based on replacing the signal states with their {\it extensions} gives {\it optimal} compression. As a result we obtain a considerable simplification of the formula for optimal compression rate within visible scheme.

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arXiv2000

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.

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arXiv2000

Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps

We provide necessary and sufficient conditions for separability of mixed states of n-particle systems. The conditions are formulated in terms of maps which are positive on product states of $n-1$ particles. The method of providing of the maps on the basis of unextendable product bases is provided. The three qubit state problem is reformulated in the form suggesting possibility of explicite characterisation of all maps needed for separability condition.

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arXiv2000

Unified approach to quantum capacities: towards quantum noisy coding theorem

Basing on unified approach to {\it all} kinds of quantum capacities we show that the rate of quantum information transmission is bounded by the maximal attainable rate of coherent information. Moreover, we show that, if for any bipartite state the one-way distillable entanglement is no less than coherent information, then one obtains Shannon-like formulas for all the capacities. The inequality also implies that the decrease of distillable entanglement due to mixing process does not exceed of corresponding loss information about a system.

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arXiv2000

Limits for entanglement measures

We show that {\it any} entanglement measure $E$ suitable for the regime of high number of entangled pairs satisfies $E_D\leq E\leq E_F$ where $E_D$ and $E_F$ are entanglement of distillation and formation respectively. We also exhibit a general theorem on bounds for distillable entanglement. The results are obtained by use of a very transparent reasoning based on the fundamental principle of entanglement theory saying that entanglement cannot increase under local operations and classical communication.

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