bibkey: mohantysharmasazimpradhanpati2022coherence
authors: Sanuja D. Mohanty; Gautam Sharma; Sk Sazim; Biswajit Pradhan; Arun K. Pati
year: 2022
title: "Creation of quantum coherence with general measurement processes"
doi: 10.1007/s11128-021-03394-5
url: https://arxiv.org/abs/2004.10875v2
claim: "The paper studies how nonselective measurements, acting by the Lüders rule with the square roots of POVM effects, create l1-norm coherence. For one-parameter qubit POVMs it computes the maximum output coherence (C+|r|)/2 and characterizes the states without coherence gain and those with maximal gain. For general two-outcome POVMs it obtains no closed form, leaves open which states admit no gain and which attain the maximal gain, and lists analytical results for two-outcome and n-outcome POVMs as future work."
strata_touched:
  - D5/S3/Quantum/Measurement/LudersCoherenceCreationOptimum
license: citation-only
triage: anchor

Mohanty, Sharma, Sazim, Pradhan and Pati, creation of coherence by measurements

S. D. Mohanty, G. Sharma, Sk Sazim, B. Pradhan and A. K. Pati, arXiv:2004.10875v2 [quant-ph]; Quantum Information Processing 21, 48 (2022). Quotations are from the v2 TeX source, with figure references replaced by bracketed descriptions.

Measurements (Section 2): a POVM $\{E_i\}$, $E_i\ge 0$, ${\sum }_i{E}_i=\mathbb{I}$, changes a state to

${\rho }^M={\sum }_i\sqrt{E_i}\rho \sqrt{E_i}$

in the non-selective case, and the coherence is the $l_1$ norm $C_{l_1}(\rho )={\sum }_{i\ne j}|{\rho }_{i,j}|$.

One-parameter POVMs (Section 3.1), for a qubit with Bloch vector $\vec{r}$:

${\max }_{\alpha ,\lambda }{C}_{l_1}({\rho }^{\prime })=\frac{1}{2}(C_{l_1}(\rho )+\sqrt{C_{l_1}(\rho {)}^2+r_3^2})$

General two-outcome POVMs $E_{\pm }=a_{\pm }\mathbb{I}\pm \vec{a}\cdot \vec{\sigma }$ (Section 3.2):

We couldn’t get the expression for ${\max }_{\{\vec{a},a_{\pm }\}}{C}_{l_1}({\rho }_{\pm }^{\prime })$ analytically […] However in this case, we don’t know yet for which states there can not be any coherence gain and for which states the coherence gain will be maximum.

Conclusion:

As a future line of work, it would be interesting to obtain the analytical results for two outcome and n-outcome POVMs.

Verified locator

Source: https://arxiv.org/abs/2004.10875v2

• DOI: https://doi.org/10.1007/s11128-021-03394-5 (Quantum Information Processing 21, 48 (2022); author list, journal, volume, issue and article number from Crossref).
• URL: https://arxiv.org/abs/2004.10875v2 (the e-print is a gzipped tar archive; member coh-measure.tex, 1020 lines, md5 4a3d0408f3156bdc86a47a97160298ce):
  • the $l_1$ coherence, l. 109;
  • non-selective measurements, l. 127–130;
  • one-parameter POVMs and their maximum, l. 184–245 (the maximum at l. 230–231);
  • general two-outcome POVMs and the question, l. 246–298;
  • the conclusion, l. 505.
• The arXiv version dates are from the arXiv metadata.