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prof. dr hab. Paweł Horodecki
Employment
- Professor at Instytut Fizyki i Informatyki Stosowanej
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total: 119
Catalog Publications
Year 2013
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Conjectured strong complementary-correlations tradeoff
PublicationWe conjecture uncertainty relations that restrict correlations between the results of measurements performed by two separate parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when one party measures a single observable and the other party measures one of two observables. The uncertainty relation does not follow from the Maassen-Uffink uncertainty relation and is much stronger...
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Experimental generation of complex noisy photonic entanglement
PublicationWe present an experimental scheme based on spontaneous parametric down-conversion to produce multiple-photon pairs in maximally entangled polarization states using an arrangement of two type-I nonlinear crystals. By introducing correlated polarization noise in the paths of the generated photons we prepare mixed-entangled states whose properties illustrate fundamental results obtained recently in quantum information theory, in particular those...
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Multiacces quantum communication and product higher rank numerical range
PublicationIn the present paper we initiate the study of the product higher rank numerical range. The latter, being a variant of the higher rank numerical range, is a natural tool for study- ing a construction of quantum error correction codes for multiple access channels. We review properties of this set and relate it to other numerical ranges, which were recently introduced in the literature. Further, the concept is applied to the construction...
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NO-BROADCASTING OF NON-SIGNALLING BOXES VIA OPERATIONS WHICH TRANSFORM LOCAL BOXES INTO LOCAL ONES
PublicationWe deal with families of probability distributions satisfying non-signalling condition, called non-signalling boxes and consider a class of operations that transform local boxes into local ones (the one that admit LHV model). We prove that any operation from this class cannot broadcast a bipartite non-local box with 2 binary inputs and outputs. We consider a function called anti-Robustness which can not decrease under these operations....
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Quantum mechanical which-way experiment with an internal degree of freedom
PublicationFor a particle travelling through an interferometer, the trade-off between the available which-way information and the interference visibility provides a lucid manifestation of the quantum mechanical wave-particle duality. Here we analyse this relation for a particle possessing an internal degree of freedom such as spin. We quantify the trade-off with a general inequality that paints an unexpectedly intricate picture of wave-particle...
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Separability in terms of a single entanglement witness
PublicationThe separability problem is formulated in terms of a characterization of a single entanglement witness. More specifically, we show that any (in general multipartite) state rho is separable if and only if a specially constructed entanglement witness W-rho is weakly optimal, i.e., its expectation value vanishes on at least one product vector. Interestingly, the witness can always be chosen to be decomposable. Our result changes the...
Year 2012
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Analytical progress on symmetric geometric discord: Measurement-based upper bounds
PublicationQuantum correlations may be measured by means of the distance of the state to the subclass ofstates having well defined classical properties. In particular, a geometric measure of asymmetricdiscord [Daki´c et al., Phys. Rev. Lett. 105, 190502 (2010)] was recently defined as the Hilbert-Schmidt distance of a given two-qubit state to the closest classical-quantum (CQ) correlated state.We analyze a geometric measure of symmetric...
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Convergence to equilibrium under a random Hamiltonian
PublicationWe analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first...
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Directed percolation effects emerging from superadditivity of quantum networks
PublicationEntanglement-induced nonadditivity of classical communication capacity in networks consisting of quantum channels is considered. Communication lattices consisting of butterfly-type entanglement-breaking channels augmented, with some probability, by identity channels are analyzed. The capacity superadditivity in the network is manifested in directed correlated bond percolation which we consider in two flavors: simply directed and...
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Quantum privacy witness
PublicationWhile it is usually known that the mean value of a single observable is enough to detect entanglement or its distillability, the counterpart of such an approach in the case of quantum privacy has been missing. Here we develop the concept of a privacy witness, i.e., a single observable that may detect the presence of the secure key even in the case of bound entanglement. Then we develop the notion of secret-key estimation based...
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Quantum-correlation breaking channels, broadcasting scenarios, and finite Markov chains
PublicationOne of the classical results concerning quantum channels is the characterization of entanglementbreakingchannels [M. Horodecki et al., Rev. Math. Phys 15, 629 (2003)]. We address the questionwhether there exists a similar characterization on the level of quantum correlations which may gobeyond entanglement. The answer is fully affirmative in the case of breaking quantum correlationsdown to the, so called, QC (Quantum-Classical)...
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Schemes of transmission of classical information via quantum channels with many senders: Discrete- and continuous-variable cases
PublicationSuperadditivity effects in the classical capacity of discrete multiaccess channels and continuous variable (CV) Gaussian MACs are analyzed. Several examples of the manifestation of superadditivity in the discrete case are provided, including, in particular, a channel which is fully symmetric with respect to all senders. Furthermore, we consider a class of channels for which input entanglement across more than two copies of the...
Year 2011
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All Nonclassical Correlations Can Be Activated into Distillable Entanglement
PublicationWe devise a protocol in which general nonclassical multipartite correlations produce a physically relevant effect, leading to the creation of bipartite entanglement. In particular, we show that the relative entropy of quantumness, which measures all nonclassical correlations among subsystems of a quantum system, is equivalent to and can be operationally interpreted as the minimum distillable entanglement generated between the system...
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Collective Uncertainty Entanglement Test
PublicationFor a given pure state of a composite quantum system we analyze the product of its projections onto aset of locally orthogonal separable pure states. We derive a bound for this product analogous to theentropic uncertainty relations. For bipartite systems the bound is saturated for maximally entangled statesand it allows us to construct a family of entanglement measures, we shall call collectibility. As thesequantities are experimentally...
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Experimental Extraction of Secure Correlations from a Noisy Private State
PublicationWe 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...
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Postulates for measures of genuine multipartite correlations
PublicationA lot of research has been done on multipartite correlations. However, it seems strange thatthere is no denition of so called genuine multipartite correlations. In this paper we propose threereasonable postulates which each measure or indicator of genuine multipartite correlations (or gen-uine multipartite entanglement) should satisfy. We also introduce degree of correlations which givespartial characterization of multipartite...
Year 2010
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A few steps more towards NPT bound entanglement
PublicationIn this paper, existence of bound entangled states with nonpositive partial transpose (NPT) is considered. As one knows, existence of such states would in particular imply nonadditivity of distillable entanglement. Moreover, it would rule out a simple mathematical description of the set of distillable states. The particular state, known to be 1-copy nondistillable and supposed to be bound entangled, is considered. The problem of...
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Are quantum correlations symmetric?
PublicationWe provide operational definition of symmetry of entanglement: An entangled state contains symmetric entanglement if its subsystems can be exchanged (swapped) by means of local operations and classical communication. We show that in general states have asymmetric entanglement. This allows to construct nonsymmetric measure of entanglement, and a parameter that reports asymmetry of entanglement contents of quantum state. We propose...
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Aspects of multistation quantum information broadcasting
PublicationWe study quantum information transmission over multiparty quantum channel. In particular, we show an equivalence of different capacity notions and provide a multiletter characterization of a capacity region for a general quantum channel with k senders and m receivers. We point out natural generalizations to the case of two-way classical communication capacity. (C) 2010 Elsevier B.V. All rights reserved.
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Efficient bounds on quantum-communication rates via their reduced variants
PublicationWe investigate one-way communication scenarios where Bob operating on his component can transfer some subsystem to the environment. We define reduced versions of quantum-communication rates and, further, prove upper bounds on a 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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