arXiv subjects

Pierre-Emmanuel Emeriau

Publications and source records attributed to Pierre-Emmanuel Emeriau.

24 records · Page 2Linked to original sources

arXiv2022

Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements

Quantum 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.

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arXiv2022

High-fidelity generation of four-photon GHZ states on-chip

Mutually entangled multi-photon states are at the heart of all-optical quantum technologies. While impressive progresses have been reported in the generation of such quantum light states using free space apparatus, high-fidelity high-rate on-chip entanglement generation is crucial for future scalability. In this work, we use a bright quantum-dot based single-photon source to demonstrate the high fidelity generation of 4-photon Greenberg-Horne-Zeilinger (GHZ) states with a low-loss reconfigurable glass photonic circuit. We reconstruct the density matrix of the generated states using full quantum-state tomography reaching an experimental fidelity to the target $|{\text{GHZ}_4}\rangle$ of $\mathcal{F}_{\text{GHZ}_4} (86.0\pm0.4)\,\%$, and a purity of $\mathcal{P}_{\text{GHZ}_4}=(76.3\pm0.6)\,\%$. The entanglement of the generated states is certified with a semi device-independent approach through the violation of a Bell-like inequality by more than 39 standard deviations. Finally, we carry out a four-partite quantum secret sharing protocol on-chip where a regulator shares with three interlocutors a sifted key with up to 1978 bits, achieving a qubit-error rate of $10.87\,\%$. These results establish that the quantum-dot technology combined with glass photonic circuitry for entanglement generation on chip offers a viable path for intermediate scale quantum computation and communication.

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arXiv2022

The Interplay between Quantum Contextuality and Wigner Negativity

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. The former is a notion superseding nonlocality that can be exhibited by quantum systems. To date, it has mostly been studied in discrete-variable scenarios. 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 continuous-variable quantum optics. Continuous-variable scenarios offer promising candidates for implementing quantum computations. Wigner negativity is known to be a necessary resource for quantum speedup with continuous variables. However contextuality has been little understood and studied in continuous-variable scenarios. We first set out a robust framework for properly treating contextuality in continuous variables. We also 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 thus establishing a continuous-variable analogue of a celebrated result by Howard et al. We then introduce experimentally-friendly witnesses for Wigner negativity of single mode and multimode quantum states, based on fidelities with Fock states, using again tools from infinite-dimensional optimisation theory. We further extend the range of previously known discrete-variable results linking contextuality and advantage into a new territory of information retrieval.

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arXiv2022

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 Bell 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, is also 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. Through Lasserre relaxations, we are able to express this infinite linear program as a hierarchy of semi-definite programs that allow to calculate the contextual fraction with increasing accuracy.

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arXiv2022

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 problem. By relaxing and restricting the corresponding linear programs, we derive two converging hierarchies of semidefinite programs, which provide numerical sequences of increasingly tighter upper and lower bounds for the threshold values. We further show that 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.

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arXiv2020

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.

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