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Search results for: THEORY OF QUANTUM INFORMATION
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Average Redundancy of the Shannon Code for Markov Sources
PublicationIt is known that for memoryless sources, the average and maximal redundancy of fixed–to–variable length codes, such as the Shannon and Huffman codes, exhibit two modes of behavior for long blocks. It either converges to a limit or it has an oscillatory pattern, depending on the irrationality or rationality, respectively, of certain parameters that depend on the source. In this paper, we extend these findings, concerning the Shannon...
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Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
PublicationNew measures of multipartite entanglement are constructedbased on two definitions of multipartite information anddifferent methods of optimizing over extensions of the states. Oneis a generalization of the squashed entanglement where one takesthe mutual information of parties conditioned on the state's extensionand takes the infimum over such extensions. Additivity ofthe multipartite squashed entanglement is proved for both versionsof...
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Types of Markov Fields and Tilings
PublicationThe method of types is one of the most popular techniques in information theory and combinatorics. However, thus far the method has been mostly applied to one-dimensional Markov processes, and it has not been thoroughly studied for general Markov fields. Markov fields over a finite alphabet of size m ≥ 2 can be viewed as models for multi-dimensional systems with local interactions. The locality of these interactions is represented...
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International Conference on the Theory and Application of Cryptology and Information Security
Conferences -
On the Limiting Distribution of Lempel-Ziv’78 Redundancy for Memoryless Sources
PublicationWe study the Lempel-Ziv'78 algorithm and show that its (normalized) redundancy rate tends to a Gaussian distribution for memoryless sources. We accomplish it by extending findings from our 1995 paper, in particular, by presenting a new simplified proof of the central limit theorem (CLT) for the number of phrases in the LZ'78 algorithm. We first analyze the asymptotic behavior of the total path length in the associated digital search...
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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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Low-dimensional bound entanglement with one-way distillable cryptographic key
PublicationIn this paper, we provide a class of bound entangled states that have positive distillable secure key rate. The smallest state of this kind is 4 circle times 4, which shows that peculiar security contained in bound entangled states does not need high-dimensional systems. We show that for these states a positive key rate can be obtained by one-way Devetak-Winter (DW) protocol. Subsequently, the volume of bound entangled key-distillable...
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On the Characteristic Graph of a Discrete Symmetric Channel
PublicationWe present some characterizations of characteristic graphs of row and/or column symmetric channels. We also give a polynomial-time algorithm that decides whether there exists a discrete symmetric channel whose characteristic graph is equal to a given input graph. In addition, we show several applications of our results.
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IEEE Information Theory Workshop on Detection, Estimation, Classification and Imaging
Conferences -
On symmetric extendibility of quantum states and its applications
PublicationThis dissertation is focused on analysis of the symmetric extendibility of quantum states and its applications in the quantum information theory, with special attention paid to the area of quantum entanglement distillation, quantum channels theory, quantum security, and monogamy of quantum entanglement in time. We analyze geometry of the set of symmetric extendible states, i.e. such states that possess symmetric extensions and...
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Quantum Coherence as a Resource
PublicationThe coherent superposition of states, in combination with the quantization of observables, represents one of the most fundamental features that mark the departure of quantum mechanics from the classical realm. Quantum coherence in many-body systems embodies the essence of entanglement and is an essential ingredient for a plethora of physical phenomena in quantum optics, quantum information, solid state physics, and nanoscale thermodynamics....
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Zero-knowledge convincing protocol on quantum bit is impossible
PublicationIt is one of fundamental features of quantum formalism that o n one hand it provides a new infor- mation processing resources and on the other hand puts funda mental constraints on the processing of quantum information implying “no-go” theorems for cloni ng [1–3], bit commitment [4, 5] and deleting [6] in quantum theory. Here we ask about possibilit y of “zero knowledge” scenario which, for its simplicity, can be considered as...
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No Quantum Realization of Extremal No-Signaling Boxes
PublicationThe study of quantum correlations is important for fundamental reasons as well as for quantum communication and information processing tasks. On the one hand, it is of tremendous interest to derive the correlations produced by measurements on separated composite quantum systems from within the set of all correlations obeying the no-signaling principle of relativity, by means of information-theoretic principles. On the other hand,...
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Quantum metrology: Heisenberg limit with bound entanglement
PublicationQuantum entanglement may provide a huge boost in the precision of parameter estimation. However, quantum metrology seems to be extremely sensitive to noise in the probe state. There is an important still open question: What type of entanglement is useful as a resource in quantum metrology? Here we raise this question in relation to entanglement distillation. We provide a counterintuitive example of a family of bound entangled states...
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Towards Resource Theory of Coherence in Distributed Scenarios
PublicationThe search for a simple description of fundamental physical processes is an important part of quantum theory. One example for such an abstraction can be found in the distance lab paradigm: if two separated parties are connected via a classical channel, it is notoriously difficult to characterize all possible operations these parties can perform. This class of operations is widely known as local operations and classical communication....
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Information content of systems as a physical principle
PublicationTo explain the conceptual gap between classical and quantum and other, hypothetical descriptions of the world, several principles have been proposed. So far, all these principles have not explicitly included the uncertainty relation. Here we introduce an information content principle ( ICP ) which represents a constrained uncertainty principle. The principle, by taking into account the encoding and decoding properties of a single physical...
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Dynamical description of quantum computing: generic nonlocality of quantumnoise
PublicationWe develop a dynamical non-Markovian description of quantum computing in the weak-coupling limit, in the lowest-order approximation. We show that the long-range memory of the quantum reservoir (such as the 1/t4 one exhibited by electromagnetic vacuum) produces a strong interrelation between the structure of noise and the quantum algorithm, implying nonlocal attacks of noise. This shows that the implicit assumption of quantum error...
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Marek Czachor prof. dr hab.
People -
Subadditivity of the minimum output entropy and superactivation of the classical capacity of quantum multiple access channels
PublicationWe study subadditivity of the minimum output entropy (Hmin) of quantum multiple access channels (MACs). We provide an example of violation of the additivity theorem for Hmin known in classical information theory. Our result is based on a fundamental property of MACs, i.e., independence of each sender. The channels used in the example can be constructed explicitly. On the basis of subadditivity of Hmin we also provide an example...
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Redundant information encoding in QED during decoherence
PublicationBroadly understood decoherence processes in quantum electrodynamics, induced by neglecting either the radiation [L. Landau, Z. Phys. 45, 430 (1927)] or the charged matter [N. Bohr and L. Rosenfeld, K. Danske Vidensk. Selsk, Math.-Fys. Medd. XII, 8 (1933)], have been studied from the dawn of the theory. However, what happens in between, when a part of the radiation may be observed, as is the case in many real-life situations, has...
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Jan Kozicki dr hab. inż. arch.
PeopleIn year 2002 after obtaining master's degree in construction was employed on Faculty of Civil and Environmental Engineering. In 2004 obtained master's degree in architecture on Faculty of Architecture focusing on a research outpost on Mars. Defended PhD in year 2007 in the field of numerical modeling. In 2013 obtained Licentiate degree in theoretical physics on University of Gdańsk. In year 2014 obtained habilitation in technical...
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Unifying Aspects of Generalized Calculus
PublicationNon-Newtonian calculus naturally unifies various ideas that have occurred over the years in the field of generalized thermostatistics, or in the borderland between classical and quantum information theory. The formalism, being very general, is as simple as the calculus we know from undergraduate courses of mathematics. Its theoretical potential is huge, and yet it remains unknown or unappreciated.
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At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited
PublicationWe address the question of whether the super-Heisenberg scaling for quantum estimation is indeed realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter-dependent dynamics. If the parameter is coupled to the one-body part of the Hamiltonian, the precision of its estimation is known to scale at most as N−1 (Heisenberg scaling) in terms of the number...
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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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From unextendible product bases to genuinely entangled subspaces
PublicationUnextendible product bases (UPBs) are interesting mathematical objects arising in composite Hilbert spaces that have found various applications in quantum information theory, for instance in a construction of bound entangled states or Bell inequalities without quantum violation. They are closely related to another important notion, completely entangled subspaces (CESs), which are those that do not contain any fully separable pure...
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Negative result about the construction of genuinely entangled subspaces from unextendible product bases
PublicationUnextendible product bases (UPBs) provide a versatile tool with various applications across different areas of quantum information theory. Their comprehensive characterization is thus of great importance and has been a subject of vital interest for over two decades now. An open question asks about the existence of UPBs, which are genuinely unextendible, i.e., they are not extendible even with biproduct vectors. In other words,...
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Principles of target DNA cleavage and the role of Mg2+ in the catalysis of CRISPR–Cas9
PublicationAt the core of the CRISPR–Cas9 genome-editing technology, the endonuclease Cas9 introduces site-specific breaks in DNA. However, precise mechanistic information to ameliorate Cas9 function is still missing. Here, multimicrosecond molecular dynamics, free energy and multiscale simulations are combined with solution NMR and DNA cleavage experiments to resolve the catalytic mechanism of target DNA cleavage. We show that the conformation...
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Jerzy Konorski dr hab. inż.
PeopleJerzy Konorski received his M. Sc. degree in telecommunications from Gdansk University of Technology, Poland, and his Ph. D. degree in computer science from the Polish Academy of Sciences, Warsaw, Poland. In 2007, he defended his D. Sc. thesis at the Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology. He has authored over 150 papers, led scientific projects funded by the European Union,...
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Blurred quantum Darwinism across quantum reference frames
PublicationQuantum Darwinism describes objectivity of quantum systems via their correlations with their environment--information that hypothetical observers can recover by measuring the environments. However, observations are done with respect to a frame of reference. Here, we take the formalism of [Giacomini, Castro-Ruiz, & Brukner. Nat Commun 10, 494 (2019)], and consider the repercussions on objectivity when changing quantum reference...
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Generic emergence of classical features in quantum Darwinism
PublicationQuantum Darwinism posits that only specific information about a quantum system that is redundantly proliferated to many parts of its environment becomes accessible and objective, leading to the emergence of classical reality. However, it is not clear under what conditions this mechanism holds true. Here we prove that the emergence of classical features along the lines of quantum Darwinism is a general feature of any quantum dynamics:...
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Consistency of Quantum Computation and the Equivalence Principle.
PublicationThe equivalence principle, being one of the building blocks of general relativity, seems to be crucial for analysis of quantum effects in gravity. In this paper we consider the relation between the equivalence principle and the consistency of quantum information processing in gravitational field. We propose an analysis with a looped evolution consisting of steps both in the gravitational field and in the accelerated reference frame....
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Purely quantum superadditivity of classical capacities of quantum multiple access channels
PublicationWe are studying classical capacities of quantum memoryless multiaccess channels in geometric terms and we are revealing a break of additivity of the Holevo-like capacity. This effect is a purely quantum mechanical one, since, as we point out, the capacity regions of all classical memoryless multiaccess channels are additive. It is the first such effect revealed in the field of classical information transmission via quantum channels.
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Quantum origins of objectivity
PublicationIn spite of all of its successes, quantum mechanics leaves us with a central problem: How does nature create a bridge from fragile quanta to the objective world of everyday experience? Here we find that a basic structure within quantum mechanics that leads to the perceived objectivity is a so-called spectrum broadcast structure. We uncover this based on minimal assumptions, without referring to any dynamical details or a concrete...
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Quantum entanglement
PublicationAll our former experience with application of quantum theory seems to say that what is predicted by quantum formalism must occur in the laboratory. But the essence of quantum formalism-entanglement, recognized by Einstein, Podolsky, Rosen, and Schrödinger-waited over 70 years to enter laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between...
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Dynamical objectivity in quantum Brownian motion
PublicationClassical objectivity as a property of quantum states —a view proposed to explain the observer-independent character of our world from quantum theory, is an important step in bridging the quantum-classical gap. It was recently derived in terms of spectrum broadcast structures for small objects embedded in noisy photon-like environments. However, two fundamental problems have arisen: a description of objective motion and applicability...
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Monitoring of the Process of System Information Broadcasting in Time
PublicationOne of the problems of quantum physics is how a measurement turns quantum, noncopyable data, towards copyable classical knowledge. We use the quantum state discrimination in a central system model to show how its evolution leads to the broadcasting of the information, and how orthogonalization and decoherence factors allow us to monitor the distance of the state in question to the one perfectly broadcasting information, in any...
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Quantifying Contextuality
PublicationContextuality is central to both the foundations of quantum theory and to the novel information processing tasks. Despite some recent proposals, it still faces a fundamental problem: how to quantify its presence? In this work, we provide a universal framework for quantifying contextuality. We conduct two complementary approaches: (i) the bottom-up approach, where we introduce a communication game, which grasps the phenomenon of...
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Robert Piotrowski dr hab. inż.
PeopleRobert Piotrowski jest absolwentem Wydziału Elektrotechniki i Automatyki (2001r., kierunek: Automatyka i Robotyka) oraz Wydziału Zarządzania i Ekonomii (2002r., kierunek: Organizacja Systemów Produkcyjnych) Politechniki Gdańskiej. Od 2005 roku jest zatrudniony na Wydziale Elektrotechniki i Automatyki, aktualnie w Katedrze Inteligentnych Systemów Sterowania i Wspomagania Decyzji. W 2005 roku obronił rozprawę doktorską (Automatyka...
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Nonadditivity of quantum and classical capacities for entanglement breaking multiple-access channels and the butterfly network
PublicationWe analyze quantum network primitives which are entanglement breaking. We show superadditivity of quantum and classical capacity regions for quantum multiple-access channels and the 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. The present effects provide a qualitative...
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Entanglement of genuinely entangled subspaces and states: Exact, approximate, and numerical results
PublicationGenuinely entangled subspaces (GESs) are those subspaces of multipartite Hilbert spaces that consist only of genuinely multiparty entangled pure states. They are natural generalizations of the well-known notion of completely entangled subspaces, which by definition are void of fully product vectors. Entangled subspaces are an important tool of quantum information theory as they directly lead to constructions of entangled states,...
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Long-distance quantum communication over noisy networks without long-time quantum memory
PublicationThe problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008)] the authors put forward an important isomorphism between storing quantum information in a dimension D and transmission...
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Leszek Ziemczonek dr
PeopleUniversity education 1973-1978 – Nicolaus Copernicus University in Toruń, University of Gdańsk in Gdańsk, Mathematical Physics, M. Sc. 1979 – Diploma of Postgraduate Studies, Pedagogics 1989 – Institute of Physics, Polish Academy of Sciences in Warsaw, Theoretical Physics, Ph. D. 2010-2012 – Diploma of Postgraduate Studies, Mathematics Training: · 09.1983 – Trieste (Italy) – International Centre for Theoretical Physics...
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Quantum corrections to 4 model solutions and applications to Heisenberg chain dynamics
PublicationThe Heisenberg spin chain is considered in φ^4 model approximation. Quantum corrections to classical solutions of the one-dimensional φ^4 model within the correspondent physics are valuated with account of rest d − 1 dimensions of a d-dimensional theory. A quantization of the model is considered in terms of space- time functional integral. The generalized zeta-function formalism is used to renormalize and evaluate the functional...
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Quantum corrections to phi^4 model solutions and applications to Heisenberg chain dynamics
PublicationThe Heisenberg spin chain is considered in φ^4 model approximation. Quantum corrections to classical solutions of the one-dimensional φ^4 model within the correspondent physics are evaluated with account of rest d−1 dimensions of a d-dimensional theory. A quantization of the model is considered in terms of spacetime functional integral. The generalized zeta-function formalism is used to renormalize and evaluate the functional integral...
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Generic appearance of objective results in quantum measurements
PublicationMeasurement is of central interest in quantum mechanics as it provides the link between the quantum world and the world of everyday experience. One of the features of everyday experience is its robust, objective character, contrasting the delicate nature of quantum systems. Here we analyze in a completely model-independent way the celebrated von Neumann measurement process, using recent techniques of information flow, studied in...
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Experimental certification of an informationally complete quantum measurement in a device-independent protocol
PublicationMinimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their d2-outcomes are enough to reconstruct any d-dimensional quantum state. For this reason, MIC-POVMs are referred to as standard measurements for quantum information.Here, we report an experiment with entangled photon pairs that certifies, for what we believe is the first...
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Information transfer during the universal gravitational decoherence
PublicationRecently Pikovski et al. (Nat Phys 11:668, 2015) have proposed in an intriguing universal decoherence mechanism, suggesting that gravitation may play a conceptually important role in the quantum-to-classical transition, albeit vanishingly small in everyday situations. Here we analyze information transfer induced by this mechanism. We show that generically on short time-scales, gravitational decoherence leads to a redundant information...
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Analytical studies of spectrum broadcast structures in quantum Brownian motion
PublicationSpectrum broadcast structures are a new and fresh concept in the quantum-to-classical transition, introduced recently in the context of decoherence and the appearance of objective features in quantum mechanics. These are specific quantum state structures, responsible for the objectivization of the decohered state of a system. Recently, they have been demonstrated by means of the well-known quantum Brownian motion model of the recoilless...
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Quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi^4 model
PublicationAnalytical form of quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi^4 model is obtained through zeta function regularisation with account of all rest variables of a d-dimensional theory. Qualitative dependence of quantum corrections on parameters of the classical systems is also evaluated for a much broader class of potentials u(x) = b^2 f(bx) + C with b and C as arbitrary real constants
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Quantum-state transfer in spin chains via isolated resonance of terminal spins
PublicationWe propose a quantum-state transfer protocol in a spin chain that requires only the control of the spins at the ends of the quantum wire. The protocol is to a large extent insensitive to inhomogeneity caused by local magnetic fields and perturbation of exchange couplings. Moreover, apart from the free evolution regime, it allows one to induce an adiabatic spin transfer, which provides the possibility of performing the transfer...