OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
Constructs an entangled state on \mathbb C^{10}\otimes\mathbb C^{10} with zero distillable secret key for the specified local-instrument protocols that complete almost surely. These allow joint local processing and authenticated two-way public communication, with no other shared private resource and an eavesdropper holding the input purification and public record. A trace-preserving PPT channel on M_{21}(\mathbb C) whose square is not entanglement breaking disproves Christandl's PPT-square conjecture.
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MANUSCRIPT 01
Entanglement with zero distillable secret key in local dimension ten
We construct an entangled state on \mathbb C^{10}\otimes\mathbb C^{10} with zero distillable secret key for the local-instrument protocols specified here. They allow joint processing of all copies and unlimited two-way public communication, with the input as the only shared private resource and an eavesdropper holding a…
Full source abstract
We construct an entangled state on \mathbb C^{10}\otimes\mathbb C^{10} with zero distillable secret key for the local-instrument protocols specified here. They allow joint processing of all copies and unlimited two-way public communication, with the input as the only shared private resource and an eavesdropper holding a purification and the complete public record. The construction also disproves the unrestricted two-map PPT-composition conjecture. A separate trace-preserving PPT channel on M_{21}(\mathbb C) has a square that is not entanglement breaking.
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New mathematical reasoning could help AI tackle harder scientific and computational problems. How reliably these skills transfer beyond mathematics will determine how much they contribute to general intelligence.