Thermodynamics of Quantum Measurement

Considering a general microscopic model for quantum measurement comprising a measurement apparatus coupled to a thermal bath, we analyze the energetic resources necessary for the realisation of quantum measurements, including the process of switching on and off the coupling between the system and the apparatus, the transition to a statistical mixture, the classical readout, and the apparatus resetting. We show via general thermodynamic arguments that the minimal required work...

Regarding the strange properties of quantum entropy and entanglement, e.g., the negative quantum conditional entropy, we revisited the foundations of quantum entropy, namely, von Neumann entropy, and raised the new method of quantum fine-grained entropy. With the applications in entanglement theory, quantum information processing, and quantum thermodynamics, we demonstrated the capability of quantum fine-grained entropy to resolve some notable confusions and problems, includi...

We show that the conservation and the non-additivity of the information, together with the additivity of the entropy make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the information non-additivity. Nevertheless, the later is also true in other fields, in which the interaction information is important. Examples are classical statistical mechanics, social statistics and financial processes. The second law of therm...

We present a partition of quantum observables in an open quantum system which is inherited from the division of the underlying Hilbert space or configuration space. It is shown that this partition leads to the definition of an inhomogeneous continuity equation for generic, non-local observables. This formalism is employed to describe the local evolution of the von Neumann entropy of a system of independent quantum particles out of equilibrium. Crucially, we find that all loca...

In 1939, von Neumann argued for the equivalence of the thermodynamic entropy and $-\text{Tr}\rho\ln\rho$, since known as the von Neumann entropy. Hemmo and Shenker (2006) recently challenged this argument by pointing out an alleged discrepancy between the two entropies in the single particle case, concluding that they must be distinct. In this article, their argument is shown to be problematic as it a) allows for a violation of the second law of thermodynamics and b) is based...

In this paper we introduce a definition for conditional energy changes due to general quantum measurements, as the change in the conditional energy evaluated before, and after, the measurement process. By imposing minimal physical requirements on these conditional energies, we show that the most general expression for the conditional energy after the measurement is simply the expected value of the Hamiltonian given the post-measurement state. Conversely, the conditional energ...

Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Here we address these questions by studying how compatibility with thermodynamics constrains the structure of quantum theory. We employ two postulates that any probabilistic theory with reasonable thermodynamic behavior ...

We introduce a quantum measurement process that is capable of characterizing an unknown state of a system almost without disturbing or collapsing it. The underlying idea is to extract information of a system from the thermodynamic quantities like work(s) and heat in a process, thereby uncovering a fundamental correspondence between information and thermodynamics. We establish an improved notion of information isolation and show that a process is isolated if it respects the fi...

By computing the local energy expectation values with respect to some local measurement basis we show that for any quantum system there are two fundamentally different contributions: changes in energy that do not alter the local von Neumann entropy and changes that do. We identify the former as work and the latter as heat. Since our derivation makes no assumptions on the system Hamiltonian or its state, the result is valid even for states arbitrarily far from equilibrium. Exa...

Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this article, we review two expositions of thermodynamics, one without reference to quantum theory, and the other quantum mechanical without probabilities of statistical mechanics. In the first, we show that entropy is an inherent property of any syst...