The PPT-squared conjecture: is the composition of two PPT channels always entanglement breaking?

Lineage and corrections

VibeMathed record: The PPT-squared conjecture: is the composition of two PPT channels always entanglement breaking? evidence for this event

Lean comparator statement: DimensionTenChannel.lean evidence for this event

Secret key from all entangled states: does every entangled state have positive distillable secret key? (Kruger-Werner Problem 24) evidence for this event

This event attributed to Unreleased internal OpenAI model

Theorem 1.3: there is an explicit trace-preserving PPT channel $\Theta$ on $M_{21}(\mathbb C)$ with $\Theta\circ\Theta$ not entanglement breaking, answering the 2012 channel question negatively with the same channel in both slots. Theorem 1.2: explicit PPT maps $\Phi_1,\Phi_2$ on $M_{10}(\mathbb C)$ (not trace preserving) whose composition has nonzero Choi matrix with no product vector in its range, refuting the unrestricted two-map Conjecture IV.1. The same pair yields the zero-key entangled state of the companion entry. Not shown: minimal dimensions, or whether every PPT channel becomes entanglement breaking after three compositions (the PPT-cubed question). parent of this event

Christandl, Muller-Hermes, Wolf, When do composed maps become entanglement breaking? (arXiv:1807.01266) evidence for this event

Lean comparator statement: DimensionTenPair.lean evidence for this event

The PPT-squared conjecture: is the composition of two PPT channels always entanglement breaking? parent of this event

BIRS workshop 12w5084 report (2012), Problem G evidence for this event

Lean solution module: OAI/Analysis/Quantum/DimensionTen/Channel.lean evidence for this event