Quantum / CONCEPT
Negativity is not the partial transpose distance to the PPT states
Ganardi, Miller, Paterek and Zukowski (arXiv:2111.11887, Quantum 6, 654) conjecture that the partial transpose distance d_T(rho, sigma) = ||rho^{T_B} - sigma^{T_B}||_1 / 2 from every state rho to the PPT states has infimum equal to the negativity N(rho) = (||rho^{T_B}||_1 - 1)/2. The equality fails: a rank-five two-qutrit state has negativity 1/34, while its distance to every PPT state is at least 2/51.
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DIRECT PREREQUISITES2
DIRECT CONSEQUENCES0
PROOF DEPTH2
DOCUMENT LINKS1
The conjectured equality fails
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RELATED KNOWLEDGE
Structural connections
- Binegativity is not monotone under one-way LOCCstructural-affinity · Closed
- Centered Kraus trace norm on finite referencesstructural-affinity · Closed
- Comparability of conical-design concurrence boundsstructural-affinity · Closed
- Finite Record Recovery Errorstructural-affinity · Closed
- Finite Reference Channel Distancestructural-affinity · Closed
- Finite Trace Distancestructural-affinity · Closed
- Negativity and structured negativity differ for a pure two-qutrit statestructural-affinity · Closed
- Real rectangular nuclear-norm additivitystructural-affinity · Closed
- The least trace-distance contraction coefficient over a classical channelstructural-affinity · Closed
- The overlap-to-purity part of Kopel's equality theoremstructural-affinity · Closed
- The upper binegativity bound of Girard and Gour failsstructural-affinity · Closed
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