arXiv subjects

Alexander Streltsov

Publications and source records attributed to Alexander Streltsov.

71 records · Page 4Linked to original sources

arXiv2016

The power of the resource theory of genuine quantum coherence

Any quantum resource theory is based on free states and free operations, i.e., states and operations which can be created and performed at no cost. In the resource theory of coherence free states are diagonal in some fixed basis, and free operations are those which cannot create coherence for some particular experimental realization. Recently, some problems of this approach have been discussed, and new sets of operations have been proposed to resolve these problems. As an example for such a problem, a quantum operation can be incoherent in one particular experimental realization, but it still can create large amount of coherence in another. This problem is resolved by the framework of genuine quantum coherence. Here, we investigate this concept further and study other more general sets of operations which cannot create coherence in any experimental realization. We analyze in detail the mathematical structure of this class of maps and use this to study possible state transformations under these operations. We show that deterministic manipulation is severely limited, even in the asymptotic settings. In particular, this framework does not have a unique golden unit, i.e., there is no single state from which all other states can be created deterministically with the free operations. On the other hand, we show that these theories allow for a richer structure in what comes to stochastic manipulation of states. In particular, we determine the optimal probability of conversion among pure states with genuinely incoherent operations. Still, the aforementioned limitations suggest that any reasonably powerful resource theory of coherence must contain free operations which can potentially create coherence in some experimental realization.

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arXiv2016

Entanglement distribution and quantum discord

Establishing entanglement between distant parties is one of the most important problems of quantum technology, since long-distance entanglement is an essential part of such fundamental tasks as quantum cryptography or quantum teleportation. In this lecture we review basic properties of entanglement and quantum discord, and discuss recent results on entanglement distribution and the role of quantum discord therein. We also review entanglement distribution with separable states, and discuss important problems which still remain open. One such open problem is a possible advantage of indirect entanglement distribution, when compared to direct distribution protocols.

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arXiv2016

Asymptotic role of entanglement in quantum metrology

Quantum systems allow one to sense physical parameters beyond the reach of classical statistics---with resolutions greater than $1/N$, where $N$ is the number of constituent particles independently probing a parameter. In the canonical phase sensing scenario the \emph{Heisenberg Limit} $1/N^{2}$ may be reached, which requires, as we show, both the relative size of the largest entangled block and the geometric measure of entanglement to be nonvanishing as $N\to\infty$. Yet, we also demonstrate that in the asymptotic $N$ limit any precision scaling arbitrarily close to the Heisenberg Limit ($1/N^{2-\varepsilon}$ with any $\varepsilon>0$) may be attained, even though the system gradually becomes noisier and separable, so that both the above entanglement quantifiers asymptotically vanish. Our work shows that sufficiently large quantum systems achieve nearly optimal resolutions despite their relative amount of entanglement being arbitrarily small. In deriving our results, we establish the continuity relation of the quantum Fisher information evaluated for a phaselike parameter, which lets us link it directly to the geometry of quantum states, and hence naturally to the geometric measure of entanglement.

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arXiv2015

Progress towards a unified approach to entanglement distribution

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 broad theoretical background for the development of such technologies. In particular, we investigate the question of whether entanglement distribution is more efficient if some amount of entanglement -- or some amount of correlations in general -- is available prior to the transmission stage of the protocol. We show that in the presence of noise the answer to this question strongly depends on the type of noise and on the way how entanglement is quantified. On the one hand, subadditive entanglement measures do not show advantage of preshared correlations if entanglement is established via combinations of single-qubit Pauli channels. On the other hand, based on the superadditivity conjecture of distillable entanglement, we provide evidence that this phenomenon occurs for this measure. These results strongly suggest that sending one half of some pure entangled state down a noisy channel is the best strategy for any subadditive entanglement quantifier, thus paving the way to a unified approach for entanglement distribution which does not depend on the nature of noise. We also provide general bounds for entanglement distribution involving quantum discord, and present a counter-intuitive phenomenon of the advantage of arbitrarily little entangled states over maximally entangled ones, which may also occur for quantum channels relevant in experiments.

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arXiv2015

Concentrating tripartite quantum information

We introduce the concentrated information of tripartite quantum states. For three parties Alice, Bob, and Charlie, it is defined as the maximal mutual information achievable between Alice and Charlie via local operations and classical communication performed by Charlie and Bob. We derive upper and lower bounds to the concentrated information, and obtain a closed expression for it on several classes of states including arbitrary pure tripartite states in the asymptotic setting. We show that distillable entanglement, entanglement of assistance, and quantum discord can all be expressed in terms of the concentrated information, thus revealing its role as a unifying informational primitive. We finally investigate quantum state merging of mixed states with and without additional entanglement. The gap between classical and quantum concentrated information is proven to be an operational figure of merit for mixed state merging in absence of additional entanglement. Contrary to pure state merging, our analysis shows that classical communication in both directions can provide advantage for merging of mixed states.

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arXiv2015

Measuring Quantum Coherence with Entanglement

Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of coherence as an operational resource are still very limited. Here we show that any degree of coherence with respect to some reference basis can be converted to entanglement via incoherent operations. This finding allows us to define a novel general class of measures of coherence for a quantum system of arbitrary dimension, in terms of the maximum bipartite entanglement that can be generated via incoherent operations applied to the system and an incoherent ancilla. The resulting measures are proven to be valid coherence monotones satisfying all the requirements dictated by the resource theory of quantum coherence. We demonstrate the usefulness of our approach by proving that the fidelity-based geometric measure of coherence is a full convex coherence monotone, and deriving a closed formula for it on arbitrary single-qubit states. Our work provides a clear quantitative and operational connection between coherence and entanglement, two landmark manifestations of quantum theory and both key enablers for quantum technologies.

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arXiv2014

Quantum Discord and its Role in Quantum Information Theory

Quantum entanglement is the most popular kind of quantum correlations, and its fundamental role in several tasks in quantum information theory like quantum cryptography, quantum dense coding, and quantum teleportation is undeniable. However, recent results suggest that various applications in quantum information theory do not require entanglement, and that their performance can be captured by a new type of quantum correlations which goes beyond entanglement. Quantum discord, introduced by Zurek more than a decade ago, is the most popular candidate for such general quantum correlations. In this work we give an introduction to this modern research direction. After a short review of the main concepts of quantum theory and entanglement, we present quantum discord and general quantum correlations, and discuss three applications which are based on this new type of correlations: remote state preparation, entanglement distribution, and transmission of correlations. We also give an outlook to other research in this direction.

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arXiv2013

Limits for entanglement distribution with separable states

Entanglement distribution with separable states has recently attracted considerable attention. Recent results suggest that quantum discord - a measure for quantum correlations beyond entanglement - is responsible for this counterintuitive phenomenon. In this work we study this question from a different perspective, and find minimal requirements for a separable state to be useful for entanglement distribution. Surprisingly, we find that the presence of quantum discord is not sufficient to ensure entanglement distribution: there exist states with nonzero quantum discord which nevertheless cannot be used for entanglement distribution. As a result, we show that entanglement distribution is not possible with rank two separable states. Our work sheds new light on the task of entanglement distribution with separable states, and reveals a new classification of quantum states with respect to their usefulness for this task.

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arXiv2013

Quantum discord cannot be shared

Niels Bohr proposed that the outcome of the measurement becomes objective and real, and, hence, classical, when its results can be communicated by classical means. In this work we revisit Bohr's postulate using modern tools from the quantum information theory. We find a full confirmation of Bohr's idea: if a measurement device is in a nonclassical state, the measurement results cannot be communicated perfectly by classical means. In this case some part of information in the measurement apparatus is lost in the process of communication: the amount of this lost information turns out to be the quantum discord. The information loss occurs even when the apparatus is not entangled with the system of interest. The tools presented in this work allow to generalize Bohr's postulate: we show that for pure system-apparatus states quantum communication does not provide any advantage when measurement results are communicated to more than one recipient. We further demonstrate the superiority of quantum communication to two recipients on a mixed system-apparatus state and show that this effect is fundamentally different from quantum state cloning.

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arXiv2012

Are general quantum correlations monogamous?

Quantum entanglement and quantum non-locality are known to exhibit monogamy, that is, they obey strong constraints on how they can be distributed among multipartite systems. Quantum correlations that comprise and go beyond entanglement are quantified by, e.g., quantum discord. It was observed recently that for some states quantum discord is not monogamous. We prove in general that any measure of correlations that is monogamous for all states and satisfies reasonable basic properties must vanish for all separable states: only entanglement measures can be strictly monogamous. Monogamy of other than entanglement measures can still be satisfied for special, restricted cases: we prove that the geometric measure of discord satisfies the monogamy inequality on all pure states of three qubits.

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arXiv2012

Quantum cost for sending entanglement

Establishing quantum entanglement between two distant parties is an essential step of many protocols in quantum information processing. One possibility for providing long-distance entanglement is to create an entangled composite state within a lab and then physically send one subsystem to a distant lab. However, is this the "cheapest" way? Here, we investigate the minimal "cost" that is necessary for establishing a certain amount of entanglement between two distant parties. We prove that this cost is intrinsically quantum, and is specified by quantum correlations. Our results provide an optimal protocol for entanglement distribution and show that quantum correlations are the essential resource for this task.

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arXiv2011

Behavior of Quantum Correlations under Local Noise

We characterize the behavior of quantum correlations under the influence of local noisy channels. Intuition suggests that such noise should be detrimental for quantumness. When considering qubit systems, we show for which channel this is indeed the case: the amount of quantum correlations can only decrease under the action of unital channels. However, non-unital channels (e.g. such as dissipation) can create quantum correlations for some initially classical state. Furthermore, for higher-dimensional systems even unital channels may increase the amount of quantum correlations. Thus, counterintuitively, local decoherence can generate quantum correlations.

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arXiv2011

Linking Quantum Discord to Entanglement in a Measurement

We show that a von Neumann measurement on a part of a composite quantum system unavoidably creates distillable entanglement between the measurement apparatus and the system if the state has nonzero quantum discord. The minimal distillable entanglement is equal to the one-way information deficit. The quantum discord is shown to be equal to the minimal partial distillable entanglement that is the part of entanglement which is lost, when we ignore the subsystem which is not measured. We then show that any entanglement measure corresponds to some measure of quantum correlations. This powerful correspondence also yields necessary properties for quantum correlations. We generalize the results to multipartite measurements on a part of the system and on the total system.

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arXiv2011

Easy implementable algorithm for the geometric measure of entanglement

We present an easy implementable algorithm for approximating the geometric measure of entanglement from above. The algorithm can be applied to any multipartite mixed state. It involves only the solution of an eigenproblem and finding a singular value decomposition, no further numerical techniques are needed. To provide examples, the algorithm was applied to the isotropic states of 3 qubits and the 3-qubit XX model with external magnetic field.

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arXiv2010

Linking a distance measure of entanglement to its convex roof

An important problem in quantum information theory is the quantification of entanglement in multipartite mixed quantum states. In this work, a connection between the geometric measure of entanglement and a distance measure of entanglement is established. We present a new expression for the geometric measure of entanglement in terms of the maximal fidelity with a separable state. A direct application of this result provides a closed expression for the Bures measure of entanglement of two qubits. We also prove that the number of elements in an optimal decomposition w.r.t. the geometric measure of entanglement is bounded from above by the Caratheodory bound, and we find necessary conditions for the structure of an optimal decomposition.

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arXiv2009

Geometric measure of entanglement compared to measures based on fidelity

One of the biggest problems in the theory of quantum information is the quantification of amount of entanglement in an arbitrary multipartite mixed state. Different axiomatic and operational measures were proposed so far. In this work we will establish a connection between geometric measure of entanglement proposed in [Phys. Rev. A 68, 042307 (2003)] and measures based on fidelity. One result will be, that geometric and revised geometric measure of entanglement proposed in [J. Phys. A: Math. Theor. 40, 3507 (2007)] are equal. Further a useful expression for fidelity is derived.

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arXiv2009

Bures measure of entanglement of an arbitrary state of two qubits

In Phys. Rev. Lett. 80, 2245 (1998) an explicit expression for entanglement of formation for any two qubit state was given. Based on this result we present an expression for the Bures measure of entanglement for two qubit states. This measure was proposed in Phys. Rev. A 57, 1619 (1998), where the authors showed that it satisfies all properties every entanglement measure must have.

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