bibkey: sazim2018binegativity authors: Sk Sazim; Natasha Awasthi year: 2018 title: “Binegativity of two qubits under noise” doi: 10.1016/j.physleta.2018.04.056 url: https://arxiv.org/abs/1711.03717v2 claim: “The introduction restates the conjecture that binegativity is monotone under LOCC and PPT channels; the paper computes its behavior under selected noise channels.” strata_touched:

• D5/S3/Quantum/Entanglement/TwoQubitBinegativityMonotonicityRefutation license: citation-only triage: anchor

Binegativity of two qubits under noise

Sk Sazim and Natasha Awasthi, Physics Letters A 382 (2018), 1852–1857.

The introduction of arXiv:1711.03717v2, p. 1, states:

On the basis of numerical evidence, it is conjectured that the binegativity behaves monotonically under both LOCC and PPT channels [15].

The abstract, p. 1, states:

Our study supports the conjecture that the binegativity is a monotone.

Reference [15] is Mark W. Girard and Gilad Gour, The binegativity of two qubits, arXiv:1701.02724v3. Its introduction, p. 1, states:

That is, we conjecture that for any two-qubit state $\sigma$ it holds that $N_2(\mathcal{E}(\sigma ))\le N_2(\sigma )$ for any LOCC (or PPT) channel $\mathcal{E}$ that outputs states of two qubits.

The Lean encoding uses two-qubit density matrices and finite one-way LOCC channels. Alice applies a complete instrument and communicates her outcome to Bob, who applies a complete channel conditional on that outcome. Forgetting the outcomes gives the double product-Kraus sum. This class is contained in LOCC. The binegativity uses the partial transpose on Bob and the negative parts of self-adjoint matrices, as in Girard and Gour.

Verified locator

• DOI: https://doi.org/10.1016/j.physleta.2018.04.056
• URL: https://arxiv.org/abs/1711.03717v2
• Restatement: arXiv v2, p. 1, introduction; source binegativity.tex, lines 109–111. Abstract support sentence: p. 1, source line 52.
• Original conjecture: https://arxiv.org/abs/1701.02724v3, p. 1, introduction; source binegativity_v9.tex, lines 192–196.