Quantum / CONCEPT
The minimum of the long-time algebra OTOC
For a block structure with sectors of type (n_J, d_J), J = 1, ..., r, and D = sum_J n_J d_J, the non-resonant long-time average of the algebra OTOC over all eigenbases of the D-dimensional Hilbert space is at least 1 - (sum_J d_J + sum_J n_J - r) / D, and the product basis attains this value. This proves the conjecture of F. Andreadakis, E. Dallas and P. Zanardi (arXiv:2312.13386, Section IV).
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH6
DOCUMENT LINKS1
The conjecture holds
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
None recorded in this release.
RELATED KNOWLEDGE
Structural connections
- A lower bound on qutrit magic from coherencestructural-affinity · Closed
- All gate orderings of an open-boundary transfer-matrix circuitstructural-affinity · Closed
- Concatenation can increase the cHaar moment normstructural-affinity · Closed
- Correlated coherence need not be monogamous for pure three-qubit statesstructural-affinity · Closed
- Entropy Increase Under Basis Pinchingstructural-affinity · Closed
- Generalized concentratable entanglement is not monotone under enlarging the subsystemstructural-affinity · Closed
- Hardware Circuit Factorsstructural-affinity · Closed
- Input Information Balancestructural-affinity · Closed
- Oblique discord: mutual information can increasestructural-affinity · Closed
- Partial Trace and Quantum Mutual Informationstructural-affinity · Closed
- QubitNormalFormStatestructural-affinity · Closed
- Rényi CMI local-channel monotonicitystructural-affinity · Closed
- The four-qubit Fredkin gate generates more than two ebits across AD:BCstructural-affinity · Closed
- The kernel and trace criteria are not equivalentstructural-affinity · Closed
- The minimum of purity plus time-reversal overlapstructural-affinity · Closed
- The original low-alpha SBW assertionstructural-affinity · Closed
- Two-qubit conditional domains need not be subalgebrasstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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