arXiv subjects

Pawel Horodecki

Publications and source records attributed to Pawel Horodecki.

At least 37 records · Page 2Linked to original sources

arXiv2011

Experimental Extraction of Secure Correlations from a Noisy Private State

We report experimental generation of a noisy entangled four-photon state that exhibits a separation between the secure key contents and distillable entanglement, a hallmark feature of the recently established quantum theory of private states. The privacy analysis, based on the full tomographic reconstruction of the prepared state, is utilized in a proof-of-principle key generation. The inferiority of distillation-based strategies to extract the key is exposed by an implementation of an entanglement distillation protocol for the produced state.

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arXiv2010

Efficient bounds on quantum communication rates via their reduced variants

We investigate one-way communication scenarios where Bob manipulating on his parts can transfer some sub-system to the environment. We define reduced versions of quantum communication rates and further, prove new upper bounds on one-way quantum secret key, distillable entanglement and quantum channel capacity by means of their reduced versions. It is shown that in some cases they drastically improve their estimation.

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arXiv2010

Contextuality offers security

The discovery of quantum key distribution by Bennett and Brassard (BB84) bases on the fundamental quantum feature: incompatibility of measurements of quantum non-commuting observables. In 1991 Ekert showed that cryptographic key can be generated at a distance with help of entangled (correlated) quantum particles. Recently Barrett, Hardy and Kent showed that the non-locality used by Ekert is itself a good resource of cryptographic key even beyond quantum mechanics. Their result paved the way to new generation of quantum cryptographic protocols - secure even if the devices are built by the very eavesdropper. However, there is a question, which is fundamental from both practical and philosophical point of view: does Nature offer security on operational level based on the original concept behind quantum cryptography - that information gain about one bservables must cause disturbance to another, incompatible one? Here we resolve this problem by using in place of non-locality another striking feature of quantum world - contextuality. It is a strong version of incompatibility manifested in the famous Kochen-Specker paradox. The crucial concept is the use of a new class of families of bipartite probability distributions which locally exhibit the Kochen-Specker paradox conditions and, in addition, exhibit perfect correlations. We show that if two persons share systems described by such a family then they can extract secure key. This is the first operational protocol that directly implements the fundamental feature of Nature: the information gain vs. disturbance trade-off. At the same time it provides natural device-independent cryptographic scheme within quantum mechanics suitable for current technology.

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arXiv2010

Contextuality offers device-independent security

The discovery of quantum key distribution by Bennett and Brassard (BB84) bases on the fundamental quantum feature: incompatibility of measurements of quantum non-commuting observables. In 1991 Ekert showed that cryptographic key can be generated at a distance with help of entangled (correlated) quantum particles. Recently Barrett, Hardy and Kent showed that the non-locality used by Ekert is itself a good resource of cryptographic key even beyond quantum mechanics. Their result paved the way to new generation of quantum cryptographic protocols - secure even if the devices are built by the very eavesdropper. However, there is a question, which is fundamental from both practical and philosophical point of view: does Nature offer security on operational level based on the original concept behind quantum cryptography - that information gain about one observable must cause disturbance to another, incompatible one? Here we resolve this problem by using another striking feature of quantum world - contextuality. It is a strong version of incompatibility manifested in the famous Kochen-Specker paradox. The crucial concept is the use of a new class of families of bipartite probability distributions . We show that if two persons share systems which locally exhibit the Kochen-Specker paradox and, in addition, exhibit perfect correlations, then they can extract secure key, even if they do not trust the quantum devices. This is the first operational protocol that directly implements the fundamental feature of Nature: the information gain vs. disturbance trade-off. For sake of proof we exhibit a new Bell's inequality which is interesting in itself. The security is proved not by exploiting strong violation of the inequality by quantum mechanics (as one usually proceeds), but rather by arguing, that quantum mechanics cannot violate it too much.

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arXiv2010

Nonadditivity of quantum and classical capacities for entanglement breaking multiple-access channels and butterfly network

We analyze quantum network primitives which are entanglement-breaking. We show superadditivity of quantum and classical capacity regions for quantum multiple-access channel and quantum butterfly network. Since the effects are especially visible at high noise they suggest that quantum information effects may be particularly helpful in the case of the networks with occasional high noise rates. To our knowledge the present effects provide the first qualitative borderline between superadditivities of bipartite and multipartite systems.

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arXiv2010

Postulates for measures of genuine multipartite correlations

A lot of research has been done on multipartite correlations. However, it seems strange that there is no definition of so called genuine multipartite correlations. In this paper we propose three reasonable postulates which each measure or indicator of genuine multipartite correlations (or genuine multipartite entanglement) should satisfy. We also introduce degree of correlations which gives partial characterization of multipartite correlations. Then, we show that covariance does not satisfy two postulates and hence, it cannot be used as an indicator of genuine multipartite correlations. Finally, we propose candidate for a measure of genuine multipartite correlations based on the work that can be drawn from local bath by means of a multipartite state.

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arXiv2009

Multipartite secret key distillation and bound entanglement

Recently it has been shown that quantum cryptography beyond pure entanglement distillation is possible and a paradigm for the associated protocols has been established. Here we systematically generalize the whole paradigm to the multipartite scenario. We provide constructions of new classes of multipartite bound entangled states, i.e., those with underlying twisted GHZ structure and nonzero distillable cryptographic key. We quantitatively estimate the key from below with help of the privacy squeezing technique.

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arXiv2009

W-like bound entangled states and secure key distillation

We construct multipartite entangled states with underlying W-type structure satisfying positive partial transpose (PPT) condition under any (N-1)|1 partition. Then we show how to distill N-partite secure key form the states using two different methods: direct application of local filtering and novel random key distillation scheme in which we adopt the idea form recent results on entanglement distillation. Open problems and possible implications are also discussed.

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arXiv2009

Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof

New measures of multipartite entanglement are constructed based on two definitions of multipartite information and different methods of optimizing over extensions of the states. One is a generalization of the squashed entanglement where one takes the mutual information of parties conditioned on the state's extension and takes the infimum over such extensions. Additivity of the multipartite squashed entanglement is proved for both versions of the multipartite information which turn out to be related. The second one is based on taking classical extensions. This scheme is generalized, which enables to construct measures of entanglement based on the {\it mixed convex roof} of a quantity, which in contrast to the standard convex roof method involves optimization over all decompositions of a density matrix rather than just the decompositions into pure states. As one of the possible applications of these results we prove that any multipartite monotone is an upper bound on the amount of multipartite distillable key. The findings are finally related to analogous results in classical key agreement.

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arXiv2009

When non i.i.d. information sources can be communicationally useful?

Information sources used for communication purposes usually are assumed to be i.i.d. type, especially as far as entanglement or nonlocality properties are concerned. Here we proposed simple scheme for detection of nonlocality of non i.i.d. sources based on the program idea which can be useful in communication tasks including quantum cryptography and communication complexity reduction. The principle of the scheme is rather general and can be applied to other problems like detection of entanglement coming from non-i.i.d sources.

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arXiv2008

Entanglement-redistribution boxes

We establish a framework to study the classical-communication properties of primitive local operations assisted by classical communication which realize various redistributions of entanglement, like, e.g., entanglement swapping. On the one hand, we analyze what local operations and how much classical communication are needed to perform them. On the other hand, we investigate whether and to what extent such primitives can help to establish classical communication when they are used in the form of black boxes available to spatially-separated users. In particular, we find that entanglement swapping costs more communication than it can signal; in this sense, entanglement swapping is a weaker primitive than quantum teleportation.

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arXiv2008

Nonadditivity effects in classical capacities of quantum multiple-access channels

We study classical capacities of quantum multi-access channels in geometric terms revealing breaking of additivity of Holevo-like capacity. This effect is purely quantum since, as one points out, any classical multi-access channels have their regions additive. The observed non-additivity in quantum version presented here seems to be the first effect of this type with no additional resources like side classical or quantum information (or entanglement) involved. The simplicity of quantum channels involved resembles butterfly effect in case of classical channel with two senders and two receivers.

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arXiv2008

General paradigm for distilling classical key from quantum states

We develop a formalism for distilling a classical key from a quantum state in a systematic way, expanding on our previous work on secure key from bound entanglement [K. Horodecki et. al., Phys. Rev. Lett. 94 (2005)]. More detailed proofs, discussion and examples are provided of the main results. Namely, we demonstrate that all quantum cryptographic protocols can be recast in a way which looks like entanglement theory, with the only change being that instead of distilling EPR pairs, the parties distill private states. The form of these general private states are given, and we show that there are a number of useful ways of expressing them. Some of the private states can be approximated by certain states which are bound entangled. Thus distillable entanglement is not a requirement for a private key. We find that such bound entangled states are useful for a cryptographic primitive we call a controlled private quantum channel. We also find a general class of states which have negative partial transpose (are NPT), but which appear to be bound entangled. The relative entropy distance is shown to be an upper bound on the rate of key. This allows us to compute the exact value of distillable key for a certain class of private states.

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arXiv2008

Entanglement-swapping boxes and their communication properties

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.

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arXiv2008

Note on genuine multipartite classical correlations

We discuss the problem of coexistence of genuine quantum multipartite correlations and classical multipartite correlations. We introduce a postulate which any measure of genuine multipartite classical correlations should satisfy. We show that covariance does not satisfy this postulate. Finally we propose a definition of genuine multipartite correlations and illustrate it with examples.

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arXiv2008

Beyond the standard entropic inequalities: stronger scalar separability criteria and their applications

Recently it was shown that if a given state fulfils the reduction criterion it must also satisfy the known entropic inequalities. Now the questions arises whether on the assumption that stronger criteria based on positive but not completely positive maps are satisfied, it is possible to derive some scalar inequalities stronger than the entropic ones. In this paper we show that under some assumptions the extended reduction criterion [H.-P. Breuer, Phys. Rev. Lett 97, 080501 (2006); W. Hall, J. Phys. A 40, 6183 (2007)] leads to some entropic--like inequalities which are much stronger than their entropic counterparts. The comparison of the derived inequalities with other separability criteria shows that such approach might lead to strong scalar criteria detecting both distillable and bound entanglement. In particular, in the case of SO(3)-invariant states it is shown that the present inequalities detect entanglement in regions in which entanglement witnesses based on extended reduction map fail. It should be also emphasized that in the case of $2\otimes N$ states the derived inequalities detect entanglement efficiently, while the extended reduction maps are useless when acting on the qubit subsystem. Moreover, there is a natural way to construct a many-copy entanglement witnesses based on the derived inequalities so, in principle, there is a possibility of experimental realization. Some open problems and possibilities for further studies are outlined.

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arXiv2007

On quantum cryptography with bipartite bound entangled states

Recently the explicit applicability of bound entanglement in quantum cryptography has been shown. In this paper some of recent results respecting this topic are reviewed. In particular relevant notions and definitions are reminded. The new construction of bound entangled states containing secure correlations is presented. It provides low dimensional 6\otimes6 bound entangled states with nonzero distillable key.

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arXiv2007

Quantum states representing perfectly secure bits are always distillable

It is proven that recently introduced states with perfectly secure bits of cryptographic key (private states representing secure bit) [K. Horodecki et al., Phys. Rev. Lett. 94, 160502 (2005)] as well as its multipartite and higher dimension generalizations always represent distillable entanglement. The corresponding lower bounds on distillable entanglement are provided. We also present a simple alternative proof that for any bipartite quantum state entanglement cost is an upper bound on distillable cryptographic key in bipartite scenario.

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