The project aims at the operational characterization of features of correlations specific to quantum systems. This will lead to a deeper understanding of Quantum Mechanics (QM) and of the behaviour of correlated systems, and contribute to the development of revolutionary Quantum Information Processing (QIP) technologies. QIP applications include the efficient simulation of quantum systems, more precise sensors, secure communications, and, ultimately, incomparably faster computers. QIP was born from the recognition that information can be processed according to the laws of QM. At the core of the advantage of QIP over classical information processing lie quantum correlations.

We work towards characterizing several forms of quantum correlations in a systematic and unified way. The results directly link to operational scenarios and applications, for example in metrology and communication. Where relevant, the characterization takes into account physical and practical constraints and limitations deriving from, e.g., the finite energy involved in physical processes and the necessarily incomplete information accessible to experimentalists.

At the core of the project are the objectives of characterizing and exploiting the quantum properties and behaviour – or, we will write in short, the *quantumness* – of correlated systems. On one hand, to take the best advantage of quantum correlations in QIP requires a targeted effort aimed at their understanding, optimization and exploitation. On the other hand, QIP fosters an operational and application-oriented approach to the analysis of quantum features. Thus, the development of QIP is inherently linked with the study of quantumness, and involves cutting-edge interdisciplinary research at the interface between Mathematics, Information Theory, Computer Science, Physics, and Foundations of Physics.

*Entanglement* corresponds to stronger-than-classical correlations that result when two or more quantum systems become so tightly intertwined that their shared properties dominate over their individual ones. Entanglement is at the heart of many QIP tasks and protocols [1]. However, the quantumness of correlations does not reduce simply to it, as quantum correlations need to be accessed and exploited by performing measurements. Based on the interplay between quantum states and local quantum measurements, the quantumness of correlations can thus assume stronger forms, like *steering* and *nonlocality*, for which entanglement is necessary but not sufficient, or weaker forms, like quantum *discord*, for which entanglement is sufficient but not necessary [2].

*Steering*, roughly speaking, is the possibility for one party of “controlling” the quantum state of the second party, going beyond what possible when dealing with correlations established only by classical means. *Nonlocality* corresponds instead to the lack of a classical model based on pre-established correlations to explain the outcomes of local measurements. Finally, *discord* is present when the extraction of correlations via measurements necessarily leads to the loss of some of the correlations. Nonlocality and steering have attracted a lot of interest in recent times [3] also in connection to *device-independent *[4] quantum cryptography [5], while discord has been scrutinized particularly for the possibility that it provides noise-resistant quantum advantage in QIP tasks [6]. Most importantly, these qualitatively different forms of the quantumness of correlations appear to be linked to – and be completely characterized by – very related operational scenarios in the area of metrology.

*Quantum metrology* deals with the measurement of parameters (e.g., the strength of a magnetic field) and discrimination procedures (e.g., between different physical evolutions, due to, for example to the presence or absence of an object, like in quantum illumination [7]) that are enhanced through the use of quantum effects [8].

The research proposed for this action involves the study of the quantumness of correlations in all of the above forms. Dr Piani will focus on obtaining a picture of quantum correlations as unified and as operational as possible.

[1] R. Horodecki et al., Rev. Mod. Phys. 81, 865 (2009).

[2] H. M. Wiseman et al., Phys. Rev. Lett. 98, 140402 (2007); N. Brunner et al., Rev. Mod. Phys. 86, 419 (2014); K. Modi et al., Rev. Mod. Phys. 84, 1655 (2012).

[3] See, e.g., P. Skrzypczyk et al., Phys. Rev. Lett. 112, 180404 (2014), and references therein.

[4] Device independence refers to the certification of properties of physical systems and of protocols independently of the specific experimental implementation. This approach provides a way to tackle the challenge of the increasing complexity of quantum experiments that makes their complete control unfeasible, or of the need for cryptographic schemes that are robust against malicious agents, including, e.g., the untrusted provider of the devices.

[5] A. Acin et al., Phys. Rev. Lett. 98, 230501 (2007).

[6] I. Georegescu, Nat. Phys. 10, 474 (2014).

[7] S. Lloyd, Science 321, 1463 (2008).

[8] V. Giovannetti et al., Nature Photonics 5, 222–229 (2011).

[9] M. Piani and J. Watrous, Phys. Rev. Lett. 102, 250501 (2009).

## Outputs of the project

Bartosz Regula, Marco Piani, Marco Cianciaruso, Thomas R. Bromley, Alexander Streltsov, Gerardo Adesso

“Converting multilevel nonclassicality into genuine multipartite entanglement”

arXiv:1704.04153

ABSTRACT: Nonclassicality in the form of quantum superposition can be related to entanglement in several frameworks, where such nonclassicality becomes the necessary and sufficient ingredient to generate entanglement under some natural interactions. Here we extend previous studies by presenting a general formalism for the conversion of nonclassicality into genuine multipartite entanglement, showing that a faithful unitary conversion between the two resources is always possible. Specializing to quantum coherence between the levels of a single quantum system as an instance of nonclassicality, we introduce explicit protocols for such a mapping. We further show that the conversion relates multilevel coherence and multipartite entanglement not only qualitatively, but also quantitatively, restricting the amount of entanglement achievable in the process and in particular yielding an equality between the two resources when quantified by fidelity-based geometric measures.

Matteo Caiaffa, Marco Piani

“Channel discrimination power of bipartite quantum states”

arXiv:1703.09656

ABSTRACT: 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.

Marco Piani

“Local Broadcasting of Quantum Correlations”

To appear in “Lectures on General Quantum Correlations and their Applications”, Fernandes Fanchini, F., de Oliveira Soares Pinto, D. & Adesso, G. (eds.)

arXiv:1608.02650

ABSTRACT: Operations that are trivial in the classical world, like accessing information without introducing any change or disturbance, or like copying information, become non-trivial in the quantum world. In this note we discuss several limitations in the local redistributing correlations, when it comes to dealing with bipartite quantum states. In particular, we focus on the task of local broadcasting, by discussing relevant no-go theorems, and by quantifying the non-classicality of correlations in terms of the degree to which local broadcasting is possible in an approximate fashion.

Marco Piani

“Hierarchy of Efficiently Computable and Faithful Lower Bounds to Quantum Discord”

Phys. Rev. Lett. 117, 080401 (2016)

DOI: https://doi.org/10.1103/PhysRevLett.117.080401

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ABSTRACT: Quantum discord expresses a fundamental nonclassicality of correlations that is more general than entanglement, but that, in its standard definition, is not easily evaluated. We derive a hierarchy of computationally efficient lower bounds to the standard quantum discord. Every nontrivial element of the hierarchy constitutes by itself a valid discordlike measure, based on a fundamental feature of quantum correlations: their lack of shareability. Our approach emphasizes how the difference between entanglement and discord depends on whether shareability is intended as a static property or as a dynamical process.

Cécilia Lancien, Sara Di Martino, Marcus Huber, Marco Piani, Gerardo Adesso, Andreas Winter

“Should Entanglement Measures be Monogamous or Faithful?”

Phys. Rev. Lett. 117, 060501 (2016)

DOI: https://doi.org/10.1103/PhysRevLett.117.060501

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ABSTRACT: “Is entanglement monogamous?” asks the title of a popular article [B. Terhal, IBM J. Res. Dev. 48, 71 (2004)], celebrating C. H. Bennett’s legacy on quantum information theory. While the answer is affirmativein the qualitative sense, the situation is less clear if monogamy is intended as a quantitative limitation on the distribution of bipartite entanglement in a multipartite system, given some particular measure of entanglement. Here, we formalize what it takes for a bipartite measure of entanglement to obey a general quantitative monogamy relation on all quantum states. We then prove that an important class of entanglement measures fail to be monogamous in this general sense of the term, with monogamy violations becoming generic with increasing dimension. In particular, we show that every additive and suitably normalized entanglement measure cannot satisfy any nontrivial general monogamy relation while at the same time faithfully capturing the geometric entanglement structure of the fully antisymmetric state in arbitrary dimension. Nevertheless, monogamy of such entanglement measures can be recovered if one allows for dimension-dependent relations, as we show explicitly with relevant examples.

Blog entry: Would you rather be monogamous or faithful?

Coverage by press: Phys.org

Alexander R. H. Smith, Marco Piani, Robert B. Mann

“Quantum reference frames associated with non-compact groups: the case of translations and boosts, and the role of mass”

Phys. Rev. A 94, 012333 (2016)

DOI: http://dx.doi.org/10.1103/PhysRevA.94.012333

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Quantum communication without a shared reference frame or the construction of a relational quantum theory requires the notion of a quantum reference frame. We analyze aspects of quantum reference frames associated with non-compact groups, specifically the group of spatial translations and Galilean boosts. We begin by demonstrating how the usually employed group average, used to dispense of the notion of an external reference frame, leads to unphysical states when applied to reference frames associated with non-compact groups. However, we show that this average does lead naturally to a reduced state on the relative degrees of freedom of a system, which was previously considered by Angelo et al. [1]. We then study in detail the informational properties of this reduced state for systems of two and three particles in Gaussian states.

Carmine Napoli, Thomas R. Bromley, Marco Cianciaruso, Marco Piani, Nathaniel Johnston, and Gerardo Adesso

“Robustness of coherence: An operational and observable measure of quantum coherence”

Phys. Rev. Lett. 116, 150502 (2016)

DOI: https://doi.org/10.1103/PhysRevLett.116.150502

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ABSTRACT: Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. Here, the robustness of coherence is defined and proven to be a full monotone in the context of the recently introduced resource theories of quantum coherence. The measure is shown to be observable, as it can be recast as the expectation value of a coherence witness operator for any quantum state. The robustness of coherence is evaluated analytically on relevant classes of states, and an efficient semidefinite program that computes it on general states is given. An operational interpretation is finally provided: the robustness of coherence quantifies the advantage enabled by a quantum state in a phase discrimination task.

Blog entry: A somewhat coherent post on a robust idea

Coverage by press: Phys.org, Daily Mail Online

Marco Piani, Marco Cianciaruso, Thomas R. Bromley, Carmine Napoli, Nathaniel Johnston, and Gerardo Adesso

“Robustness of asymmetry and coherence of quantum states”

Phys. Rev. A 93, 042107 (2016)

DOI: https://doi.org/10.1103/PhysRevA.93.042107

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ABSTRACT: Quantum states may exhibit asymmetry with respect to the action of a given group. Such an asymmetry of states can be considered a resource in applications such as quantum metrology, and it is a concept that encompasses quantum coherence as a special case. We introduce explicitly and study the robustness of asymmetry, a quantifier of asymmetry of states that we prove to have many attractive properties, including efficient numerical computability via semidefinite programming and an operational interpretation in a channel discrimination context. We also introduce the notion of asymmetry witnesses, whose measurement in a laboratory detects the presence of asymmetry. We prove that properly constrained asymmetry witnesses provide lower bounds to the robustness of asymmetry, which is shown to be a directly measurable quantity itself. We then focus our attention on coherence witnesses and the robustness of coherence, for which we prove a number of additional results; these include an analysis of its specific relevance in phase discrimination and quantum metrology, an analytical calculation of its value for a relevant class of quantum states, and tight bounds that relate it to another previously defined coherence monotone.