Hyperentanglement in intermediate phase-space planes: benchmarking a photon-pair source for quantum key distribution

Murilo H. Magiotto; Millena B. Novaes; Wesley B. Cardoso; Ardiley T. Avelar; 1 Paulo H. Souto Ribeiro; Stephen P. Walborn; Guilherme L. Zanin; Rafael M. Gomes

arXiv · 2610.20005

Hyperentanglement in intermediate phase-space planes: benchmarking a photon-pair source for quantum key distribution

Murilo H. Magiotto·Millena B. Novaes·Wesley B. Cardoso·Ardiley T. Avelar·1 Paulo H. Souto Ribeiro·Stephen P. Walborn·Guilherme L. Zanin·Rafael M. Gomes

View original source ↗Read source document ↗Export metadata ↓

Abstract

We characterize a source of photon pairs simultaneously entangled in polarization and in the transverse spatial degree of freedom, with the spatial measurements performed in intermediate planes of the fractional Fourier transform. The source consists of two crossed type-I crystals in a non-collinear geometry, such that the transverse variables carry information about the crystal of origin. Detection in the crystal plane reveals this information completely and destroys the polarization entanglement, so that a scheme using the near and far fields as conjugate spatial bases cannot support a parallel polarization channel. In intermediate planes both spatial bases combine position and momentum, such that the which-crystal information is partially erased, and the polarization entanglement survives in all four combinations of spatial bases. Applying Bell and Einstein-Podolsky-Rosen criteria to the same photon pairs certifies both degrees of freedom simultaneously. We evaluate quantum bit error rates and asymptotic secret key rates in each degree of freedom, and find that the source delivers two simultaneously usable channels per photon pair.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Murilo H. Magiotto, Millena B. Novaes, Wesley B. Cardoso, Ardiley T. Avelar, 1 Paulo H. Souto Ribeiro, Stephen P. Walborn, Guilherme L. Zanin, Rafael M. Gomes. 2026-10-14. Hyperentanglement in intermediate phase-space planes: benchmarking a photon-pair source for quantum key distribution. https://arxiv.org/abs/2610.20005

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

All you need is Trotter

The work here enables a cost scaling of $\tilde{O}\left( \frac{T ^{1+o(1)}\,{\rm log}^2 (1/ε)}{\varepsilon}\right)$ and maximum depth $\tilde{O}\left( \frac{T^{1+o(1)}\,{\rm log} (1/ε)}{\varepsilon}\right)$ for estimating observables after some Hamiltonian evolution $e^{i H T}$ using no extra block-encoding qubits, where $ε$ is the algorithmic error of the target Hamiltonian evolution and $\varepsilon$ is the statistical error from the observable estimation. Throughout, $\tilde{O}$ suppresses factors that are doubly logarithmic in $1/ε$ (i.e. ${\rm polyloglog}(1/ε)$), which are subdominant to the displayed ${\rm polylog}(1/ε)$ factors. This is achieved through product formulas, stable interpolation (Chebyshev), and to calculate the needed fractional queries, cardinal sine interpolation is used. This is an improvement over similar work using interpolation methods which have a superlinear scaling of the form $5^p T^{1+1/p}$, where $p$ is the order of the product formula used and an improvement on required qubits over Quantum Signal Processing methods while maintaining scaling with ${\rm polylog}{1/ε}$. This is accomplished through an optimized and variable (with $T$) order $p$. The slightly better $\log^2(1/ε)$ compared to $\log^3(1/ε)$ comes from the use of cardinal sine interpolation compared to other methods using Chebyshev interpolation and product formulas. The work presented here also provides an alternative to Quantum Signal Processing techniques to calculate observables or amplitudes after a fractional query evolution with a cost $O(T\log{1/ε})$ through this cardinal sine interpolation.

quant-ph↗

arXiv2026

Relativistic generalization of Feynman's path integral on the basis of extended Lagrangians

In the extended Lagrange formalism of classical point dynamics, the system's dynamics is parametrized along a system evolution parameter $s$, and the physical time $t$ is treated as a \emph{dependent} variable $t(s)$ on equal footing with all other configuration space variables $q^{i}(s)$. In the action principle, the conventional classical action $L dt$ is then replaced by the generalized action $L_{e}ds$. A direct reparametrization of the conventional action yields an extended Lagrangian that is homogeneous of degree one in the velocities. A regular extended Lagrangian that is not homogeneous of degree one can also reproduce the conventional dynamics on a suitably selected invariant hypersurface. With this representation, the physical motion takes place on a hypersurface within a symplectic extended phase space of even dimension. The formal similarity of conventional and extended Lagrange formalisms provides a direct connection with the proper-time path integral approach to relativistic quantum physics. To provide an example, the non-homogeneous extended Lagrangian $L_{e}$ of a classical relativistic spinless point particle in an external electromagnetic field will be presented. This extended Lagrangian is a quadratic function in the velocities, and its selected zero-energy hypersurface is the classical mass shell. With this $L_{e}$, the generalized path integral first yields an evolution equation in $s$. Imposing the corresponding quantum mass-shell condition then yields the Klein-Gordon equation as the physical wave equation. This establishes the relation between the classical extended Lagrangian description and proper-time quantization for a charged spin-zero particle.

quant-ph↗

arXiv2026

Reliable Entropy Estimation from Observed Statistics for Device-Independent Quantum Cryptography

This paper introduces a numerical framework for establishing lower bounds on the conditional von-Neumann entropy in device-independent quantum cryptography and randomness extraction scenarios. Leveraging a hierarchy of semidefinite programs derived from the Navascués-Pironio-Acin (NPA) hierarchy, our tool enables efficient computation of entropy bounds based solely on observed statistics, assuming the validity of quantum mechanics. The method's computational efficiency is ensured by its reliance on projective operators within the non-commutative polynomial optimization problem. The method facilitates provable bounds for extractable randomness in noisy scenarios and aligns with modern entropy accumulation theorems. Consequently, the framework offers an adaptable tool for practical quantum cryptographic protocols, expanding secure communication possibilities in untrusted environments.

quant-ph↗