On a Recent Conjecture by Z. Van Herstraeten and N. J. Cerf for the Quantum Wigner Entropy

Dias, Nuno C.; Prata, João N.

http://hdl.handle.net/10400.26/58504

Use this identifier to reference this record.

Name:	Description:	Size:	Format:
On a Recent Conjecture by Z. Van Herstraeten and N. J. Cerf for the Quantum Wigner Entropy.pdf		440.9 KB	Adobe PDF	Download

Send Feedback

Authors

Dias, Nuno C.

Prata, João N.

Abstract(s)

We address a recent conjecture stated by Z. Van Herstraeten and N. J. Cerf. They claim that the Shannon entropy for positive Wigner functions is bounded below by a positive constant, which can be attained only by Gaussian pure states. We introduce an alternative definition of entropy for all absolutely integrable Wigner functions, which is the Shannon entropy for positiveWigner functions. Moreover, we are able to prove, in arbitrary dimension, that this entropy is indeed bounded below by a positive constant, which is not very distant from the constant suggested by Van Herstraeten and Cerf. We also prove an analogous result for another conjecture stated by the same authors for the R´enyi entropy of positive Wigner functions. As a by-product we prove a new inequality for the radar-ambiguity function (and for the Wigner distribution) which is reminiscent of Lieb’s inequalities.

URI

http://hdl.handle.net/10400.26/58504

Citation

Dias, N. C., & Prata, J. N. (2023). On a Recent Conjecture by Z. Van Herstraeten and N. J. Cerf for the Quantum Wigner Entropy. Annales Henri Poincaré, 24(7), 2341–2362.