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Denis Rosset

Publications and source records attributed to Denis Rosset.

At least 19 recordsLinked to original sources
arXiv2022

Possibilistic approach to network nonlocality

The investigation of Bell nonlocality traditionally relies on joint probabilities of observing certain measurement outcomes. In this work we explore a possibilistic approach, where only patterns of possible outcomes matter, and apply it to Bell nonlocality in networks with independent sources. We present various algorithms for determining whether a given outcome pattern can be achieved via classical resources or via non-signaling resources. Next we illustrate these methods considering the triangle and square networks (with binary outputs and no inputs), identifying patterns that are incompatible with the network structure, as well as patterns that imply nonlocality. In particular, we obtain an example of quantum nonlocality in the square network with binary outcomes. Moreover, we show how to construct certificates for detecting the nonlocality of a certain pattern, in the form of nonlinear Bell-type inequalities involving joint probabilities. Finally, we show that these inequalities remain valid in the case where the sources in the network become partially correlated.

quant-ph↗
arXiv2021

Noncommutative polynomial optimization under symmetry

We present a general framework to exploit the symmetries present in the Navascu{\'e}s-Pironio-Ac{\'i}n semidefinite relaxations that approximate invariant noncommutative polynomial optimization problems. We put equal emphasis on the moment and sum-of-squares dual approaches, and provide a pedagogical and formal introduction to the Navascu{\'e}s-Pironio-Ac{\'i}n technique before working out the impact of symmetries present in the problem. Using our formalism, we compute analytical sum-of-square certificates for various Bell inequalities, and prove a long-standing conjecture about the exact maximal quantum violation of the CGLMP inequalities for dimension 3 and 4. We also apply our technique to the Sliwa inequalities in the Bell scenario with three parties with binary measurements settings/outcomes. Symmetry reduction is key to scale the applications of the NPA relaxation, and our formalism encompasses and generalizes the approaches found in the literature.

quant-ph↗
arXiv2021

Receiver-Device-Independent Quantum Key Distribution Protocols

We discuss quantum key distribution protocols and their security analysis, considering a receiver-device-independent (RDI) model. The sender's (Alice's) device is partially characterized, in the sense that we assume bounds on the overlaps of the prepared quantum states. The receiver's (Bob's) device requires no characterisation and can be represented as a black-box. Our protocols are therefore robust to any attack on Bob, such as blinding attacks. In particular, we show that a secret key can be established even when the quantum channel has arbitrarily low transmission by considering RDI protocols exploiting sufficiently many states. Finally, we discuss how the hypothesis of bounded overlaps can be naturally applied to practical devices.

quant-ph↗
arXiv2021

Certifying Numerical Decompositions of Compact Group Representations

We present a performant and rigorous algorithm for certifying that a matrix is close to being a projection onto an irreducible subspace of a given group representation. This addresses a problem arising when one seeks solutions to semi-definite programs (SDPs) with a group symmetry. Indeed, in this context, the dimension of the SDP can be significantly reduced if the irreducible representations of the group action are explicitly known. Rigorous numerical algorithms for decomposing a given group representation into irreps are known, but fairly expensive. To avoid this performance problem, existing software packages -- e.g. RepLAB, which motivated the present work -- use randomized heuristics. While these seem to work well in practice, the problem of to which extent the results can be trusted arises. Here, we provide rigorous guarantees applicable to finite and compact groups, as well as a software implementation that can interface with RepLAB. Under natural assumptions, a commonly used previous method due to Babai and Friedl runs in time O(n^5) for n-dimensional representations. In our approach, the complexity of running both the heuristic decomposition and the certification step is O(max{n^3 log n, D d^2 log d}), where d is the maximum dimension of an irreducible subrepresentation, and D is the time required to multiply elements of the group. A reference implementation interfacing with RepLAB is provided.

math.RT↗
arXiv2020

Algebraic and geometric properties of local transformations

Some properties of physical systems can be characterized from their correlations. In that framework, subsystems are viewed as abstract devices that receive measurement settings as inputs and produce measurement outcomes as outputs. The labeling convention used to describe these inputs and outputs does not affect the physics; and relabelings are easily implemented by rewiring the input and output ports of the devices. However, a more general class of operations can be achieved by using correlated preprocessing and postprocessing of the inputs and outputs. In contrast to relabelings, some of these operations irreversibly lose information about the underlying device. Other operations are reversible, but modify the number of cardinality of inputs and/or outputs. In this work, we single out the set of deterministic local maps as the one satisfying two equivalent constructions: an operational definition from causality, and an axiomatic definition reminiscent of the definition of quantum completely positive trace-preserving maps. We then study the algebraic properties of that set. Surprisingly, the study of these fundamental properties has deep and practical applications. First, the invariant subspaces of these transformations directly decompose the space of correlations/Bell inequalities into nonsignaling, signaling and normalization components. This impacts the classification of Bell and causal inequalities, and the construction of assemblages/witnesses in steering scenarios. Second, the left and right invertible deterministic local operations provide an operational generalization of the liftings introduced by Pironio [J. Math. Phys., 46(6):062112 (2005)]. Not only Bell-local, but also causal inequalities can be lifted; liftings also apply to correlation boxes in a variety of scenarios.

quant-ph↗
arXiv2020

Postquantum common-cause channels: the resource theory of local operations and shared entanglement

We define the type-independent resource theory of local operations and shared entanglement (LOSE). This allows us to formally quantify postquantumness in common-cause scenarios such as the Bell scenario. Any nonsignaling bipartite quantum channel which cannot be generated by LOSE operations requires a postquantum common cause to generate, and constitutes a valuable resource. Our framework allows LOSE operations that arbitrarily transform between different types of resources, which in turn allows us to undertake a systematic study of the different manifestations of postquantum common causes. Only three of these have been previously recognized, namely postquantum correlations, postquantum steering, and non-localizable channels, all of which are subsumed as special cases of resources in our framework. Finally, we prove several fundamental results regarding how the type of a resource determines what conversions into other resources are possible, and also places constraints on the resource's ability to provide an advantage in distributed tasks such as nonlocal games, semiquantum games, steering games, etc.

quant-ph↗
arXiv2020

Genuine Network Multipartite Entanglement

The standard definition of genuine multipartite entanglement stems from the need to assess the quantum control over an ever-growing number of quantum systems. We argue that this notion is easy to hack: in fact, a source capable of distributing bipartite entanglement can, by itself, generate genuine $k$-partite entangled states for any $k$. We propose an alternative definition for genuine multipartite entanglement, whereby a quantum state is genuinely network $k$-entangled if it cannot be produced by applying local trace-preserving maps over several $k$-partite states distributed among the parties, even with the aid of global shared randomness. We provide analytic and numerical witnesses of genuine network entanglement, and we reinterpret many past quantum experiments as demonstrations of this feature.

quant-ph↗
arXiv2019

Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

Mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) are crucial to many conceptual and practical aspects of quantum theory. Here, we develop their role in quantum nonlocality by: i) introducing families of Bell inequalities that are maximally violated by $d$-dimensional MUBs and SICs respectively, ii) proving device-independent certification of natural operational notions of MUBs and SICs, and iii) using MUBs and SICs to develop optimal-rate and nearly optimal-rate protocols for device independent quantum key distribution and device-independent quantum random number generation respectively. Moreover, we also present the first example of an extremal point of the quantum set of correlations which admits physically inequivalent quantum realisations. Our results elaborately demonstrate the foundational and practical relevance of the two most important discrete Hilbert space structures to the field of quantum nonlocality.

quant-ph↗
arXiv2019

Type-independent Characterization of Spacelike Separated Resources

Quantum theory describes multipartite objects of various types: quantum states, nonlocal boxes, steering assemblages, teleportages, distributed measurements, channels, and so on. Such objects describe, for example, the resources shared in quantum networks. Not all such objects are useful, however. In the context of space-like separated parties, devices which can be simulated using local operations and shared randomness are useless, and it is of paramount importance to be able to practically distinguish useful from useless quantum resources. Accordingly, a body of literature has arisen to provide tools for witnessing and quantifying the nonclassicality of objects of each specific type. In the present work, we provide a framework which subsumes and generalizes all of these resources, as well as the tools for witnessing and quantifying their nonclassicality.

quant-ph↗
arXiv2019

Quantum Inflation: A General Approach to Quantum Causal Compatibility

Causality is a seminal concept in science: Any research discipline, from sociology and medicine to physics and chemistry, aims at understanding the causes that could explain the correlations observed among some measured variables. While several methods exist to characterize classical causal models, no general construction is known for the quantum case. In this work, we present quantum inflation, a systematic technique to falsify if a given quantum causal model is compatible with some observed correlations. We demonstrate the power of the technique by reproducing known results and solving open problems for some paradigmatic examples of causal networks. Our results may find applications in many fields: from the characterization of correlations in quantum networks to the study of quantum effects in thermodynamic and biological processes.

quant-ph↗
arXiv2019

The type-independent resource theory of local operations and shared randomness

In space-like separated experiments and other scenarios where multiple parties share a classical common cause but no cause-effect relations, quantum theory allows a variety of nonsignaling resources which are useful for distributed quantum information processing. These include quantum states, nonlocal boxes, steering assemblages, teleportages, channel steering assemblages, and so on. Such resources are often studied using nonlocal games, semiquantum games, entanglement-witnesses, teleportation experiments, and similar tasks. We introduce a unifying framework which subsumes the full range of nonsignaling resources, as well as the games and experiments which probe them, into a common resource theory: that of local operations and shared randomness (LOSR). Crucially, we allow these LOSR operations to locally change the type of a resource, so that players can convert resources of any type into resources of any other type, and in particular into strategies for the specific type of game they are playing. We then prove several theorems relating resources and games of different types. These theorems generalize a number of seminal results from the literature, and can be applied to lessen the assumptions needed to characterize the nonclassicality of resources. As just one example, we prove that semiquantum games are able to perfectly characterize the LOSR nonclassicality of every resource of any type (not just quantum states, as was previously shown). As a consequence, we show that any resource can be characterized in a measurement-device-independent manner.

quant-ph↗
arXiv2019

Measurement Device Independent Verification of Quantum Channels

The capability to reliably transmit and store quantum information is an essential building block for future quantum networks and processors. Gauging the ability of a communication link or quantum memory to preserve quantum correlations is therefore vital for their technological application. Here, we experimentally demonstrate a measurement-device-independent protocol for certifying that an unknown channel acts as an entanglement-preserving channel. Our results show that, even under realistic experimental conditions, including imperfect single-photon sources and the various kinds of noise---in the channel or in detection---where other verification means would fail or become inefficient, the present verification protocol is still capable of affirming the quantum behaviour in a faithful manner without requiring any trust on the measurement device.

quant-ph↗
arXiv2018

SymDPoly: symmetry-adapted moment relaxations for noncommutative polynomial optimization

Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able to discover automatically and exploit the symmetries present in the problem formulation. We also provide an open source software library written in Scala ( https://denisrosset.github.io/symdpoly ) that computes symmetry-adapted semidefinite relaxations with interfaces to a variety of open-source and commercial semidefinite solvers. We discuss the advantages of symmetrization, namely reductions in memory use, computation time, and increase in the solution precision.

quant-ph↗
arXiv2018

Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation

We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The technique, which we make publicly available through a user-friendly software package, relies on the exploitation of symmetries present in the optimisation problem to reduce the number of variables and the block sizes in semidefinite relaxations. It is widely applicable in problems encountered in quantum information theory and enables computations that were previously too demanding. We demonstrate its advantages and general applicability in several physical problems. In particular, we use it to robustly certify the non-projectiveness of high-dimensional measurements in a black-box scenario based on self-tests of $d$-dimensional symmetric informationally complete POVMs.

quant-ph↗
arXiv2018

Regularising data for practical randomness generation

Non-local correlations that obey the no-signalling principle contain intrinsic randomness. In particular, for a specific Bell experiment, one can derive relations between the amount of randomness produced, as quantified by the min-entropy of the output data, and its associated violation of a Bell inequality. In practice, due to finite sampling, certifying randomness requires the development of statistical tools to lower-bound the min-entropy of the data as a function of the estimated Bell violation. The quality of such bounds relies on the choice of certificate, i.e., the Bell inequality whose violation is estimated. In this work, we propose a method for choosing efficiently such a certificate. It requires sacrificing a part of the output data in order to estimate the underlying correlations. Regularising this estimate then allows one to find a Bell inequality that is well suited for certifying practical randomness from these specific correlations. We then study the effects of various parameters on the obtained min-entropy bound and explain how to tune them in a favourable way. Lastly, we carry out several numerical simulations of a Bell experiment to show the efficiency of our method: we nearly always obtain higher min-entropy rates than when we use a pre-established Bell inequality, namely the Clauser-Horne-Shimony-Holt inequality.

quant-ph↗
arXiv2018

Preliminary investigation of a new state estimation technique using device-independent maximum likelihood estimation

In quantum state tomography, the estimated frequencies do not correspond directly to a physical quantum state, due to statistical fluctuations. Thus, one resorts to point estimators that return the state that matches observations the best, and a variety of estimators have been proposed -- linear inversion, least squares, maximum likelihood (ML) -- each making different trade-offs. In this short note, we investigate an alternative approach inspired by device-independent quantum information protocols. We embed a tomographic complete set of measurement operators within the framework of a Bell scenario, and first regularize the estimated frequencies using a device-independent maximum likelihood algorithm. We then run the standard maximum likelihood algorithm to estimate the underlying quantum state. In this preliminary investigation, we do not observe significant differences in the reconstructed state when using the new algorithm.

quant-ph↗
arXiv2018

Self-testing quantum states and measurements in the prepare-and-measure scenario

The goal of self-testing is to characterize an a priori unknown quantum system based solely on measurement statistics, i.e. using an uncharacterized measurement device. Here we develop self-testing methods for quantum prepare-and-measure experiments, thus not necessarily relying on entanglement and/or violation of a Bell inequality. We present noise-robust techniques for self-testing sets of quantum states and measurements, assuming an upper bound on the Hilbert space dimension. We discuss in detail the case of a $2 \rightarrow 1$ random access code with qubits, for which we provide analytically optimal self-tests. The simplicity and noise robustness of our methods should make them directly applicable to experiments.

quant-ph↗