Informationally complete sets of physical quantities

Luca Callegaro, Francesca Romana Pennecchi, Walter Bich

The paper ``Physics without determinism: Alternative interpretations of classical physics'' [Phys. Rev. A 100, 062107 (2019)] defines finite information quantities (FIQ). A FIQ expresses the available information about the value of a physical quantity. We show that a change in the measurement unit does not preserve the information carried by a FIQ and therefore that the definition provided in the paper is not complete.

Neal G. Anderson

Howard L. Resnikoff

Kaito Watanabe, Ryuji Takagi

Work extraction is one of the most central processes in quantum thermodynamics. However, the prior analysis of optimal extractable work has been restricted to a limited operational scenario where complete information about the initial state is given. Here, we introduce a general framework of black box work extraction, which addresses the inaccessibility of information on the initial state. We show that the optimal extractable work in the black box setting is completely characterized by the performance of a composite hypothesis testing task, a fundamental problem in information theory. We employ this general relation to reduce the asymptotic black box work extraction to the quantum Stein's lemma in composite hypothesis testing, allowing us to provide their exact characterization in terms of the Helmholtz free energy. We also show a new quantum Stein's lemma motivated in this physical setting, where a composite hypothesis contains a certain correlation. Our Letter exhibits the importance of information about the initial state and gives a new interpretation of the quantities in the composite quantum hypothesis testing, encouraging the interplay between the physical settings and the information theory.

Caesar P. Viazminsky, James P. Vary

We decompose the Hilbert space of wave functions into two subspaces, and assign to a given observable two effective representatives that act in the model space. The first serves to determine some of the eigenvalues of the full observable, while the second serves to determine its matrix elements, in any basis in one of the subspaces, in terms of quantities pertaining to the model space. We also show that if the Hamiltonian of a physical system possesses symmetries then these symmetries continue to hold for its effective representatives of the first type. Maximum information about the system can be obtained in terms of two sets of effective representatives. The first set of representatives is complete. Other observables that do not commute with all members of the complete set have only one type of representative.