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Search results for: BOUND ENTANGLED
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On quantum cryptography with bipartite bound entangled states
PublicationOstatnio 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...
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W-like bound entangled states and secure key distillation
PublicationWe 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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Rank two bibartite bound entangled states do not exist.
PublicationWykazano, 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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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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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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Completely entangled subspaces of entanglement depth k
PublicationWe introduce a class of entangled subspaces: completely entangled subspaces of entanglement depth k (k-CESs). These are subspaces of multipartite Hilbert spaces containing only pure states with an entanglement depth of at least k. We present an efficient construction of k-CESs of any achievable dimensionality in any multipartite scenario. Further, we discuss the relation between these subspaces and unextendible product bases (UPBs)....
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Simple sufficient condition for subspace to be completely or genuinely entangled
PublicationWe 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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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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Multipartite secret key distillation and bound entanglement
PublicationRecently 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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Bound on Bell inequalities by fraction of determinism and reverse triangle inequality
PublicationIt is an established fact that entanglement is a resource. Sharing an entangled state leads to nonlocal correlations and to violations of Bell inequalities. Such nonlocal correlations illustrate the advantage of quantum resources over classical resources. In this paper, we quantitatively study Bell inequalities with 2 × n inputs. As found in Gisin et al. [Int. J. Quantum. Inform. 05, 525 (2007)], quantum mechanical correlations...
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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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General paradigm for distilling classical key from quantum states
PublicationIn 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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Quantum entanglement in time
PublicationIn 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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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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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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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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Quantum key distribution based on private states: Unconditional security over untrusted channels with zero quantum capacity
PublicationIn 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...
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Experimental certification of more than one bit of quantum randomness in the two inputs and two outputs scenario
PublicationOne of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing...
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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...