← 研踪 PaperTrailarXiv:2611.04363 · v1
A Conditional Quantum Kac-Bernstein Theorem
首次提交 2026-11-03 13:49
版本更新 2026-11-03 13:49
雷达观测 2026-11-04 23:40
摘要
We establish a conditional quantum Kac-Bernstein theorem for mixing of two independent, finite-mode bosonic inputs with quantum memories. We characterize exactly when the outputs are conditionally independent given both memories. Each input then decomposes into orthogonal memory sectors sharing a common Gaussian state on the physical system and a bosonic memory factor, up to sector-dependent physical displacements. In particular, triviality of the common bosonic factor implies separability of the inputs, as occurs whenever either memory has finite-dimensional support.
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v1 · 2026-11-03 13:49 · 最新观测版本
A Conditional Quantum Kac-Bernstein Theorem
We establish a conditional quantum Kac-Bernstein theorem for mixing of two independent, finite-mode bosonic inputs with quantum memories. We characterize exactly when the outputs are conditionally independent given both memories. Each input then decomposes into orthogonal memory sectors sharing a common Gaussian state on the physical system and a bosonic memory factor, up to sector-dependent physical displacements. In particular, triviality of the common bosonic factor implies separability of the inputs, as occurs whenever either memory has finite-dimensional support.
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