Speaker:  Hiroyasu Tajima

Date: May 9th (Mon.) 17:00-

Title:Title: Beyond i.i.d. in the Resource Theory of Asymmetry: An Information-Spectrum Approach for Quantum Fisher Information

Abstract: 

Energetic coherence is a valuable resource for various operations, including precise measurement of time and acceleration of quantum manipulations. Recently, it has been shown that the theory of energetic coherence, called the resource theory of asymmetry, has a thermodynamic structure, as do entanglement theory and quantum thermodynamics. 

In the so-called i.i.d. regime, where identical copies of a state are converted into identical copies of another state, the convertibility is entirely determined by the amount of energetic coherence measured by the quantum Fisher information (QFI) [1]. This fact means that QFI takes the place of entropy in thermodynamics [2] and entanglement entropy in entanglement theory [3]. So far, such a correspondence between energetic coherence and entropy is known only in the i.i.d. regime. In entanglement theory and quantum thermodynamics in the non-i.i.d. regime [4], entropy-related quantities based on the information-spectrum method [5] reveal a non-equilibrium thermodynamics structure [6]. Still, it has been an open question whether a similar structure exists for energetic coherence. A big problem is that the information-spectrum method is limited to entropy and its variants. Since QFI is completely different from entropy, the information-spectrum approach is not applicable to QFI.

In this talk, we solve the above problem by constructing an information-spectrum method applicable to the quantum Fisher information content [7]. As a result, we establish a general theory of the pure-state convertibility in the non-i.i.d. regime of the resource theory of asymmetry. The given theory reveals a non-equilibrium thermodynamic structure of energetic coherence in the non-i.i.d. regime, based on QFI rather than entropy. 

[1] I. Marvian, Nature Communications 11, 25 (2020).

[2] E. H. Lieb, J. Yngvason Phys.Rept. 310 1 (1999).

[3] C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Physical Review A 53, 2046 (1996).

[4] M. Hayashi, in IEEE International Symposium on Information Theory, 2003. Proceedings. 431 (2003)

[5] T. S. Han, Information-Spectrum Methods in Information Theory (textbook), (2003).

[6]  E. H. Lieb and J. Yngvason, Proceedings of the Royal

Society A: Mathematical, Physical and Engineering Sciences 470, 20140192 (2014).

[7] K. Yamaguchi and H. Tajima, arXiv:2204.08439 (2022).