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Michal Horodecki

Publications and source records attributed to Michal Horodecki.

At least 73 records · Page 4Linked to original sources
arXiv2004

Local versus non-local information in quantum information theory: formalism and phenomena

In spite of many results in quantum information theory, the complex nature of compound systems is far from being clear. In general the information is a mixture of local, and non-local ("quantum") information. To make this point more clear, we develop and investigate the quantum information processing paradigm in which parties sharing a multipartite state distill local information. The amount of information which is lost because the parties must use a classical communication channel is the deficit. This scheme can be viewed as complementary to the notion of distilling entanglement. After reviewing the paradigm, we show that the upper bound for the deficit is given by the relative entropy distance to so-called psuedo-classically correlated states; the lower bound is the relative entropy of entanglement. This implies, in particular, that any entangled state is informationally nonlocal i.e. has nonzero deficit. We also apply the paradigm to defining the thermodynamical cost of erasing entanglement. We show the cost is bounded from below by relative entropy of entanglement. We demonstrate the existence of several other non-local phenomena. For example,we prove the existence of a form of non-locality without entanglement and with distinguishability. We analyze the deficit for several classes of multipartite pure states and obtain that in contrast to the GHZ state, the Aharonov state is extremely nonlocal (and in fact can be thought of as quasi-nonlocalisable). We also show that there do not exist states, for which the deficit is strictly equal to the whole informational content (bound local information). We then discuss complementary features of information in distributed quantum systems. Finally we discuss the physical and theoretical meaning of the results and pose many open questions.

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arXiv2004

The Universal Composable Security of Quantum Key Distribution

The existing unconditional security definitions of quantum key distribution (QKD) do not apply to joint attacks over QKD and the subsequent use of the resulting key. In this paper, we close this potential security gap by using a universal composability theorem for the quantum setting. We first derive a composable security definition for QKD. We then prove that the usual security definition of QKD still implies the composable security definition. Thus, a key produced in any QKD protocol that is unconditionally secure in the usual definition can indeed be safely used, a property of QKD that is hitherto unproven. We propose two other useful sufficient conditions for composability. As a simple application of our result, we show that keys generated by repeated runs of QKD degrade slowly.

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arXiv2004

Common origin of no-cloning and no-deleting principles - Conservation of information

We discuss the role of the notion of information in the description of physical reality. We consider theories for which dynamics is linear with respect to stochastic mixing. We point out that the no-cloning and no-deleting principles emerge in any such theory, if law of conservation of information is valid, and two copies contain more information than one copy. We then describe the quantum case from this point of view.

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arXiv2004

Bounds on localisable information via semidefinite programming

We investigate so-called localisable information of bipartite states and a parallel notion of information deficit. Localisable information is defined as the amount of information that can be concentrated by means of classical communication and local operations where only maximally mixed states can be added for free. The information deficit is defined as difference between total information contents of the state and localisable information. We consider a larger class of operations: the so called PPT operations, which in addition preserve maximally mixed state (PPT-PMM operations). We formulate the related optimization problem as sedmidefnite program with suitable constraints. We then provide bound for fidelity of transition of a given state into product pure state on Hilbert space of dimension d. This allows to obtain general upper bound for localisable information (and also for information deficit). We calculated the bounds exactly for Werner states and isotropic states in any dimension. Surprisingly it turns out that related bounds for information deficit are equal to relative entropy of entanglement (in the case of Werner states - regularized one). We compare the upper bounds with lower bounds based on simple protocol of localisation of information.

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arXiv2004

Locking entanglement measures with a single qubit

We study the loss of entanglement of bipartite state subjected to discarding or measurement of one qubit. Examining the behavior of different entanglement measures, we find that entanglement of formation, entanglement cost, and logarithmic negativity are lockable measures in that it can decrease arbitrarily after measuring one qubit. We prove that any convex and asymptotically non-continuous measure is lockable. As a consequence, all the convex roof measures can be locked. Relative entropy of entanglement is shown to be a non-lockable measure.

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arXiv2004

Classical information deficit and monotonicity on local operations

We investigate classical information deficit: a candidate for measure of classical correlations emerging from thermodynamical approach initiated in [Phys. Rev. Lett 89, 180402]. It is defined as a difference between amount of information that can be concentrated by use of LOCC and the information contained in subsystems. We show nonintuitive fact, that one way version of this quantity can increase under local operation, hence it does not possess property required for a good measure of classical correlations. Recently it was shown by Igor Devetak, that regularised version of this quantity is monotonic under LO. In this context, our result implies that regularization plays a role of "monotoniser".

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arXiv2004

Thermodynamics of quantum informational systems - Hamiltonian description

It is often claimed, that from a quantum system of d levels, and entropy S and heat bath of temperature T one can draw kT(ln d -S) amount of work. However, the usual arguments based on Szilard engine are not fully rigorous. Here we prove the formula within Hamiltonian description of drawing work from a quantum system and a heat bath, at a cost of entropy of the system. We base on the derivation of thermodynamical laws and quantities in [R. Alicki, J. Phys. A, 12, L103 (1979)] within a weak coupling limit. Our result provides fully physical scenario for extracting thermodynamical work from quantum correlations [J. Oppenheim et al. Phys. Rev. Lett. 89, 180402 (2002)]. We also derive Landauer principle as a consquence of second law within the considered model.

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arXiv2003

Cloning of orthogonal mixed states entails irreversibility

Orthogonal pure states can be cloned as well as deleted. However if there is an initial disorder in the system, that is for orthogonal mixed states, one cannot perform deletion. And cloning, in such cases, necessarily produces an irreversibility, in the form of leakage of information into the environment.

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arXiv2003

Quantification of quantum correlation of ensemble of states

We present first measure of quantum correlation of an ensemble of multiparty states. It is based on the idea of minimal entropy production in a locally distinguishable basis measurement. It is shown to be a relative entropy distance from a set of ensembles. For bipartite ensembles, which span the whole bipartite Hilbert space, the measure is bounded below by average relative entropy of entanglement. We naturally obtain a monotonicity axiom for any measure of quantum correlation of ensembles. We evaluate this measure for certain cases. Subsequently we use this measure to propose a complementarity relation between our measure and the accessible information obtainable about the ensemble under local operations. The measure along with the monotonicity axiom are well-defined even for the case of a single system, where the complementarity relation is seen to be yet another face of the "Heisenberg uncertainty relation".

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arXiv2003

Locally accessible information: How much can the parties gain by cooperating?

We investigate measurements of bipartite ensembles restricted to local operations and classical communication and find a universal Holevo-like upper bound on the locally accessible information. We analyze our bound and exhibit a class of states which saturate it. Finally, we link the bound to the problem of quantification of the nonlocality of the operations necessary to extract locally unaccessible information.

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arXiv2003

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.

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arXiv2003

Locking classical correlation in quantum states

We show that there exist bipartite quantum states which contain large hidden classical correlation that can be unlocked by a disproportionately small amount of classical communication. In particular, there are $(2n+1)$-qubit states for which a one bit message doubles the optimal classical mutual information between measurement results on the subsystems, from $n/2$ bits to $n$ bits. States exhibiting this behavior need not be entangled. We study the range of states exhibiting this phenomenon and bound its magnitude.

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arXiv2003

Reversible transformations from pure to mixed states, and the unique measure of information

Transformations from pure to mixed states are usually associated with information loss and irreversibility. Here, a protocol is demonstrated allowing one to make these transformations reversible. The pure states are diluted with a random noise source. Using this protocol one can study optimal transformations between states, and from this derive the unique measure of information. This is compared to irreversible transformations where one does not have access to noise. The ideas presented here shed some light on attempts to understand entanglement manipulations and the inevitable irreversibility encountered there where one finds that mixed states can contain "bound entanglement".

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arXiv2003

Compressing compound states

Quantum compression can be thought of not only as compression of a signal, but also as a form of cooling. In this view, one is interested not in the signal, but in obtaining purity. In compound systems, one may be interested to cool the system to obtain {\it local purity} by use of local operations and classical communication [Oppenheim et al. Phys. Rev. Lett. 89,180402 (2002)]. Here we compare it with usual compression and find that it can be represented as compression with suitably restricted means.

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arXiv2003

Are there phase transitions in information space?

The interplay between two basic quantities -- quantum communication and information -- is investigated. Quantum communication is an important resource for quantum states shared by two parties and is directly related to entanglement. Recently, the amount of local information that can be drawn from a state has been shown to be closely related to the non-local properties of the state. Here we consider both formation and extraction processes, and analyze informational resources as a function of quantum communication. The resulting diagrams in information space allow us to observe phase-like transitions when correlations become classical.

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arXiv2003

Information as a resource in distributed quantum systems

A new paradigm for distributed quantum systems where information is a valuable resource is developed. After finding a unique measure for information, we construct a scheme for it's manipulation in analogy with entanglement theory. In this scheme instead of maximally entangled states, two parties distill local states. We show that, surprisingly, the main tools of entanglement theory are general enough to work in this opposite scheme. Up to plausible assumptions, we show that the amount of information that must be lost during the protocol of concentration of local information can be expressed as the relative entropy distance from some special set of states.

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arXiv2002

Are the laws of entanglement theory thermodynamical?

We argue that on its face, entanglement theory satisfies laws equivalent to thermodynamics if the theory can be made reversible by adding certain bound entangled states as a free resource during entanglement manipulation. Subject to plausible assumptions, we prove that this is not the case in general, and discuss the implications of this for the thermodynamics of entanglement.

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