A universal complementarity identity for polarized double-slit interferometry

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autore principale: Gil, José J.
Natura: Preprint
Pubblicazione: 2026
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866916063422185472
author Gil, José J.
author_facet Gil, José J.
contents An exact identity is established among four experimentally accessible quantities in polarized double-slit interferometry: the phase-reference-dependent in-phase and quadrature components $V_A$ and $V_N$ of fringe visibility, the path predictability $\mathcal{P}$, and the mixedness $\mathcal{I}$ of the reduced path state satisfy $V_A^2+V_N^2+\mathcal{P}^2+\mathcal{I}^2=1$. The identity is an algebraic consequence of positivity and holds for every normalized path--polarization density matrix. It contains the Greenberger--Yasin predictability bound and, for globally pure path--polarization states, the Jakob--Bergou complete-complementarity equality; it is also connected with Englert's distinguishability relation when polarization carries which-path information. The separation $V^2=V_A^2+V_N^2$ resolves visibility into two components measurable by phase-shifted interferometry. Within a fixed real basis and a fixed phase convention, the quadrature-sensitive component is read from the antisymmetric sector of the Hermitian decomposition $ρ=A+iN$. A maximum-entropy reconstruction is included as an interpretation of how measurements sensitive to the two sectors constrain an inferred state, but the identity itself does not depend on that reconstruction.
format Preprint
id arxiv_https___arxiv_org_abs_2604_18760
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A universal complementarity identity for polarized double-slit interferometry
Gil, José J.
Quantum Physics
Optics
An exact identity is established among four experimentally accessible quantities in polarized double-slit interferometry: the phase-reference-dependent in-phase and quadrature components $V_A$ and $V_N$ of fringe visibility, the path predictability $\mathcal{P}$, and the mixedness $\mathcal{I}$ of the reduced path state satisfy $V_A^2+V_N^2+\mathcal{P}^2+\mathcal{I}^2=1$. The identity is an algebraic consequence of positivity and holds for every normalized path--polarization density matrix. It contains the Greenberger--Yasin predictability bound and, for globally pure path--polarization states, the Jakob--Bergou complete-complementarity equality; it is also connected with Englert's distinguishability relation when polarization carries which-path information. The separation $V^2=V_A^2+V_N^2$ resolves visibility into two components measurable by phase-shifted interferometry. Within a fixed real basis and a fixed phase convention, the quadrature-sensitive component is read from the antisymmetric sector of the Hermitian decomposition $ρ=A+iN$. A maximum-entropy reconstruction is included as an interpretation of how measurements sensitive to the two sectors constrain an inferred state, but the identity itself does not depend on that reconstruction.
title A universal complementarity identity for polarized double-slit interferometry
topic Quantum Physics
Optics
url https://arxiv.org/abs/2604.18760