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Search results for: quantum information

  • Quantum key distribution based on private states: Unconditional security over untrusted channels with zero quantum capacity

    Publication
    • K. Horodecki
    • M. Horodecki
    • P. Horodecki
    • D. Leung
    • J. Oppenheim

    - IEEE TRANSACTIONS ON INFORMATION THEORY - Year 2008

    In this paper, we prove unconditional security for a quantum key distribution (QKD) protocol based on distilling pbits (twisted ebits) from an arbitrary untrusted state that is claimed to contain distillable key. Our main result is that we can verify security using only public communication-via parameter estimation of the given untrusted state. The technique applies even to bound-entangled states, thus extending QKD to the regime...

  • Redundant information encoding in QED during decoherence

    Publication

    - PHYSICAL REVIEW A - Year 2018

    Broadly 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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  • Method for universal detection of two-photon polarization entanglement

    Publication
    • K. Bartkiewicz
    • P. Horodecki
    • K. Lemr
    • A. Miranowicz
    • K. Życzkowski

    - PHYSICAL REVIEW A - Year 2015

    Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental implementation of a necessary and sufficient test of entanglement has been designed even for a general two-qubit state. Here we propose an experimental method for detecting a collective universal...

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  • The Ellenbogen's “Matter as Software” Concept for Quantum Computer Implementation. C60 and X@C60 Molecules as Available Molecular Building Blocks (MBBs) for Tip-Based Nanofabrication (TBN) of Quantum Computing Devices

    Publication

    - Quantum Matter - Year 2015

    The TBN bottom-up strategy of building quantum devices from C60 and X@C60 MBBs is proposed as an extension of the Ellenbogen's “Matter as Software” idea to quantum information processing. The capped SW or DW CNT STM tip is considered as device for manipulating C60 and X@C60 molecules. In this article, the possibility of using easily available on the market C60 Fullerene and endohedral X@C60 molecules together with commercial CNT...

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  • Characterizing the Performance of <span class="sc">xor</span> Games and the Shannon Capacity of Graphs

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2014

    In this Letter we give a set of necessary and sufficient conditions such that quantum players of a two-party xor game cannot perform any better than classical players. With any such game, we associate a graph and examine its zero-error communication capacity. This allows us to specify a broad new class of graphs for which the Shannon capacity can be calculated. The conditions also enable the parametrization of new families of games...

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  • Non-Perfect Propagation of Information to a Noisy Environment with Self-Evolution

    Publication

    - ENTROPY - Year 2022

    We study the non-perfect propagation of information for evolving a low-dimensional environment that includes self-evolution as well as noisy initial states and analyse the interrelations between the degree of objectivization and environment parameters. In particular, we consider an analytical model of three interacting qubits and derive its objectivity parameters. The numerical analysis shows that the quality of the spectrum broadcast...

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  • At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

    Publication

    - Physical Review X - Year 2018

    We 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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  • General paradigm for distilling classical key from quantum states

    Publication

    - IEEE TRANSACTIONS ON INFORMATION THEORY - Year 2009

    In this paper, we develop a formalism for distilling aclassical key from a quantum state in a systematic way, expandingon our previous work on a secure key from bound entanglement(Horodecki et al., 2005). More detailed proofs, discussion, andexamples are provided of the main results. Namely, we demonstratethat all quantum cryptographic protocols can be recast in away which looks like entanglement theory, with the only changebeing...

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  • Decoherence-free communication over multiaccess quantum channels

    In this paper we consider decoherence-free communication over multiple access and k-user quantum channels. First, we concentrate on a hermitian unitary noise model U for a two-access bi-unitary channel and show that in this case a decoherence-free code exists if the space of Schmidt matrices of an eigensubspace of U exhibits certain properties of decomposability. Then, we show that our technique is also applicable for generic random unitary...

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  • Unifying Aspects of Generalized Calculus

    Publication

    - ENTROPY - Year 2020

    Non-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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  • Increased Certification of Semi-device Independent Random Numbers using Many Inputs and More Postprocessing

    Publication
    • P. A. Mironowicz
    • A. Tavakoli
    • A. Hameedi
    • B. Marques
    • M. Pawłowski
    • M. Bourennane

    - NEW JOURNAL OF PHYSICS - Year 2016

    Quantum communication with systems of dimension larger than two provides advantages in information processing tasks. Examples include higher rates of key distribution and random number generation. The main disadvantage of using such multi-dimensional quantum systems is the increased complexity of the experimental setup. Here, we analyze a not-so-obvious problem: the relation between randomness certification and computational requirements...

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  • Vibrational Quenching of Optically Pumped Carbon Dimer Anions

    Publication
    • M. Nötzold
    • R. Wild
    • C. Lochmann
    • T. Rahim
    • S. P. Melath
    • K. Dulitz
    • B. P. Mant
    • J. Franz
    • F. A. Gianturco
    • R. Wester

    - PHYSICAL REVIEW LETTERS - Year 2023

    Careful control of quantum states is a gateway to research in many areas of science such as quantum information, quantum-controlled chemistry, and astrophysical processes. Precise optical control of molecular ions remains a challenge due to the scarcity of suitable level schemes, and direct laser cooling has not yet been achieved for either positive or negative molecular ions. Using a cryogenic wire trap, we show how the internal...

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  • Experimental generation of complex noisy photonic entanglement

    Publication
    • K. Dobek
    • M. Karpiński
    • R. Demkowicz-Dobrzański
    • K. Banaszek
    • P. Horodecki

    - LASER PHYSICS - Year 2013

    We 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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  • Towards Resource Theory of Coherence in Distributed Scenarios

    Publication

    - Physical Review X - Year 2017

    The 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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  • From unextendible product bases to genuinely entangled subspaces

    Publication

    - PHYSICAL REVIEW A - Year 2018

    Unextendible 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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  • Principles of target DNA cleavage and the role of Mg2+ in the catalysis of CRISPR–Cas9

    Publication
    • Ł. Nierzwicki
    • P. R. Arantes
    • M. Jinek
    • G. Lisi
    • G. Palermo
    • K. East
    • J. Binz
    • R. Vsu
    • A. Mohd
    • E. Skeens
    • M. Pacesa

    - Nature Catalysis - Year 2022

    At 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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  • On thermal stability of topological qubit in Kitaev's 4D model

    Publication

    - OPEN SYSTEMS & INFORMATION DYNAMICS - Year 2010

    We analyse stability of the four-dimensional Kitaev model-a candidate for scalable quantum memory - in finite temperature within the weak coupling Markovian limit. It is shown that, below a critical temperature, certain topological qubit observables X and Z possess relaxation times exponentially long in the size of the system. Their construction involves polynomial in system size algorithm which uses as an input the results of...

  • Negative result about the construction of genuinely entangled subspaces from unextendible product bases

    Publication

    Unextendible 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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  • Eu2Mg3Bi4: Competing Magnetic Orders on a Buckled Honeycomb Lattice

    Publication
    • M. Marshall
    • F. Wang
    • T. Klimczuk
    • R. S. Dissanayaka Mudiyanselage
    • M. Greenblatt
    • D. Walker
    • W. Xie

    - CHEMISTRY OF MATERIALS - Year 2022

    The honeycomb lattice and its derived variants provide information on modeling and designing quantum magnets. A novel magnetic material, Eu2Mg3Bi4, which stabilizes in a previously unknown buckled honeycomb lattice, was discovered by high-pressure and high-temperature methods. We report here on the synthesis exploration of pure single crystals, structural determination of the buckled honeycomb lattice of europium moments, and experimental observation...

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  • Two examples of Quantum Dynamical Semigroups

    The Hamiltonians of the considered bi-partite systems are of the form $$ H_{S,R} = H_S /times 1_R + Q_{S} /times M_R + 1_S /times H_R $$ Subindex $S$ corresponds to the observed system and $R$ to the reservoir (the enviroment of $S$). Two classes of systems are distinguished: the discrete-continuous...

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  • Entanglement of genuinely entangled subspaces and states: Exact, approximate, and numerical results

    Publication

    - PHYSICAL REVIEW A - Year 2019

    Genuinely 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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  • Quantifying Contextuality

    Publication
    • A. Grudka
    • K. Horodecki
    • M. Horodecki
    • P. Horodecki
    • R. Horodecki
    • P. Joshi
    • W. Kłobus
    • A. Wójcik

    - PHYSICAL REVIEW LETTERS - Year 2014

    Contextuality 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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  • Mixed, quantum-classical description of electron density transfer in the collision process

    Publication

    - MOLECULAR PHYSICS - Year 2024

    In this work, we investigate an ion-atom model describing the time-dependent evolution of electron density during the collision. For a S3+- H system, numerical simulations are based on classical trajectory calculations, and the electron density behaviour is described with the time-dependent Schrödinger equation. We apply the finite difference method to obtain quantitative insights into the charge transfer dynamics, providing detailed...

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  • The symmetric extendibility of quantum states

    Studies on the symmetric extendibility of quantum states have become particularly important in the context of the analysis of one-way quantum measures of entanglement, and the distillability and security of quantum protocols. In this paper we analyze composite systems containing a symmetric extendible part, with particular attention devoted to the one-way security of such systems. Further, we introduce a new one-way entanglement...

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  • Interactions of telomeric proteins with nucleic acids: sequence recognition on intact and oxidatively damaged telomeres

    Publication

    - Year 2019

    Telomeres are complex nucleoprotein assemblies that play a vital role in the maintenance of functional ends of linear chromosomes. Telomeric DNA, composed of tandem repeats of the 5'-TTAGGG-3' motif, solves the so-called end replication problem: as chromosomes shorten with each cell division, no information is lost, and the telomere can be re-extended. In the cell, many protein factors regulate telomere length, nuclear positioning...

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  • Amplifying the Randomness of Weak Sources Correlated With Devices

    Publication

    - IEEE TRANSACTIONS ON INFORMATION THEORY - Year 2017

    The problem of device-independent randomness amplification against no-signaling adversaries has so far been studied under the assumption that the weak source of randomness is uncorrelated with the (quantum) devices used in the amplification procedure. In this paper, we relax this assumption, and reconsider the original protocol of Colbeck and Renner using a Santha-Vazirani (SV) source. To do so, we introduce an SV-like condition...

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  • Magnetic field mapping along a NV-rich nanodiamond-doped fiber

    Publication
    • A. Filipkowski
    • M. Mrózek
    • G. Stępniewski
    • M. Ficek
    • D. Pysz
    • W. Gawlik
    • R. Buczyński
    • A. M. Wojciechowski
    • M. Klimczak

    - APPLIED PHYSICS LETTERS - Year 2024

    Integration of NV−-rich diamond with optical fibers enables guiding quantum information on the spin state of the NV− color center. Diamond-functionalized optical fiber sensors have been demonstrated with impressive sub-nanotesla magnetic field sensitivities over localized magnetic field sources, but their potential for distributed sensing remains unexplored. The volumetric incorporation of diamonds into the optical fiber core allows...

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  • Experimental and Theoretical Screening for Green Solvents Improving Sulfamethizole Solubility

    Publication

    - Materials - Year 2021

    Solubility enhancement of poorly soluble active pharmaceutical ingredients is of crucial importance for drug development and processing. Extensive experimental screening is limited due to the vast number of potential solvent combinations. Hence, theoretical models can offer valuable hints for guiding experiments aimed at providing solubility data. In this paper, we explore the possibility of applying quantum-chemistry-derived...

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  • Direct estimation of linear and nonlinear functionals of quantum state

    Publication
    • A. Ekert
    • C. M. Alves
    • D. K. Oi
    • M. Horodecki
    • P. Horodecki
    • L. C. Kwek

    - PHYSICAL REVIEW LETTERS - Year 2002

    We present a simple quantum network, based on the controlled-SWAP gate, that can extract certain properties of quantum states without recourse to quantum tomography. It can be used as a basic building block for direct quantum estimations of both linear and nonlinear functionals of any density operator. The network has many potential applications ranging from purity tests and eigenvalue estimations to direct characterization of...

  • The Role of Electrostatics in Enzymes: Do Biomolecular Force Fields Reflect Protein Electric Fields?

    Publication

    - Journal of Chemical Information and Modeling - Year 2020

    Preorganization of large, directionally oriented, electric fields inside protein active sites has been proposed as a crucial contributor to catalytic mechanism in many enzymes, and it may be efficiently investigated at the atomistic level with molecular dynamics simulations. Here, we evaluate the ability of the AMOEBA polarizable force field, as well as the additive Amber ff14SB and Charmm C36m models, to describe the electric...

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  • Calculating the Partition Coefficients of Organic Solvents in Octanol/Water and Octanol/Air

    Publication

    - Journal of Chemical Information and Modeling - Year 2019

    Partition coefficients define how a solute is distributed between two immiscible phases at equilibrium. The experimental estimation of partition coefficients in a complex system can be an expensive, difficult, and time-consuming process. Here a computational strategy to predict the distributions of a set of solutes in two relevant phase equilibria is presented. The octanol/water and octanol/air partition coefficients are predicted...

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  • Quantum entanglement

    Publication

    - REVIEWS OF MODERN PHYSICS - Year 2009

    All 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

    Publication

    Classical 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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  • Structure of the Resource Theory of Quantum Coherence

    Publication
    • A. Streltsov
    • S. Rana
    • P. Boes
    • R. Eisert

    - PHYSICAL REVIEW LETTERS - Year 2017

    Quantum coherence is an essential feature of quantum mechanics which is responsible for the departure between the classical and quantum world. The recently established resource theory of quantum coherence studies possible quantum technological applications of quantum coherence, and limitations that arise if one is lacking the ability to establish superpositions. An important open problem in this context is a simple characterization...

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  • Hybrid no-signaling-quantum correlations

    Publication

    - NEW JOURNAL OF PHYSICS - Year 2022

    Fundamental investigations in non-locality have shown that while the no-signaling principle alone is not sufficient to single out the set of quantum non-local correlations, local quantum mechanics and no-signaling together exactly reproduce the set of quantum correlations in the two-party Bell scenario. Here, we introduce and study an intermediate hybrid no-signaling quantum set of non-local correlations that we term HNSQ in the...

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  • Quantum entanglement in time

    Publication

    In this paper we present a concept of quantum entanglement in time in a context of entangled consistent histories. These considerations are supported by presentation of necessary tools closely related to those acting on a space of spatial multipartite quantum states. We show that in similarity to monogamy of quantum entanglement in space, quantum entanglement in time is also endowed with this property for a particular history....

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  • Quantum communication complexity advantage implies violation of a Bell inequality

    Publication

    - PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA - Year 2016

    We obtain a general connection between a quantum advantage in communication complexity and non-locality. We show that given any protocol offering a (sufficiently large) quantum advantage in communication complexity, there exists a way of obtaining measurement statistics which violate some Bell inequality. Our main tool is port-based teleportation. If the gap between quantum and classical communication complexity can grow arbitrarily...

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  • Quantum origins of objectivity

    Publication

    - PHYSICAL REVIEW A - Year 2015

    In 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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  • Tip-Based Nanofabrication as a Rapid Prototyping Tool for Quantum Science and Technology

    Publication

    Tip-Based Nanofabication as a Rapid Prototyping Tool for Quantum Science and Technology discusses the development of cantilevered nanotips techniques of quantum devices prototyping and how they evolved from scanning probe microscopy. Also covered are the advantages and future prospects of atomic resolution capability and how to use this enabling technology as a rapid prototyping tool for quantum science and technology.

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  • Quantum-correlation breaking channels, broadcasting scenarios, and finite Markov chains

    Publication

    - PHYSICAL REVIEW A - Year 2012

    One 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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  • The decay of quantum correlations between quantum dot spin qubits and the characteristics of its magnetic-field dependence

    Publication

    - EPL-EUROPHYS LETT - Year 2014

    We address the question of the role of quantum correlations beyond entanglement in the context of quantum magnetometry. We study the evolution of the rescaled variant of the geometric quantum discord of two electron-spin qubits interacting with an environment of nuclear spins via the hyperfine interaction. We have found that quantum correlations display a strong magnetic-field sensitivity which can be utilized for decoherence-driven...

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  • Direct detection of quantum entanglement

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2002

    Basing on positive maps separability criterion we propose the experimentally viable, direct detection of quantum entanglement. It is efficient and does not require any a priori knowledge about the state. For two qubits it provides a sharp (i.e., “if and only if”) separability test and estimation of amount of entanglement. We view this method as a new form of quantum computation, namely, as a decision problem with quantum data structure.

  • Efficient bounds on quantum-communication rates via their reduced variants

    Publication

    - PHYSICAL REVIEW A - Year 2010

    We 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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  • Quantum strategies for rendezvous and domination tasks on graphs with mobile agents

    Publication

    - PHYSICAL REVIEW A - Year 2024

    This paper explores the application of quantum nonlocality, a renowned and unique phenomenon acknowledged as a valuable resource. Focusing on an alternative application, we demonstrate its quantum advantage for mobile agents engaged in specific distributed tasks without communication. The research addresses the significant challenge of rendezvous on graphs and introduces a distributed task for mobile agents grounded in the graph...

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  • Objectivity in the non-Markovian spin-boson model

    Publication

    - PHYSICAL REVIEW A - Year 2017

    Objectivity constitutes one of the main features of the macroscopic classical world. An important aspect of the quantum-to-classical transition issue is to explain how such a property arises from the microscopic quantum theory. Recently, within the framework of open quantum systems, there has been proposed such a mechanism in terms of the so-called spectrum broadcast structures. These are multipartite quantum states of the system...

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  • Entangled Histories vs. the Two-State-Vector Formalism - Towards a Better Understanding of Quantum Temporal Correlations

    Publication

    The Two-State-Vector formalism and the Entangled Histories formalism are attempts to betterunderstand quantum correlations in time. Both formalisms share some similarities, but they are notidentical, having subtle differences in their interpretation and manipulation of quantum temporalstructures. However, the main objective of this paper is to prove that, with appropriately definedscalar products, both formalisms can be...

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  • Remarkable visible-light induced hydrogen generation with ZnIn2S4 microspheres/CuInS2 quantum dots photocatalytic system

    Publication
    • O. Cavdar
    • A. Malankowska
    • D. Amgar
    • P. Mazierski
    • J. Łuczak
    • W. Lisowski
    • A. Zaleska-Medynska

    - INTERNATIONAL JOURNAL OF HYDROGEN ENERGY - Year 2021

    A new and active material in the form of ZnIn2S4 microspheres decorated by CuInS2 quantum dots have been obtained by hydrothermal method for the first time. The optimum amount of CuInS2 quantum dots (1.13 wt.%) introduced into rection medium during ZnIn2S4 microspheres synthesis increased the photocatalytic H2 generation rate by 2.5 times than that of bare ZnIn2S4 photocatalysis under visible light irradiation. This sample exhibited...

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  • Swapping Space for Time: An Alternative to Time-Domain Interferometry

    Publication

    Young's double-slit experiment [1] requires two waves produced simultaneously at two different points in space. In quantum mechanics the waves correspond to a single quantum object, even as complex as a big molecule. An interference is present as long as one cannot tell for sure which slit is chosen by the object. The more we know about the path, the worse the interference. In the paper we show that quantum mechanics allows for...

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  • Quantum corrections to phi^4 model solutions and applications to Heisenberg chain dynamics

    The 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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  • Quantum corrections to 4 model solutions and applications to Heisenberg chain dynamics

    The 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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