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M. Piani

Publications and source records attributed to M. Piani.

At least 19 recordsLinked to original sources
arXiv2017

A formalism for steering with local quantum measurements

We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signalling assemblages via non-positive local hidden-state models. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone.

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arXiv2014

Quantifying non-classical and beyond-quantum correlations in the unified operator formalism

Acin et al. introduced a unified framework for the study of no-signalling correlations. Such a framework is based on the notion of local quantum measurements, but, in order to account for beyond-quantum correlations, global pseudo-states that are not positive semidefinite are allowed. After a short review of the formalism, we consider its use in the quantification of both general non-local and beyond-quantum correlations. We argue that the unified framework for correlations provides a simple approach to such a quantification, in particular when the quantification is meant to be operational and meaningful in a resource-theory scenario, i.e., when considering the processing of resources by means of non-resources. We relate different notions of robustness of correlations, both at the level of (pseudo-)states and abstract probability distributions, with particular focus on the beyond-quantum robustness of correlations and pseudo-states. We revisit known results and argue that, within the unified framework, the relation between the two levels---that of operators and that of probability distributions---is very strict. We point out how the consideration of robustness at the two levels leads to a natural framework for the quantification of entanglement in a device-independent way. Finally, we show that the beyond-quantum robustness of the non-positive operators needed to achieve beyond-quantum correlations coincides with their negativity and their distance from the set of quantum states. As an example, we calculate the beyond-quantum robustness for the case of a noisy Popescu-Rohrlich box.

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arXiv2012

Quantum discord bounds the amount of distributed entanglement

The ability to distribute quantum entanglement is a prerequisite for many fundamental tests of quantum theory and numerous quantum information protocols. Two distant parties can increase the amount of entanglement between them by means of quantum communication encoded in a carrier that is sent from one party to the other. Intriguingly, entanglement can be increased even when the exchanged carrier is not entangled with the parties. However, in light of the defining property of entanglement stating that it cannot increase under classical communication, the carrier must be quantum. Here we show that, in general, the increase of relative entropy of entanglement between two remote parties is bounded by the amount of non-classical correlations of the carrier with the parties as quantified by the relative entropy of discord. We study implications of this bound, provide new examples of entanglement distribution via unentangled states and put further limits on this phenomenon.

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arXiv2011

Operational interpretations of quantum discord

Quantum discord quantifies non-classical correlations going beyond the standard classification of quantum states into entangled and unentangled ones. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first operational meaning in terms of entanglement consumption in an extended quantum state merging protocol. We further relate the asymmetry of quantum discord with the performance imbalance in quantum state merging and dense coding.

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arXiv2010

Universal resources for approximate and stochastic measurement-based quantum computation

We investigate which quantum states can serve as universal resources for approximate and stochastic measurement-based quantum computation, in the sense that any quantum state can be generated from a given resource by means of single-qubit (local) operations assisted by classical communication. More precisely, we consider the approximate and stochastic generation of states, resulting e.g. from a restriction to finite measurement settings or from possible imperfections in the resources or local operations. We show that entanglement-based criteria for universality obtained for the exact, deterministic case can be lifted to the much more general approximate, stochastic case, moving from the idealized situation considered in previous works, to the practically relevant context of non-perfect state preparation. We find that any entanglement measure fulfilling some basic requirements needs to reach its maximum value on some element of an approximate, stochastic universal family of resource states, as the resource size grows. This allows us to rule out various families of states as being approximate, stochastic universal. We provide examples of resources that are efficient approximate universal, but not exact deterministic universal. We also study the robustness of universal resources for measurement-based quantum computation under realistic assumptions about the (imperfect) generation and manipulation of entangled states, giving an explicit expression for the impact that errors made in the preparation of the resource have on the possibility to use it for universal approximate and stochastic state preparation. Finally, we discuss the relation between our entanglement-based criteria and recent results regarding the uselessness of states with a high degree of geometric entanglement as universal resources.

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arXiv2010

Unified Framework for Correlations in Terms of Local Quantum Observables

We provide a unified framework for nonsignalling quantum and classical multipartite correlations, allowing all to be written as the trace of some local (quantum) measurements multiplied by an operator. The properties of this operator define the corresponding set of correlations.We then show that if the theory is such that all local quantum measurements are possible, one obtains the correlations corresponding to the extension of Gleason's Theorem to multipartite systems. Such correlations coincide with the quantum ones for one and two parties, but we prove the existence of a gap for three or more parties.

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arXiv2009

Inseparability criteria based on matrices of moments

Inseparability criteria for continuous and discrete bipartite quantum states based on moments of annihilation and creation operators are studied by developing the idea of Shchukin-Vogel criterion [Phys. Rev. Lett. {\bf 95}, 230502 (2005)]. If a state is separable, then the corresponding matrix of moments is separable too. Thus, we derive generalized criteria, based on the separability properties of the matrix of moments, are thus derived. In particular, a new criterion based on realignment of moments in the matrix is proposed as an analogue of the standard realignment criterion for density matrices. Other inseparability inequalities are obtained by applying positive maps to the matrix of moments. Usefulness of the Shchukin-Vogel criterion to describe bipartite-entanglement of more than two modes is demonstrated: We obtain some previously known three-mode inseparability criteria originally derived from the Cauchy-Schwarz inequality, and we introduce new ones.

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arXiv2009

Quantum repeaters with imperfect memories: cost and scalability

Memory dephasing and its impact on the rate of entanglement generation in quantum repeaters is addressed. For systems that rely on probabilistic schemes for entanglement distribution and connection, we estimate the maximum achievable rate per employed memory for our optimized partial nesting protocol. We show that, for any given distance $L$, the polynomial scaling of rate with distance can only be achieved if quantum memories with coherence times on the order of $L/c$ or longer, with $c$ being the speed of light in the channel, are available. The above rate degrades as a power of $\exp[-\sqrt{(L/c)/ τ_c}]$ with distance when the coherence time $τ_c \ll L/c$.

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arXiv2009

All entangled states are useful for channel discrimination

We prove that every entangled state is useful as a resource for the problem of minimum-error channel discrimination. More specifically, given a single copy of an arbitrary bipartite entangled state, it holds that there is an instance of a quantum channel discrimination task for which this state allows for a correct discrimination with strictly higher probability than every separable state.

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arXiv2009

Broadcast copies reveal the quantumness of correlations

We study the quantumness of bipartite correlations by proposing a quantity that combines a measure of total correlations -- mutual information -- with the notion of broadcast copies -- i.e., generally nonfactorized copies -- of bipartite states. By analyzing how our quantity increases with the number of broadcast copies, we are able to classify classical, separable, and entangled states. This motivates the definition of the broadcast regularization of mutual information, the asymptotic minimal mutual information per broadcast copy, which we show to have many properties of an entanglement measure.

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arXiv2009

Relative Entropy of Entanglement and Restricted Measurements

We introduce variants of relative entropy of entanglement based on the optimal distinguishability from unentangled states by means of restricted measurements. In this way, we are able to prove that the standard regularized entropy of entanglement is strictly positive for all multipartite entangled states. In particular, this implies that the asymptotic creation of a multipartite entangled state by means of local operations and classical communication always requires the consumption of a non-local resource at a strictly positive rate.

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arXiv2007

Quantumness of ensemble from no-broadcasting principle

Quantum information, though not precisely defined, is a fundamental concept of quantum information theory which predicts many fascinating phenomena and provides new physical resources. A basic problem is to recognize the features of quantum systems responsible for those phenomena. One of such important features is that non-commuting quantum states cannot be broadcast: two copies cannot be obtained out of a single copy, not even reproduced marginally on separate systems. We focus on the difference of information contents between one copy and two copies which is a basic manifestation of the gap between quantum and classical information. We show that if the chosen information measure is the Holevo quantity, the difference between the information contents of one copy and two copies is zero if and only if the states can be broadcast. We propose a new approach in defining measures of quantumness of ensembles based on the difference of information contents between the original ensemble and the ensemble of duplicated states. We comment about the permanence property of quantum states and the recently introduced superbroadcasting operation. We also provide an Appendix where we discuss the status of quantum information in quantum physics, basing on the so-called isomorphism principle.

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arXiv2007

On quantum advantage in dense coding

The quantum advantage of dense coding is studied, considering general encoding quantum operations. Particular attention is devoted to the case of many senders, and it is shown that restrictions on the possible operations on the senders' side may make some quantum state useless for dense-coding. It is shown, e.g., that some states are useful for dense coding if the senders can communicate classically (but not quantumly), yet they cannot be used for dense coding, if classical communication is not allowed. These no-go results are actually independent of the particular quantification of the quantum advantage, being valid for any reasonable choice. It is further shown that the quantum advantage of dense coding satisfies a monogamy relation with the so-called entanglement of purification.

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arXiv2006

Class of PPT bound entangled states associated to almost any set of pure entangled states

We analyze a class of entangled states for bipartite $d \otimes d$ systems, with $d$ non-prime. The entanglement of such states is revealed by the construction of canonically associated entanglement witnesses. The structure of the states is very simple and similar to the one of isotropic states: they are a mixture of a separable and a pure entangled state whose supports are orthogonal. Despite such simple structure, in an opportune interval of the mixing parameter their entanglement is not revealed by partial transposition nor by the realignment criterion, i.e. by any permutational criterion in the bipartite setting. In the range in which the states are Positive under Partial Transposition (PPT), they are not distillable; on the other hand, the states in the considered class are provably distillable as soon as they are Nonpositive under Partial Transposition (NPT). The states are associated to any set of more than two pure states. The analysis is extended to the multipartite setting. By an opportune selection of the set of multipartite pure states, it is possible to construct mixed states which are PPT with respect to any choice of bipartite cuts and nevertheless exhibit genuine multipartite entanglement. Finally, we show that every $k$-positive but not completely positive map is associated to a family of nondecomposable maps.

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arXiv2005

On quantum non-signalling boxes

A classical non-signalling (or causal) box is an operation on classical bipartite input with classical bipartite output such that no signal can be sent from a party to the other through the use of the box. The quantum counterpart of such boxes, i.e. completely positive trace-preserving maps on bipartite states, though studied in literature, have been investigated less intensively than classical boxes. We present here some results and remarks about such maps. In particular, we analyze: the relations among properties as causality, non-locality and entanglement; the connection between causal and entanglement breaking maps; the characterization of causal maps in terms of the classification of states with fixed reductions. We also provide new proofs of the fact that every non-product unitary transformation is not causal, as well as for the equivalence of the so-called semicausality and semilocalizability properties.

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arXiv2004

Quantum dynamical semigroups and non-decomposable positive maps

We study dynamical semigroups of positive, but not completely positive maps on finite-dimensional bipartite systems and analyze properties of their generators in relation to non-decomposability and bound-entanglement. An example of non-decomposable semigroup leading to a 4x4-dimensional bound-entangled density matrix is explicitly obtained.

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arXiv2003

Complete positivity and dissipative factorized dynamics: some comments

After reviewing the main properties of time-evolutions of open quantum systems, some considerations about the positivity of factorized Markovian dynamics for bipartite systems are made. In particular, it is shown that the positivity of the whole time-evolution in general does not ask for the complete positivity of the single system time-evolutions, if they are allowed to differ. However, they must be completely positive if one is a small perturbation of the other, which is the typical situation for open systems in a heat bath.

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