Quantumness of correlations, quantumness of ensembles and quantum data hiding

Piani, Marco; Narasimhachar, Varun; Calsamiglia, John

doi:10.1088/1367-2630/16/11/113001

Cited by 31 publications

(62 citation statements)

References 69 publications

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“…It is easy to show that the square Bures and Hellinger distances d 2 Bu and d 2 He satisfy the flags condition, so that Proposition 3 applies in particular to these distances. The result applies to the trace distance d 1 as well, see [75].…”

Section: Response To Local Measurements and Unitary Perturbationsmentioning

confidence: 80%

“…The bounds d Bu (ρ, σ) 2 ≤ d 1 (ρ, σ) and d He (ρ, σ) 2 ≤ d 1 (ρ, σ), which are consequences of (74) and (75), have been first proven in the C * -algebra setting by Araki [4] and Holevo [42], respectively. An upper bound on d 1 (ρ, σ) similar to the one in (75) but with d Bu replaced by d He (which is weaker than the bound in (75) because of (74)) has been also derived by Holevo.…”

Section: Comparison Of the Bures Hellinger And Trace Distancesmentioning

confidence: 99%

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Geometric Measures of Quantum Correlations with Bures and Hellinger Distances

Spehner

Illuminati

Orszag

et al. 2017

Quantum Science and Technology

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Section: Response To Local Measurements and Unitary Perturbationsmentioning

confidence: 80%

Section: Comparison Of the Bures Hellinger And Trace Distancesmentioning

confidence: 99%

Geometric Measures of Quantum Correlations with Bures and Hellinger Distances

Spehner

Illuminati

Orszag

et al. 2017

Quantum Science and Technology

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“…All entangled states necessarily possess discord, but also unentangled states can. Discord plays a basic role in quantum information processing, being linked to the impossibility of local broadcasting of correlations and information [33], to quantum data hiding [34], to quantum data locking [35], to entanglement distribution [36,37], to quantum metrology [38], to quantum cryptography [39]. Here we shed light on the role of discord in the latter.…”

Section: Lemma 1 For Any ρ Ab and Any Product State σmentioning

confidence: 99%

Channel discrimination power of bipartite quantum states

Caiaffa¹,

Piani²

2018

Phys. Rev. A

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We quantify the usefulness of a bipartite quantum state in the ancilla-assisted channel discrimination of arbitrary quantum channels, formally defining a worst-case-scenario channel discrimination power for bipartite quantum states. We show that such a quantifier is deeply connected with the operator Schmidt decomposition of the state. We compute the channel discrimination power exactly for pure states, and provide upper and lower bounds for general mixed states. We show that highly entangled states can outperform any state that passes the realignment criterion for separability. Furthermore, while also unentangled states can be used in ancilla-assisted channel discrimination, we show that the channel discrimination power of a state is bounded by its quantum discord. PACS numbers:A quantum channel is the most general linear transformation a quantum system can undergo, capturing mathematically the notion of physical process and playing the role of basic block in quantum information processing [1]. A fundamental task that falls under the umbrella of quantum metrology [2, 3] is channel discrimination [4]. Channel discrimination is the task of telling apart two or more known channels which are each applied with some random a priori distribution to an input of our choice; think of the situation where we want to probe the presence or absence of a known magnetic field. In the prototypical and simplest case, two channels are applied just once with equal a priori probability distribution, and we perform a measurement on the output probe trying to infer the which-channel information. The goal is that of identifying the channel applied, with the highest possible probability of success. Channel discrimination is typically performed by tailoring the state of the input probe to the channels to be discriminated. In general, the wrong choice of input might not only make the probability of correct identification less than optimal, but it might make it altogether impossible, in the sense that, for some choice of input state, the output state could be the same for both channels, even when the latter differ.

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“…The surprisal of measurement recoverability quantifies the necessary disturbance introduced by manipulating locally (on B) the state ρ AB , through measurement and preparation. Notice that this can be generalized to any class of maps that correspond to a non-trivial (local) manipulation (see [20]), i.e., one can consider …”

Section: Of the Formmentioning

confidence: 99%

Hierarchy of Efficiently Computable and Faithful Lower Bounds to Quantum Discord

Piani

2016

Phys. Rev. Lett.

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Quantum discord expresses a fundamental non-classicality of correlations more general than quantum entanglement. We combine the no-local-broadcasting theorem, semidefinite-programming characterizations of quantum fidelity and quantum separability, and a recent breakthrough result of Fawzi and Renner about quantum Markov chains to provide a hierarchy of computationally efficient lower bounds to quantum discord. Such a hierarchy converges to the surprisal of measurement recoverability introduced by Seshadreesan and Wilde, and provides a faithful lower bound to quantum discord already at the lowest non-trivial level. Furthermore, the latter constitutes by itself a valid discord-like measure of the quantumness of correlations. PACS numbers:Introduction.-Correlations in quantum mechanics exhibit non-classical features that include non-locality [1], steering [2], entanglement [3], and quantum discord [4]. Quantum correlations play a fundamental role in quantum information processing and quantum technologies [5], which go from quantum cryptography [6] to quantum metrology [7]. While both non-locality and steering are manifestations of entanglement, quantum discord is a more general form of quantumness of correlations that includes entanglement but goes beyond it. In particular, almost all distributed states exhibit discord [8]. This fact calls for fully elevating the study of quantum discord to the quantitative level, since just certifying that discord is present may be considered of limited interest. While several approaches to the quantification of discord have been already proposed (see, e.g. [4,[9][10][11][12][13][14][15][16][17][18][19][20][21][22] and references therein), in this paper we significantly push forward a meaningful, reliable, and practical quantitative approach to the study of quantum discord that is based on fundamental quantum features of quantum correlations, and at the same time is computationally friendly.

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Quantumness of correlations, quantumness of ensembles and quantum data hiding

Cited by 31 publications

References 69 publications

Geometric Measures of Quantum Correlations with Bures and Hellinger Distances

Geometric Measures of Quantum Correlations with Bures and Hellinger Distances

Channel discrimination power of bipartite quantum states

Hierarchy of Efficiently Computable and Faithful Lower Bounds to Quantum Discord

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