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The Hypercube Went From Empty to Nearly Maximally Entangled
Below log₂ n depth an extensive subsystem stayed unentangled; at logarithmic depth every subsystem approached maximum entanglement within a constant factor.
Summary
Below log₂ n depth an extensive subsystem stayed unentangled; at logarithmic depth every subsystem approached maximum entanglement within a constant factor.
A theoretical analysis of random hypercube linear-optical networks starts with all modes squeezed and tracks how subsystem entanglement develops with circuit depth. Below log₂ n, the authors prove that an extensive subsystem has no entanglement. At depth proportional to log n, ensemble-averaged entanglement in every subsystem comes within a constant factor of its maximum. The transition parallels recent arguments for logarithmic-depth average-case sampling hardness in Gaussian boson sampling. This is a mathematical result about a random network ensemble, not an experimental demonstration or a general statement about every optical circuit.
Why it matters
Below log₂ n depth an extensive subsystem stayed unentangled; at logarithmic depth every subsystem approached maximum entanglement within a constant factor.
Limits and context
- This is a mathematical result about a random network ensemble, not an experimental demonstration or a general statement about every optical circuit.
Key claims
Below log₂ n depth an extensive subsystem stayed unentangled; at logarithmic depth every subsystem approached maximum entanglement within a constant factor.
Qualification: This is a mathematical result about a random network ensemble, not an experimental demonstration or a general statement about every optical circuit.
Evidence: source-2026-09-14-014
Sources
- arXiv preprint 2609.12043arXiv · primary research
Corrections
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