arXiv subjects

Eloi Descamps

Publications and source records attributed to Eloi Descamps.

7 recordsLinked to original sources

arXiv2026

Non-Gaussianity from superselection rules

The quantum theory of the electromagnetic field enables the description of multiphoton states exhibiting nonclassical statistical properties, often reflected in non-Gaussian phase-space distributions. While non-Gaussianity alone does not fully characterize quantum states, several classifications have been proposed to hierarchize non-Gaussian states according to physically or informationally relevant resources. Here, we provide a physical interpretation of non-Gaussianity and connect it to a computational perspective by showing how a prominent classification-the stellar rank-emerges as a limiting case of the roots of polynomials that univocally represent bosonic states defined with a quantized phase reference, namely the Majorana polynomials. A direct consequence of our results is a revised interpretation of both the stellar rank and non-Gaussianity itself: when superselection rules are properly taken into account, quadrature non-Gaussianity - and nonzero stellar rank - act as witnesses of particle entanglement, rather than being linked with photon addition to Gaussian states as previously assumed. In addition, we show that because the stellar rank depends on a specific choice of coherent states, its relation to computational resources and potential quantum advantage is inherently basis-dependent, being naturally tied to quadrature eigenstates as the computational basis. Motivated by this observation, we generalize the notion of stellar rank to arbitrary computational bases, thereby establishing it as a genuine witness of bosonic resources that may enable quantum advantage.

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arXiv2025

Heisenberg-Weyl bosonic phase spaces: emergence, constraints and quantum informational resources

Phase space quasi-probability functions provide powerful representations of quantum states and operators, as well as criteria for assessing quantum computational resources. In discrete, odd-dimensional systems (qudits), protocols involving only non-negative phase space distributions can be efficiently classically simulated. For bosonic systems, defined in continuous variables, phase space negativities are likewise necessary to prevent efficient classical simulation of the underlying physical processes. However, when quantum information is encoded in bosonic systems, this connection becomes subtler: as negativity is only a necessary property for potential quantum advantage, encoding (i.e., physical) states may exhibit large negativities while still corresponding to architectures that remain classically simulable. Several frameworks have attempted to relate non-negativity of states and gates in the computational phase space to non-negativity of processes in the physical bosonic phase space, but a consistent correspondence remains elusive. Here, we introduce a general framework that connects the physical phase space structure of bosonic systems to their encoded computational representations across arbitrary dimensions and encodings. This framework highlights the key role of the reference frame-equivalently, the choice of vacuum-in defining the computational basis and linking its phase space simulability properties to those of the physical system. Finally, we provide computational and physical interpretations of the planar (quadrature-like) phase space limit, where genuinely quantum features may gradually vanish, yielding classically simulable behavior.

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arXiv2025

Resources for bosonic metrology: quantum-enhanced precision from a superselection rule perspective

Bosonic systems, particularly in quantum optics and atomic physics, are leading platforms for achieving quantum enhanced precision in parameter estimation. By exploiting properties such as mode and particle entanglement, it is possible to attain precisions that surpass the shot noise limit with respect to key resources like probe number or energy. Yet the mechanisms by which these bosonic resources enable quantum enhancement remain unclear. Consequently, the design of optimal probes and evolutions often relies on case by case analyses, where continuous and discrete variable regimes are treated separately and their connection is still unclear. We develop a comprehensive framework for quantum metrology that unifies all known precision enhancement mechanisms based on bosonic systems. Our approach employs a superselection rule compliant representation of the electromagnetic field that explicitly includes the phase reference, thereby enforcing total particle number conservation and bridging the discrete and continuous limits of quantum optics and symmetric massive systems. Within this unified formalism, of which established results emerge as special cases, we identify the distinct roles of mode and particle entanglement for quantum enhanced precision. The framework further provides general measurement optimization strategies for arbitrary multimode entangled probe states and naturally incorporates noise and non-unitary dynamics, ensuring applicability to realistic experimental conditions.

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arXiv2025

Unified framework for bosonic quantum information encoding, resources and universality from superselection rules

A convenient way to represent quantum optical states is through the quadrature basis of single-modes of the field. This framework provides intuitive definitions for quasi-classical states, their phase-space representations, and enables the definition of a universal gate set. In this widely adopted representation of quantum optics, most pure states consist of coherent superpositions of photon-number states. However, this approach neglects the particle-number superselection rule - which prohibits coherence between states of differing photon numbers - and implicitly assumes a phase reference. We adopt a representation of quantum optical states that respects the superselection rule and revisit key tools and results in quantum optics and information encoding within quantum optics. This approach preserves the intuitive aspects of the traditional quadrature representation while unifying insights from quantum optics with those from symmetric spin-like and angular momentum systems. More than just an alternative representation, we show that a superselection rule-compliant framework provides a unified formalism for all bosonic encodings, from single-photon to continuous-variable encodings. This perspective allows for a precise characterization of the roles of Gaussian and non-Gaussian resources, as well as the interplay between modes and states in quantum universality and potential computational advantage.

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arXiv2025

Approaching maximal precision of Hong-Ou-Mandel interferometry with non-perfect visibility

In quantum mechanics, the precision achieved in parameter estimation using a quantum state as a probe is determined by the measurement strategy employed. The ultimate quantum limit of precision is bounded by a value set by the state and its dynamics. Theoretical results have revealed that in interference measurements with two possible outcomes, this limit can be reached under ideal conditions of perfect visibility and zero losses. However, in practice, this cannot be achieved, so precision {\it never} reaches the quantum limit. But how do experimental setups approach precision limits under realistic circumstances? In this work we provide a general model for precision limits in two-photon Hong-Ou-Mandel interferometry for non-perfect visibility. We show that the scaling of precision with visibility depends on the effective area in time-frequency phase space occupied by the state used as a probe, and we find that an optimal scaling exists. We demonstrate our results experimentally for different states in a set-up where the visibility can be controlled and reaches up to $99.5\%$. In the optimal scenario, a ratio of $0.97$ is observed between the experimental precision and the quantum limit, establishing a new benchmark in the field.

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arXiv2024

Superselection rules and bosonic quantum computational resources

We present a method to systematically identify and classify quantum optical non-classical states as classical/non-classical based on the resources they create on a bosonic quantum computer. This is achieved by converting arbitrary bosonic states into multiple modes, each occupied by a single photon, thereby defining qubits of a bosonic quantum computer. Starting from a bosonic classical-like state in a representation that explicitly respects particle number super-selection rules, we apply universal gates to create arbitrary superpositions of states with the same total particle number. The non-classicality of the corresponding states can then be associated to the operations they induce in the quantum computer. We also provide a correspondence between the adopted representation and the more conventional one in quantum optics, where superpositions of Fock states describe quantum optical states, and we identify how multi-mode states can lead to quantum advantage. Our work contributes to establish a seamless transition from continuous to discrete properties of quantum optics while laying the grounds for a description of non-classicality and quantum computational advantage that is applicable to spin systems as well.

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arXiv2023

Quantum metrology using time-frequency as quantum continuous variables: Resources, sub shot-noise precision and phase space representation

We study the role of the electromagnetic field's frequency in time precision measurements using single photons as a paradigmatic system. For such, we independently identify the contributions of intensity and spectral resources and show that both can play a role on the scaling of the precision of parameter estimation with the number of probes. We show in particular that it is possible to observe a quadratic scaling using quantum mode correlations only and explicit the mathematical expression of states saturating the Heisenberg limit. We also provide a geometrical and phase space interpretation of our results, and observe a curious quantum-to-classical-like transition on scaling by modifying the spectral variance of states. Our results connect discrete and continuous aspects of single photons and quantum optics by considering from a quantum mechanical perspective the role of frequency.

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