Search results for: GENUINELY ENTANGLED SUBSPACE, GENUINELY MULTIPARTY ENTANGLEMENT, COMPLETELY ENTANGLED SUBSPACE, ENTANGLEMENT, SPACES OF MATRICES OF BOUNDED RANK - Bridge of Knowledge

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Search results for: GENUINELY ENTANGLED SUBSPACE, GENUINELY MULTIPARTY ENTANGLEMENT, COMPLETELY ENTANGLED SUBSPACE, ENTANGLEMENT, SPACES OF MATRICES OF BOUNDED RANK

Search results for: GENUINELY ENTANGLED SUBSPACE, GENUINELY MULTIPARTY ENTANGLEMENT, COMPLETELY ENTANGLED SUBSPACE, ENTANGLEMENT, SPACES OF MATRICES OF BOUNDED RANK

  • Simple sufficient condition for subspace to be completely or genuinely entangled

    Publication

    - NEW JOURNAL OF PHYSICS - Year 2021

    We introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We...

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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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  • An approach to constructing genuinely entangled subspaces of maximal dimension

    Publication

    Genuinely entangled subspaces (GESs) are the class of completely entangled subspaces that contain only genuinely multiparty entangled states. They constitute a particularly useful notion in the theory of entanglement but also have found an application, for instance, in quantum error correction and cryptography. In a recent study (Demianowicz and Augusiak in Phys Rev A 98:012313, 2018), we have shown how GESs can be efficiently...

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  • Universal construction of genuinely entangled subspaces of any size

    Publication

    We put forward a simple construction of genuinely entangled subspaces – subspaces supporting only genuinely multipartite entangled states – of any permissible dimensionality for any number of parties and local dimensions. The method uses nonorthogonal product bases, which are built from totally nonsingular matrices with a certain structure. We give an explicit basis for the constructed subspaces. An immediate consequence of our...

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  • Constructing genuinely entangled multipartite states with applications to local hidden variables and local hidden states models

    Publication

    - PHYSICAL REVIEW A - Year 2018

    Building upon the results of R. Augusiak et al. [Phys. Rev. Lett. 115, 030404 (2015)] we develop a general approach to the generation of genuinely entangled multipartite states of any number of parties from genuinely entangled states of a fixed number of parties, in particular, the bipartite entangled ones. In our approach, certain isometries whose output subspaces are either symmetric or genuinely entangled in some multipartite...

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  • A few steps more towards NPT bound entanglement

    Publication

    - IEEE TRANSACTIONS ON INFORMATION THEORY - Year 2010

    In 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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  • 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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  • 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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  • Entanglement and Nonlocality are Inequivalent for Any Number of Parties

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2015

    Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that these two phenomena are inequivalent, as there exist entangled states of two parties that do not violate any Bell inequality. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such a relation in multipartite...

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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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  • Progress towards a unified approach to entanglement distribution

    Publication

    - PHYSICAL REVIEW A - Year 2015

    Entanglement distribution is key to the success of secure communication schemes based on quantum mechanics, and there is a strong need for an ultimate architecture able to overcome the limitations of recent proposals such as those based on entanglement percolation or quantum repeaters. In this work we provide a broad theoretical background for the development of such technologies. In particular, we investigate the question of whether...

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  • Collective Uncertainty Entanglement Test

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2011

    For 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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  • Local hidden–variable models for entangled quantum states

    Publication

    While entanglement and violation of Bell inequalities were initially thought to be equivalent quantum phenomena, we now have different examples of entangled states whose correlations can be described by local hidden-variable models and, therefore, do not violate any of the Bell inequalities. We provide an up-to-date overview of the existing literature regarding local hidden-variable models for entangled quantum states, in both...

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  • All Nonclassical Correlations Can Be Activated into Distillable Entanglement

    Publication
    • M. Piani
    • S. Gharibian
    • G. Adesso
    • J. Calsamigilia
    • P. Horodecki
    • A. Winter

    - PHYSICAL REVIEW LETTERS - Year 2011

    We 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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  • 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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  • 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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  • Inequivalence of entanglement, steering, and Bell nonlocality for general measurements

    Publication
    • M. Quintino
    • T. Vértesi
    • D. Cavalcanti
    • R. Augusiak
    • M. Demianowicz
    • A. Acín
    • N. Brunner

    - PHYSICAL REVIEW A - Year 2015

    Einstein-Podolsky-Rosen steering is a form of inseparability in quantum theory commonly acknowledged to be intermediate between entanglement and Bell nonlocality. However, this statement has so far only been proven for a restricted class of measurements, namely, projective measurements. Here we prove that entanglement, one-way steering, two-way steering, and nonlocality are genuinely different considering general measurements,...

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  • W-like bound entangled states and secure key distillation

    Publication

    We construct multipartite entangled states with underlying W-type structuresatisfying positive partial transpose (PPT) condition under any (N −1)|1 partition. Then we showhow to distill a N-partite secure key from the states using two different methods: direct applicationof local filtering and novel random key distillation scheme in which we adopt the idea from recentresults on entanglement distillation. Open problems and possible...

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  • Quantum metrology: Heisenberg limit with bound entanglement

    Publication

    - PHYSICAL REVIEW A - Year 2015

    Quantum 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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  • Dynamics of quantum entanglement

    Publication

    - PHYSICAL REVIEW A - Year 2002

    A model of discrete dynamics of entanglement of a bipartite quantum state is considered. It involves a global unitary dynamics of the system and periodic actions of local bistochastic or decaying channel. For initially pure states the decay of entanglement is accompanied by an increase of von Neumann entropy of the system. We observe and discuss revivals of entanglement due to unitary interaction of subsystems. For some mixed states...

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  • Rank two bibartite bound entangled states do not exist.

    Publication

    - THEORETICAL COMPUTER SCIENCE - Year 2003

    Wykazano, że nie istnieją stany rzędu dwa które zawierałyby splątanie. Pokazano związki między lokalnym a globalnym rzędem macierzy gęstości oraz ewentualną możliwością wydestylowania kwantowego splątania.

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  • Multipartite secret key distillation and bound entanglement

    Publication

    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 Greenberger-Horne-Zeilinger (GHZ) structure and nonzero distillable...

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  • Entanglement-redistribution boxes

    Publication

    - PHYSICAL REVIEW A - Year 2008

    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...

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  • Constructive entanglement test from triangle inequality

    Publication

    - Journal of Physics A-Mathematical and Theoretical - Year 2014

    We derive a simple lower bound on the geometric measure of entanglement for mixed quantum states in the case of a general multipartite system. The main ingredient of the presented derivation is the triangle inequality applied to the root infidelity distance in the space of density matrices. The obtained bound leads to entanglement criteria with a straightforward interpretation. The proposed criteria provide an experimentally accessible,...

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  • Sensitivity of entanglement decay of quantum-dot spin qubits to the external magnetic field

    Publication

    - PHYSICAL REVIEW A - Year 2014

    We study the decay of entanglement of quantum-dot electron-spin qubits under hyperfine-interaction-mediated decoherence.We show that two-qubit entanglement of a single entangled initial state may exhibit decay characteristic of two disentanglement regimes in a single sample, when the externalmagnetic field is changed. The transition is manifested by the suppression of time-dependent entanglement oscillations which are superimposed...

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  • Sudden death of effective entanglement

    Publication

    - PHYSICAL REVIEW A - Year 2010

    Sudden death of entanglement is a well-known effect resulting from the finite volume of separable states. We study the case when the observer has a limited measurement capability and analyze the effective entanglement (i.e., entanglement minimized over the output data). We show that in the well-defined system of two quantum dots monitored by single-electron transistors, one may observe a sudden death of effective entanglement when...

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

    Publication
    • D. Yang
    • K. Horodecki
    • M. Horodecki
    • P. Horodecki
    • J. Oppenheim
    • W. Song

    - IEEE TRANSACTIONS ON INFORMATION THEORY - Year 2009

    New 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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  • 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.

  • Entangled Religions

    Journals

    eISSN: 2363-6696

  • Entanglement-swapping boxes and their communication properties

    Publication

    - PHYSICAL REVIEW A - Year 2008

    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...

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  • Entangled rendezvous: a possible application of Bell non-locality for mobile agents on networks

    Publication

    Rendezvous is an old problem of assuring that two or more parties, initially separated, not knowing the position of each other, and not allowed to communicate, are striving to meet without pre-agreement on the meeting point. This problem has been extensively studied in classical computer science and has vivid importance to modern and future applications. Quantum non-locality, like Bell inequality violation, has shown that in many...

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  • Subspace Algorithms for Face Verification

    Publication

    - Year 2011

    W rzeczywistych zastosowaniach problem weryfikacji wydaje się ważniejszy od klasyfikacji. Na ogół dysponujemy jedynie niewielkim zbiorem obrazów uczących reprezentujących daną osobę, a naszym zadaniem jest podjęcie decyzji odnośnie tego, czy nowo pozyskana fotografia jest do nich wystarczająco podobna - bez użycia oddzielnego zbioru przykładów negatywnych. W takim przypadku uzasadnione wydaje się zastosowanie metody podprzestrzeni,...

  • Separability in terms of a single entanglement witness

    Publication

    - PHYSICAL REVIEW A - Year 2013

    The 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...

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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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  • On structural physical approximations and entanglement breaking maps

    Publication

    - JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL - Year 2011

    Very recently, a conjecture saying that the so-called structural physical approximations (SPAs) to optimal positive maps (optimal entanglement witnesses) give entanglement breaking (EB) maps (separable states) has been posed (Korbicz et al 2008 Phys. Rev. A 78 062105). The main purpose of this contribution is to explore this subject. First, we extend the set of entanglement witnesses supporting the conjecture. Then, we ask whether...

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  • Homology algorithm based on acyclic subspace

    Publication

    - COMPUTERS & MATHEMATICS WITH APPLICATIONS - Year 2008

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  • Low-dimensional bound entanglement with one-way distillable cryptographic key

    Publication

    - IEEE TRANSACTIONS ON INFORMATION THEORY - Year 2008

    In 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...

  • 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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  • A Subspace-Splitting Moment-Matching Model-Order Reduction Technique for Fast Wideband FEM Simulations of Microwave Structures

    This article describes a novel model-order reduction (MOR) approach for efficient wide frequency band finite-element method (FEM) simulations of microwave components. It relies on the splitting of the system transfer function into two components: a singular one that accounts for the in-band system poles and a regular part that has no in-band poles. In order to perform this splitting during the reduction process, the projection...

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  • On quantum cryptography with bipartite bound entangled states

    Publication

    Ostatnio pokazano bezpośrednie zastosowanie splątania związanego w kryptografii kwantowej. W niniejszym artykule dokonano przeglądu niektórych najnowszych osiągnięć dotyczących tego zagadnienia. W szczególności przypomniano istotne pojęcia i definicje. Ponadto podano nową konstrukcję stanów o splątaniu związanym, posiadających bezpieczne korelacje, dostarczając w ten sposób niskowymiarowe (6x6) stany o splątaniu związanym z niezerowym...

  • Can Communication Power of Separable Correlations Exceed That of Entanglement Resource?

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2014

    The scenario of remote state preparation with a shared correlated quantum state and one bit of forward communication [B. Dakić et al., Nat. Phys. 8, 666 (2012)] is considered. Optimization of the transmission efficiency is extended to include general encoding and decoding strategies. The importance of the use of linear fidelity is recognized. It is shown that separable states cannot exceed the efficiency of entangled states by...

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

    Publication

    - PHYSICAL REVIEW A - Year 2010

    We 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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  • 12 [Chapter]. Bound entanglement

    Publication

    - Year 2007

    Kwantowe splątanie jest jednym z podstawowych elementów kwantowej teorii informacji. Jak wiadomo niskowymiarowe (2otimes 2 i 2otimes 3) splątane stany kwantowe są zawsze destylowalne. W wyższych wymiarach jednak istnieją stany, które mimo, że są splątane nie pozwalają na destylację. Ten rodzaj splątania, nazywany związanym, jest często trudny do wykrycia i pozornie bezużyteczny. Jak pokazują jednak liczne badania splątanie związane...

  • Direct detection of quantum entanglement

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

    - Year 2003

    Poddano dyskusji teorię splątania w kontekście historycznym. Omówiono detekcję splątania przy użyciu sieci złożonej z bramek kwantowych.

  • Locking entanglement with a single qubit

    Publication

    - Year 2005

    Badamy utratę plątania dwuczęściowego stanu narażanego na odrzucenie lub pomiar jednego kubitu.

  • Complementarity between entanglement-assisted and quantum distributed random access code

    Publication

    - PHYSICAL REVIEW A - Year 2017

    Collaborative communication tasks such as random access codes (RACs) employing quantum resources have manifested great potential in enhancing information processing capabilities beyond the classical limitations. The two quantum variants of RACs, namely, quantum random access code (QRAC) and the entanglement-assisted random access code (EARAC), have demonstrated equal prowess for a number of tasks. However, there do exist specific...

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  • Uncertainty quantification of modal parameter estimates obtained from subspace identification: An experimental validation on a laboratory test of a large-scale wind turbine blade

    Publication

    - ENGINEERING STRUCTURES - Year 2022

    The uncertainty afflicting modal parameter estimates stems from e.g., the finite data length, unknown, or partly measured inputs and the choice of the identification algorithm. Quantification of the related errors with the statistical Delta method is a recent tool, useful in many modern modal analysis applications e.g., damage diagnosis, reliability analysis, model calibration. In this paper, the Delta method-based uncertainty...

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  • Bound entanglement maximally violating Bell inequalities: quantum entanglement is not fully equivalent to cryptographic security

    Publication

    W pracy pokazano, że czterokubitowy stan o splątaniu związanym może maksymalnie łamać prostą nierówność Bella podobną do standardowej nierówności CHSH. Prostota rozważanego układu oraz odporność splątania sprawiają, że łamanie to jest obiecujące dla współczesnej technologii eksperymentalnej. Z drugiej strony, splątanie tego stanu nie pozwala na destylację bezpiecznego klucza kryptograficznego, zatem ani splątanie, ani maksymalne...

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  • On the distillation of cryptographic key from multipartie entangled quantum states

    Publication

    - Year 2008

    Celem pracy było uzupełnienie ogólnego paradygmatu destylacji bezpiecznego klucza kryptograficznego z dwucząstkowych stanów splątanych, a w szczegolności znalezienie nowych konstrukcji stanów kwantowych o splątaniu związanym z niezerowym destylowanym kluczem kryptograficznym. Kolejnym celem pracy było uogólnienie powyższego paradygmatu dwucząstkowego na przypadek wielu cząstek. W szczególności sformułowanie definicji wielocząstkowych...

  • Secure key from bound entanglement

    Publication

    - Year 2005

    Scharakteryzowaliśmy zestaw dzielonych kwantowych stanów, który zawiera kryptograficznie prywatny klucz. Pozwala nam to przerobić teorię prywatności jako paradygmat blisko związany z tą, która jest używana w manipulacjach splątania.