Measurement of noncanonical variables

Lev Vaidman A

Anindya Ghose Choudhury, Asesh Roy Chowdhury

Ruo-Xun Zhai, Che Sun

We extend the Carathéodory principle of the second law to quantum thermodynamics, where energy levels depend on macroscopic variables such as volume and magnetic field. This extension introduces the concept of quantum thermodynamic integrability (QTI), providing an alternative foundation for statistical mechanics. QTI is characterized by the path independence of work and heat within the thermodynamic manifold, locally described by energy levels and specific thermodynamic parameters. Within this framework, temperature naturally emerges as an integrating factor, enabling the derivation of both canonical and noncanonical states from the entropy integrable equations based on QTI. Notably, noncanonical states, which become particularly significant outside the thermodynamic limit, reveal the existence of informational correlations in finite-size thermodynamic systems.

Baidyanath Misra

Z. Hradil, Jaroslav Řeháček, Pablo de la Hoz +2 more

Rotated quadratures carry the phase-dependent information of the electromagnetic field, so they are somehow conjugate to the photon number. We analyze this noncanonical pair, finding an exact uncertainty relation, as well as a couple of weaker inequalities obtained by relaxing some restrictions of the problem. We also find the intelligent states saturating that relation and complete their characterization by considering extra constraints on the second-order moments of the variables involved. Using these moments, we construct performance measures tailored to diagnose photon-added and Schr\"odinger-cat-like states, among others.

Sacha Greenfield, Mordecai Waegell, Justin Dressel