Spectral moments and entropy rigidity of quantum channels: a three-mode photonic witness

arXiv:1209.5233v3 Announce Type: replace Abstract: Majorization and von Neumann entropy provide related but inequivalent descriptions of spectral disorder in quantum optical states. We investigate the channels preserving these descriptions and propose a three-mode photonic test of their difference. For channels with equal input and output dimensions, we show that constant output purity and third spectral moment on the unitary orbit of one simple-spectrum state determine the majorization-preserving channel forms, without assuming unitality.For qubits, output purity alone is sufficient. Preservation of entropy equality is substantially more restrictive: in dimension $d\geqslant3$, even a local condition near the maximally mixed state permits only replacement and unitary channels. Qubits admit an additional depolarizing family, but this exception disappears under extension by an idle auxiliary qubit. We construct exactly entropy-matched qutrit inputs whose output entropies split at cubic order under nontrivial depolarizing noise. A proposed single-photon implementation uses three optical modes, randomized Weyl transformations and population or spectral-moment measurements.Explicit expressions are also obtained for preparation mismatch,readout uncertainty and input-independent loss. The results connect quadratic and cubic spectral information with experimentally interpretable tests of quantum-channel structure.

Abstract:Majorization and von Neumann entropy provide related but inequivalent descriptions of spectral disorder in quantum optical states. We investigate the channels preserving these descriptions and propose a three-mode photonic test of their difference. For channels with equal input and output dimensions, we show that constant output purity and third spectral moment on the unitary orbit of one simple-spectrum state determine the majorization-preserving channel forms, without assuming this http URL qubits, output purity alone is sufficient. Preservation of entropy equality is substantially more restrictive: in dimension $d\geqslant3$, even a local condition near the maximally mixed state permits only replacement and unitary channels. Qubits admit an additional depolarizing family, but this exception disappears under extension by an idle auxiliary qubit. We construct exactly entropy-matched qutrit inputs whose output entropies split at cubic order under nontrivial depolarizing noise. A proposed single-photon implementation uses three optical modes, randomized Weyl transformations and population or spectral-moment this http URL expressions are also obtained for preparation mismatch,readout uncertainty and input-independent loss. The results connect quadratic and cubic spectral information with experimentally interpretable tests of quantum-channel structure.

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Operator Algebras (math.OA)

arXiv:1209.5233 [quant-ph]

(or arXiv:1209.5233v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.1209.5233 Focus to learn more arXiv-issued DOI via DataCite

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Spectral moments and entropy rigidity of quantum channels: a three-mode photonic witness

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