16 research outputs found
Quantum Advantage in Information Retrieval
Random access codes have provided many examples of quantum advantage in
communication, but concern only one kind of information retrieval task. We
introduce a related task - the Torpedo Game - and show that it admits greater
quantum advantage than the comparable random access code. Perfect quantum
strategies involving prepare-and-measure protocols with experimentally
accessible three-level systems emerge via analysis in terms of the discrete
Wigner function. The example is leveraged to an operational advantage in a
pacifist version of the strategy game Battleship. We pinpoint a characteristic
of quantum systems that enables quantum advantage in any bounded-memory
information retrieval task. While preparation contextuality has previously been
linked to advantages in random access coding we focus here on a different
characteristic called sequential contextuality. It is shown not only to be
necessary and sufficient for quantum advantage, but also to quantify the degree
of advantage. Our perfect qutrit strategy for the Torpedo Game entails the
strongest type of inconsistency with non-contextual hidden variables, revealing
logical paradoxes with respect to those assumptions.Comment: 15 pages, 11 figures; new presentation, additional figures and
reference
Continuous-variable nonlocality and contextuality
Contextuality is a non-classical behaviour that can be exhibited by quantum
systems. It is increasingly studied for its relationship to
quantum-over-classical advantages in informatic tasks. To date, it has largely
been studied in discrete variable scenarios, where observables take values in
discrete and usually finite sets. Practically, on the other hand,
continuous-variable scenarios offer some of the most promising candidates for
implementing quantum computations and informatic protocols. Here we set out a
framework for treating contextuality in continuous-variable scenarios. It is
shown that the Fine--Abramsky--Brandenburger theorem extends to this setting,
an important consequence of which is that nonlocality can be viewed as a
special case of contextuality, as in the discrete case. The contextual
fraction, a quantifiable measure of contextuality that bears a precise
relationship to Bell inequality violations and quantum advantages, can also be
defined in this setting. It is shown to be a non-increasing monotone with
respect to classical operations that include binning to discretise data.
Finally, we consider how the contextual fraction can be formulated as an
infinite linear program, and calculated with increasing accuracy using
semi-definite programming approximations.Comment: 27 pages including 6 pages supplemental material, 2 figure
Corrected Bell and Noncontextuality Inequalities for Realistic Experiments
Contextuality is a feature of quantum correlations. It is crucial from a
foundational perspective as a nonclassical phenomenon, and from an applied
perspective as a resource for quantum advantage. It is commonly defined in
terms of hidden variables, for which it forces a contradiction with the
assumptions of parameter-independence and determinism. The former can be
justified by the empirical property of non-signalling or non-disturbance, and
the latter by the empirical property of measurement sharpness. However, in
realistic experiments neither empirical property holds exactly, which leads to
possible objections to contextuality as a form of nonclassicality, and
potential vulnerabilities for supposed quantum advantages. We introduce
measures to quantify both properties, and introduce quantified relaxations of
the corresponding assumptions. We prove the continuity of a known measure of
contextuality, the contextual fraction, which ensures its robustness to noise.
We then bound the extent to which these relaxations can account for
contextuality, via corrections terms to the contextual fraction (or to any
noncontextuality inequality), culminating in a notion of genuine contextuality,
which is robust to experimental imperfections. We then show that our result is
general enough to apply or relate to a variety of established results and
experimental setups.Comment: 20 pages + 14 pages of appendices, 3 figure
Perceval: A Software Platform for Discrete Variable Photonic Quantum Computing
We introduce Perceval, an evolutive open-source software platform for
simulating and interfacing with discrete variable photonic quantum computers,
and describe its main features and components. Its Python front-end allows
photonic circuits to be composed from basic photonic building blocks like
photon sources, beam splitters, phase shifters and detectors. A variety of
computational back-ends are available and optimised for different use-cases.
These use state-of-the-art simulation techniques covering both weak simulation,
or sampling, and strong simulation. We give examples of Perceval in action by
reproducing a variety of photonic experiments and simulating photonic
implementations of a range of quantum algorithms, from Grover's and Shor's to
examples of quantum machine learning. Perceval is intended to be a useful
toolkit both for experimentalists wishing to easily model, design, simulate, or
optimise a discrete variable photonic experiment, and for theoreticians wishing
to design algorithms and applications for discrete-variable photonic quantum
computing platforms
Relation entre contextualité quantique et négativité de la fonction de Wigner
Quantum physics has revolutionised our way of conceiving nature and is now bringing about a new technological revolution. The use of quantum information in technology promises to supersede the so-called classical devices used nowadays. Understanding what features are inherently non-classical is crucial for reaching better-than-classical performance. This thesis focuses on two nonclassical behaviours: quantum contextuality and Wigner negativity. To date, contextuality has mostly been studied in discrete-variable scenarios, where observables take values in discrete and usually finite sets. In those scenarios, contextuality has been shown to be necessary and sufficient for advantages in some cases. On the other hand, negativity of the Wigner function is another unsettling non-classical feature of quantum states that originates from phase-space formulation in quantum optics. Wigner negativity is known to be a necessary resource for quantum speedup. We set out a robust framework for properly treating contextuality in continuous variables. We quantify contextuality in such scenarios by using tools from infinite-dimensional optimisation theory. Building upon this, we show that Wigner negativity is equivalent to contextuality in continuous variables with respect to Pauli measurements. We then introduce experimentally-friendly witnesses for Wigner negativity of multimode quantum states, based on fidelities with Fock states which again uses infinite-dimensional linear programming techniques. We further extend the range of previously known discrete-variable results linking contextuality and advantage into a new territory of discrete variable information retrieval.La physique quantique a révolutionné notre façon de concevoir la nature et provoque une nouvelle révolution technologique. L'utilisation de l'information quantique dans la technologie promet de supplanter les dispositifs dits classiques utilisés de nos jours. Il est essentiel de comprendre quelles caractéristiques sont intrinsèquement non classiques pour atteindre des performances supérieures à celles des dispositifs actuels. Cette thèse se concentre sur deux comportements non classiques : la contextualité quantique et la négativité de Wigner. Jusqu'à présent, la contextualité a surtout été étudiée dans des scénarios à variables discrètes, où les observables prennent des valeurs dans des ensembles discrets et généralement finis. Il a été démontré que la contextualité est nécessaire et suffisante pour les avantages dans certains cas. D'autre part, la négativité de la fonction de Wigner est une autre caractéristique non classique troublante des états quantiques qui provient de la formulation de l'espace de phase en optique quantique. La négativité de la fonction de Wigner est connue pour être une ressource nécessaire à l'accélération quantique. Nous établissons un cadre robuste pour traiter la contextualité dans les variables continues. Nous quantifions la contextualité dans de tels scénarios en utilisant des outils de la théorie de l'optimisation en dimension infinie. Nous montrons que la négativité de Wigner est équivalente à la contextualité dans les variables continues pour les mesures de Pauli. Nous introduisons ensuite des témoins expérimentaux pour la négativité de Wigner des états quantiques multimodes, basés sur les fidélités avec les états de Fock
Relation entre contextualité quantique et négativité de la fonction de Wigner
La physique quantique a révolutionné notre façon de concevoir la nature et provoque une nouvelle révolution technologique. L'utilisation de l'information quantique dans la technologie promet de supplanter les dispositifs dits classiques utilisés de nos jours. Il est essentiel de comprendre quelles caractéristiques sont intrinsèquement non classiques pour atteindre des performances supérieures à celles des dispositifs actuels. Cette thèse se concentre sur deux comportements non classiques : la contextualité quantique et la négativité de Wigner. Jusqu'à présent, la contextualité a surtout été étudiée dans des scénarios à variables discrètes, où les observables prennent des valeurs dans des ensembles discrets et généralement finis. Il a été démontré que la contextualité est nécessaire et suffisante pour les avantages dans certains cas. D'autre part, la négativité de la fonction de Wigner est une autre caractéristique non classique troublante des états quantiques qui provient de la formulation de l'espace de phase en optique quantique. La négativité de la fonction de Wigner est connue pour être une ressource nécessaire à l'accélération quantique. Nous établissons un cadre robuste pour traiter la contextualité dans les variables continues. Nous quantifions la contextualité dans de tels scénarios en utilisant des outils de la théorie de l'optimisation en dimension infinie. Nous montrons que la négativité de Wigner est équivalente à la contextualité dans les variables continues pour les mesures de Pauli. Nous introduisons ensuite des témoins expérimentaux pour la négativité de Wigner des états quantiques multimodes, basés sur les fidélités avec les états de Fock.Quantum physics has revolutionised our way of conceiving nature and is now bringing about a new technological revolution. The use of quantum information in technology promises to supersede the so-called classical devices used nowadays. Understanding what features are inherently non-classical is crucial for reaching better-than-classical performance. This thesis focuses on two nonclassical behaviours: quantum contextuality and Wigner negativity. To date, contextuality has mostly been studied in discrete-variable scenarios, where observables take values in discrete and usually finite sets. In those scenarios, contextuality has been shown to be necessary and sufficient for advantages in some cases. On the other hand, negativity of the Wigner function is another unsettling non-classical feature of quantum states that originates from phase-space formulation in quantum optics. Wigner negativity is known to be a necessary resource for quantum speedup. We set out a robust framework for properly treating contextuality in continuous variables. We quantify contextuality in such scenarios by using tools from infinite-dimensional optimisation theory. Building upon this, we show that Wigner negativity is equivalent to contextuality in continuous variables with respect to Pauli measurements. We then introduce experimentally-friendly witnesses for Wigner negativity of multimode quantum states, based on fidelities with Fock states which again uses infinite-dimensional linear programming techniques. We further extend the range of previously known discrete-variable results linking contextuality and advantage into a new territory of discrete variable information retrieval
Witnessing Wigner Negativity
Negativity of the Wigner function is arguably one of the most striking
non-classical features of quantum states. Beyond its fundamental relevance, it
is also a necessary resource for quantum speedup with continuous variables. As
quantum technologies emerge, the need to identify and characterize the
resources which provide an advantage over existing classical technologies
becomes more pressing. Here we derive witnesses for Wigner negativity of single
mode and multimode quantum states, based on fidelities with Fock states, which
can be reliably measured using standard detection setups. They possess a
threshold expectation value indicating whether the measured state has a
negative Wigner function. Moreover, the amount of violation provides an
operational quantification of Wigner negativity. We phrase the problem of
finding the threshold values for our witnesses as an infinite-dimensional
linear optimisation. By relaxing and restricting the corresponding linear
programs, we derive two hierarchies of semidefinite programs, which provide
numerical sequences of increasingly tighter upper and lower bounds for the
threshold values. We further show that both sequences converge to the threshold
value. Moreover, our witnesses form a complete family - each Wigner negative
state is detected by at least one witness - thus providing a reliable method
for experimentally witnessing Wigner negativity of quantum states from few
measurements. From a foundational perspective, our findings provide insights on
the set of positive Wigner functions which still lacks a proper
characterisation.Comment: 28 pages + 37 pages of appendices, 6 figures, 4 tables. v2: Added
link to the set of Wigner positive states. v3: Extension to the multimode
setting. v4: Accepted to Quantum; fixed typo
Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements
21 pages + 4 pages of appendices, 1 figureQuantum computers will provide considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups is challenging. In the continuous-variable setting - a promising paradigm for the realisation of universal, scalable, and fault-tolerant quantum computing - contextuality and Wigner negativity have been perceived as two such distinct resources. Here we show that they are in fact equivalent for the standard models of continuous-variable quantum computing. While our results provide a unifying picture of continuous-variable resources for quantum speedup, they also pave the way towards practical demonstrations of continuous-variable contextuality, and shed light on the significance of negative probabilities in phase-space descriptions of quantum mechanics
Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements
21 pages + 4 pages of appendices, 1 figureQuantum computers will provide considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups is challenging. In the continuous-variable setting - a promising paradigm for the realisation of universal, scalable, and fault-tolerant quantum computing - contextuality and Wigner negativity have been perceived as two such distinct resources. Here we show that they are in fact equivalent for the standard models of continuous-variable quantum computing. While our results provide a unifying picture of continuous-variable resources for quantum speedup, they also pave the way towards practical demonstrations of continuous-variable contextuality, and shed light on the significance of negative probabilities in phase-space descriptions of quantum mechanics