bibkey: gwozdz2014discordspontaneous
authors: Marek Gwóźdź; Lech Jakóbczyk
year: 2014
title: "Spontaneous emission can locally create quantum discord out of classical correlations"
doi: 10.1007/s11128-013-0639-0
url: https://arxiv.org/abs/1306.0130v2
claim: "For two qubits, the paper relates the normalized geometric discord to the maximal mutual correlation, proves C_M(ρ) ≥ √D_G^A(ρ) for Bell-diagonal states, and conjectures from numerical simulations that it holds for all mixed two-qubit states."
strata_touched:
  - D5/S3/Quantum/Information/GeometricDiscordMutualCorrelationBound
license: citation-only
triage: anchor

Spontaneous emission can locally create quantum discord out of classical correlations

Marek Gwóźdź and Lech Jakóbczyk, arXiv:1306.0130v2 (quant-ph), 2013-11-02; published in Quantum Inf. Process. 13 (2014) 171–183. Quotations are from the v2 TeX source.

The geometric discord (Section II):

D_{G}^{A}(\ro)=\frac{d}{d-1};\min\limits_{\PP^{A}},||\ro-\PP^{A}(\ro)||_{2}^{2},

||m||_{2}=\sqrt{\tr (m,m^{\dagger})}.

The maximal mutual correlation (Section II):

C_{M}(\ro)=\sup\limits_{a,b},|\omega_{\ro}(ab)-\omega_{\ro}(a)\omega_{\ro}(b)|.\label{maxtot}

In the formula (\ref{maxtot}), the supremum is taken over all elements $a\in \text{cA}$ and $b\in \text{cB}$ such that $||a||=||b||=1$.

The conjecture (Section II):

C_{M}(\ro)\geq \sqrt{D_{G}^{A}(\ro)}\geq N(\ro).\label{nierow}

The second inequality was shown in Ref. \cite{Adesso} whereas the first one can be proved analytically for Bell-diagonal states and numerical simulations suggest that it is valid for all mixed two-qubit states \cite{J}.

Verified locator

• URL: https://arxiv.org/abs/1306.0130v2 (v2, 2013-11-02; source discord_spontem_revised.tex, md5 cc53f0dea35470c8bbc958f4431cad65): the geometric discord (l. 186–196), the measured state (l. 199–203), the maximal mutual correlation (l. 292–297) and the conjecture (l. 341–348).
• DOI: 10.1007/s11128-013-0639-0 (Quantum Inf. Process. 13, 171–183). The published text was not read.