trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Finite Density States and Quantum Channels

Canonical finite density states and completely positive trace-preserving channels.

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DIRECT CONSEQUENCES36
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THEOREM

Channel composition agrees with sequential state evolution

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Finite Density States and Quantum ChannelsFinite Density States andQuantum ChannelsEmpirical and Reflexive Completeness SeparateEmpirical and ReflexiveCompleteness SeparateFibonacci carry output algebraFibonacci carry output algebraThe three-state root-fidelity Holevo boundThe three-state root-fidelityHolevo boundSupport-Aware Quantum Relative EntropySupport-Aware Quantum RelativeEntropyPositive Pauli Clock OrderPositive Pauli Clock OrderThe six-cycle graph state is not strongly 2-resistantThe six-cycle graph state isnot strongly 2-resistantFinite Sector Channel ModelFinite Sector Channel ModelFinite Sector Channel OptimalityFinite Sector ChannelOptimalityFull separability and exchanged diagonalsFull separability and exchangeddiagonalsSelective LOCC can increase the Moreau-Yosida entanglement of formationSelective LOCC can increase theMoreau-Yosida entanglement offormationQutrit Threshold SharingQutrit Threshold SharingSector Schmidt EncodingsSector Schmidt EncodingsIndependent Source Noise in a Quantum TriangleIndependent Source Noise in aQuantum TriangleUniversal Replacement Capacity GrowthUniversal Replacement CapacityGrowthFinite Density PurificationFinite Density PurificationFinite Reference Channel DistanceFinite Reference ChannelDistanceFinite Kraus Quantum ChannelsFinite Kraus Quantum ChannelsFinite Trace DistanceFinite Trace DistancePure-qubit affine geometryPure-qubit affine geometryConditional min-entropy of noisy unitariesConditional min-entropy ofnoisy unitariesTwo-qubit conditional domains need not be subalgebrasTwo-qubit conditional domainsneed not be subalgebrasPurify-and-clone is not optimal for one-site worst-case riskPurify-and-clone is not optimalfor one-site worst-case riskOptimal quantum states depend on the Renyi ordersOptimal quantum states dependon the Renyi ordersA counterexample to Zhang–Wu–Fei superadditivityA counterexample toZhang–Wu–Fei superadditivityActual Adaptive Low-Instrument EffectsActual Adaptive Low-InstrumentEffectsConditional subentropy and guessingConditional subentropy andguessingComplete retained golden historiesComplete retained goldenhistoriesVisible Adaptive Physical Record LawVisible Adaptive PhysicalRecord LawBroadcasting channels need have neither extremumBroadcasting channels need haveneither extremumThe Thue-Morse prefix 01101001 needs more than one qubitThe Thue-Morse prefix 01101001needs more than one qubitRetainedLocalProtocolRetainedLocalProtocolDeterminant-integral subentropyDeterminant-integral subentropyGuessing probabilityGuessing probabilityA strong-subadditivity counterexample for subentropyA strong-subadditivitycounterexample for subentropyThe Perito Bell bound and its attaining strategyThe Perito Bell bound and itsattaining strategyFlat-pair endpoint homomorphismsFlat-pair endpointhomomorphisms
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Lean sourceResearch workspace
Status
Closed
Depth
0
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/Foundation/FiniteStateChannel
Repository path
D5/S3/Quantum/Foundation/FiniteStateChannel.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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