Quantum Information
Entanglement, separability, and other problems studied within quantum information theory.
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One Haar State Looks Like Many Stated in the source’s Open Problems section as a conjecture it believes true, with the note that it could neither prove it nor find it proved or even formalised anywhere. The source proves a strictly weaker pointwise domination bound, its Lemma 2, sufficient for its own applications and silent about total variation distance. 5 open |
Pseudorandom Quantum StatesQuantum CryptographyQuantum Informationothertight-boundadaptation (ai) | |
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No Self-Reduction for LSN Conjecture 5.20 of the source. It proves no random self-reduction exists from an arbitrary worst-case QNCP instance into LSN, naming exchange symmetry between code and error as the obstruction, and proves the tableau-randomizing barrier conditionally on the scrambling gap being polynomially related to eps. It is explicit that this is not an impossibility for random self-reductions in general. 4 open |
Average Case HardnessLearning Parity With NoiseQuantum InformationStabilizer Codesimpossibilityadaptation (ai) | |
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Best Separable State, constant completeness error Open: whether the paper’s 2^{Otilde(sqrt n)}-time algorithm for Best Separable State extends from perfect (and near-perfect, 1-1/n) completeness to any constant completeness error c < 1. The paper conjectures the affirmative and lists this first among its open questions; no partial result at any intermediate error is reported. 5 open |
Quantum InformationSum Of Squaresassumption |
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