trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Concealment does not determine the adjoint kernel

Complete dephasing and complete depolarization on a qubit conceal every pair of finite POVMs, although their adjoint kernels on Hermitian operators are different.

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DIRECT PREREQUISITES3
DIRECT CONSEQUENCES20
PROOF DEPTH7
DOCUMENT LINKS0
THEOREM

All density matrices are tomographically complete

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Local-unitary inequivalence of two weight-isometric pairs of stabilizer codesLocal-unitary inequivalence oftwo weight-isometric pairs ofstabilizer codesA qutrit obstruction to positive/CP factorization of the channel transposeA qutrit obstruction topositive/CP factorization ofthe channel transposeData processing fails for the cumulant-based Renyi functional at every order above oneData processing fails for thecumulant-based Renyi functionalat every order above oneConcealment does not determine the adjoint kernelConcealment does not determinethe adjoint kernelTwo unbounded entanglement gaps with one qubitTwo unbounded entanglement gapswith one qubitStrict separation of measured and Uhlmann average fidelitiesStrict separation of measuredand Uhlmann average fidelitiesSignalling-game value equalitySignalling-game value equalityAn adaptive query advantage for four qubit statesAn adaptive query advantage forfour qubit statesAn extreme POVM with rank vector (3,3,2,2,2,2,2,2)An extreme POVM with rankvector (3,3,2,2,2,2,2,2)FourQubitParentConstructionFourQubitParentConstructionWeighted multicopy designs need not be optimalWeighted multicopy designs neednot be optimalThe optimal coherence created by qubit measurementsThe optimal coherence createdby qubit measurementsAn identity ancilla defeats maximal measurement coherence monotonicityAn identity ancilla defeatsmaximal measurement coherencemonotonicityBinary measurement incompatibility under pure lossBinary measurementincompatibility under pure lossStationarity of quadratic POVM variationsStationarity of quadratic POVMvariationsBroadcasting channels need have neither extremumBroadcasting channels need haveneither extremumOptimal visibility for calibrated joint measurementsOptimal visibility forcalibrated joint measurementsMitra's white-noise conjecture for qubit observablesMitra's white-noise conjecturefor qubit observablesRico–Życzkowski nonlinear monotone refutationRico–Życzkowski nonlinearmonotone refutationAmending coherence-breaking iterates with one unitaryAmending coherence-breakingiterates with one unitaryOptimality of the coefficient in the entanglement-breaking norm inequalityOptimality of the coefficientin the entanglement-breakingnorm inequalityHeisenberg Channel Compression EquivalenceHeisenberg Channel CompressionEquivalenceProjective tests do not characterize channel compatibilityProjective tests do notcharacterize channelcompatibilityOne measurement does not force noncontextualityOne measurement does not forcenoncontextuality
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Lean sourceResearch workspace
Status
Closed
Depth
7
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/QuantumChannels/ConcealmentKernelNecessityRefutation
Repository path
D5/S3/Quantum/QuantumChannels/ConcealmentKernelNecessityRefutation.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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