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Filippus S. Roux

Publications and source records attributed to Filippus S. Roux.

At least 19 recordsLinked to original sources
arXiv2026

Notes an tagged vector space

A generalisation is provided for the notion of tags, often found in physics notation. The properties of tags and their extractors are discussed. It leads to the definition of tagged vector spaces. It is applied in the context of quantum optics, to provide a mathematical description for Dirac notation as used in physics. The commutation relations for ladder operators and a symplectic phase space are derived as consequences of the properties of tagged vector spaces. To incorporate the spatiotemporal and spin degrees of freedom, tags are indexed by functions, leading to a functional representation.

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arXiv2026

Nature abhors macroscopic superpositions

Superpositions of mass distributions can potentially lead to entanglement with the geometry of spacetime. Here we show that there exists a natural reluctance for macroscopic mass distributions to form such superpositions. The macroscopic superposition is modeled as a Schr{ö}dinger cat state. The reluctance manifests as a dip in the total energy of the Schr{ö}dinger cat state as a function of the separation distance between the terms in the superposition. The dip in the energy provides an opposing force preventing the formation of the superposition. A generalization of this phenomenon addressing the measurement problem is also discussed.

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arXiv2025

Tagged vector space, Part II: function space index and the implied functional integration measure

The definition of quantum states in terms of tagged vector spaces is generalized to incorporate the spatiotemporal and spin degrees of freedom. Considering a tagged vector space where the index space is a function space, representing the additional degrees of freedom, we obtained axioms for the tags that include a completeness condition expressed in terms of a functional integral with an abstract functional integration measure. Using these axioms, we derive a generating functional for the moments of this functional integration measure. These moments are then used to evaluate the functional integrals of Gaussian functionals, leading to expressions in accordance with those obtained as generalizations of equivalent integrals over a finite number of integration variables. For a Gaussian functional used as a probability distributions, we show that its moments, obtained with this functional integration measure, satisfy Carleman's condition, indicating that the measure is unique.

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arXiv2025

Evolution of moments in atmospheric scintillation

Evolution equations for the moments of a photonic quantum state propagating through atmospheric turbulence are derived. These evolution equations are obtain from an evolution equation for the characteristic functional of the state, incorporating all spatiotemporal degrees of freedom. The measured quantities, such as the intensity or photon distribution, of the evolving state can be expressed in terms of such moments without having to know the exact final state. The case of an initial coherent state is considered as an example.

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arXiv2024

Fermion quadrature bases for Wigner functionals

A Grassmann functional phase space is formulated for the definition of fermionic Wigner functionals by identifying suitable fermionic operators that are analogues to boson quadrature operators. Instead of the Majorana operators, we use operators that are defined with relative spin transformations between the ladder operators. The eigenstates of these operators are shown to provide orthogonal bases, provided that the dual space is defined with the incorporation of a spin transformation. These bases then serve as quadrature bases in terms of which Wigner functionals are defined in a way equivalent to the bosonic case. As an application, we consider a two-level fermion system.

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arXiv2024

Spatiotemporal effects in heralded state preparation

Heralding, which is often used for preparing quantum optical states, is studied to determine the effects of the spatiotemporal properties of the process. Incorporating all the spatiotemporal degrees of freedom, we follow a Wigner functional approach to consider cases where these states are prepared to have Wigner functionals with negative regions, being suitable resources for quantum information technologies. General expressions are derived for single-photon-subtracted and single-photon-added states. As examples, we consider the photon-subtracted squeezed vacuum state, the photon-added coherent state, and the photon-added thermal state. The Wigner functional approach reveals the importance of the spatiotemporal transformations imposed by the experimental conditions.

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arXiv2023

Quantum transport of high-dimensional spatial information with a nonlinear detector

Information exchange between two distant parties, where information is shared without physically transporting it, is a crucial resource in future quantum networks. Doing so with high-dimensional states offers the promise of higher information capacity and improved resilience to noise, but progress to date has been limited. Here we demonstrate how a nonlinear parametric process allows for arbitrary high-dimensional state projections in the spatial degree of freedom, where a strong coherent field enhances the probability of the process. This allows us to experimentally realise quantum transport of high-dimensional spatial information facilitated by a quantum channel with a single entangled pair and a nonlinear spatial mode detector. Using sum frequency generation we upconvert one of the photons from an entangled pair resulting in high-dimensional spatial information transported to the other. We realise a d=15 quantum channel for arbitrary photonic spatial modes which we demonstrate by faithfully transferring information encoded into orbital angular momentum, Hermite-Gaussian and arbitrary spatial mode superpositions, without requiring knowledge of the state to be sent. Our demonstration merges the nascent fields of nonlinear control of structured light with quantum processes, offering a new approach to harnessing high-dimensional quantum states, and may be extended to other degrees of freedom too.

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arXiv2023

Non-Markovian evolution of multiphoton states in turbulence

An evolution equation for multiphoton states propagating through turbulence is derived without making a Markovian approximation. The state is represented as a Wigner functional to incorporate all spatiotemporal degrees of freedom. The resulting non-Markovian evolution equation is used to argue that initial Gaussian states do not remain Gaussian during propagation. Possible solutions of this evolution equation are discussed.

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arXiv2022

Distortions produced in optical homodyne tomography

An analysis of the homodyne tomography process that is often used to determine the Wigner functions of quantum optical states is performed to consider the effects of the spatiotemporal degrees of freedom. The homodyne tomography process removes those parts of the input state that are not associated with the mode of the local oscillator by tracing out those degrees of freedom. Using a functional approach to incorporate all the spatiotemporal degrees of freedom, we find that this reduction in the degrees of freedom introduces distortions in the observed Wigner function. The analysis also shows how the homodyne tomography process introduces a resolution that depends on the strength of the local oscillator. As examples, we consider coherent states, Fock states and squeezed vacuum states.

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arXiv2022

Nonlinear interferometry in all spatiotemporal degrees of freedom

The effects of the spatiotemporal degrees of freedom on the practical implementation of an SU(1,1) interferometry is investigated. A recently developed Wigner functional approach is used to obtain the phase sensitivity of such an SU(1,1) interferometry in terms of all the spatiotemporal degrees of freedom. It reveals how experimental scale parameters affect the performance of the interferometer. The analysis provides information that would be useful for quantum metrology applications.

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arXiv2021

Toolbox for non-classical state calculations

Computational challenges associated with the use of Wigner functions to identify non-classical properties of states are addressed with the aid of generating functions. It allows the computation of the Wigner functions of photon-subtracted states for an arbitrary number of subtracted photons. Both the formal definition of photon-subtracted states in terms of ladder operators and the experimental implementation with heralded photon detections are analyzed. These techniques are demonstrated by considering photon subtraction from squeezed thermal states as well as squeezed Fock states. Generating functions are also used for the photon statistics of these states. These techniques reveal various aspects of the parameter dependences of these states.

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arXiv2021

Stimulated parametric down-conversion for spatiotemporal metrology

A detailed analysis of the stimulated parametric down-conversion (PDC) process is performed to investigate the effects of the spatiotemporal degrees of freedom. The analysis provides information that would be useful for PDC-based metrology applications. Using a Wigner functional approach, we obtain the parametric down-converted state as the Bogoliubov transformed input state, in terms of Bogoliubov kernel functions. The result is used to consider the case for a coherent state seeding stimulated PDC. We also compute the background which is obtained from spontaneous PDC.

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arXiv2020

Spatiotemproal effects on squeezing measurements

The role of the spatiotemporal degrees of freedom in the preparation and observation of squeezed photonic states, produced by parametric down-conversion, is investigated. The analysis is done with the aid of a functional approach under the semi-classical approximation and the thin-crystal approximation. It is found that the squeezed state loses its minimum uncertainty property as the efficiency of down-conversion is increased, in a way that depends on the conditions of the homodyne measurements with which the amount of squeezing is determined.

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arXiv2020

Parametric down-conversion beyond the semi-classical approximation

Using a perturbative approach, we investigate the parametric down-conversion process without the semi-classical approximation. A Wigner functional formalism, which incorporates both the spatiotemproal degrees of freedom and the particle-number degrees of freedom is used to perform the analysis. First, we derive an evolution equation for the down-conversion process in the nonlinear medium. Then we use the perturbative approach to solve the equation. The leading order contribution is equivalent to the semi-classical solution. The next-to-leading order contribution provides a solution that includes the evolution of the pump field as a quantum field.

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arXiv2020

Wigner functional theory for quantum optics

Using the quadrature bases that incorporate the spatiotemporal degrees of freedom, we develop a Wigner functional theory for quantum optics, as an extension of the Moyal formalism. Since the spatiotemporal quadrature bases span the complete Hilbert space of all quantum optical states, it does not require factorization as a tensor product of discrete Hilbert spaces. The Wigner functions associated with such a space become functionals and operations are expressed by functional integrals -- the functional version of the star product. The resulting formalism enables tractable calculations for scenarios where both spatiotemporal degrees of freedom and particle-number degrees of freedom are relevant. To demonstrate the approach, we compute examples of Wigner functionals for a few well-known states and operators.

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arXiv2020

Entanglement of truncated quantum states

We investigate the impact of Hilbert-space truncation upon the entanglement of an initially maximally entangled $m\times m$ bipartite quantum state, after propagation under an entanglement-preserving $n \times n$ ($n\geq m$) unitary. Truncation -- physically enforced, e.g., by a detector's finite cross section -- projects the state onto an $s \times s$-dimensional subspace ($3\leq s \leq n$). For a random local unitary evolution, we obtain a simple analytical formula that expresses the truncation-induced entanglement loss as a function of $n$, $m$ and $s$.

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arXiv2020

Quantifying entanglement of parametric down-converted states in all degrees of freedom

The amount of entanglement that exists in a parametric down-converted state is investigated in terms of all the degrees of freedom of the state. We quantify the amount of entanglement by the Schmidt number of the state, represented as a pure bipartite state by tagging the down-converted photons in terms of orthogonal states of polarization with the aid of type II phase-matching. To facilitate our calculations, we use a Wigner functional approach, which allows the incorporation of the full infinite dimensional spatiotemporal degrees of freedom. A quantitative example with reasonably achievable experimental conditions is considered to demonstrate that extremely large Schmidt numbers are achievable.

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