How do we have to Change Quantum Mechanics in Order to Describe Separated Systems?

Petr Hájíček

Careful analysis of cluster separability opens a way to a completely new understanding of preparation and registration procedures for microsystems: they are changes of separation status. An important observation is that quantum mechanics does not specify what happens to systems when they change their separation status. New rules that close this gap can therefore be added without disturbing the logic of quantum mechanics. Another important observation is that registration apparatuses for microsystems must contain detectors and that their readings are signals from detectors. This leads to further restrictions on measurability of observables, especially for macroscopic quantum systems. Beltrametti-Cassinelli-Lahti model is used to show how this approach leads to solution of the measurement problem.

Diederik Aerts

Eiji Konishi

Abstract In quantum mechanics, we define the measuring system M in a selective measurement by two conditions. Firstly, when we define the measured system S as the system in which the non-selective measurement part acts, M is independent from the measured system S as a quantum system in the sense that any time-dependent process in the total system S + M is divisible into parts for S and M . Secondly, when we can separate S and M from each other without changing the unitary equivalence class of the state of S from that obtained by the partial trace of M , the eigenstate selection in the selective measurement cannot be realized. In order for such a system M to exist, we show that in one selective measurement of an observable of a quantum system S 0 of particles in S , there exists a negative entropy transfer from M to S that can be directly transformed into an amount of Helmholtz free energy of where T is the thermodynamic temperature of the system S . Equivalently, an extra amount of work, , is required to be done by the system M .

Dirk Aerts

Eiji Konishi

In quantum mechanics, we define the measuring system $M$ in a selective measurement by two conditions. Firstly, when we define the measured system $S$ as the system in which the non-selective measurement part acts, $M$ is independent from the measured system $S$ as a quantum system in the sense that any time-dependent process in the total system $S+M$ is divisible into parts for $S$ and $M$. Secondly, when we can separate $S$ and $M$ from each other without changing the unitary equivalence class of the state of $S$ from that obtained by the partial trace of $M$, the eigenstate selection in the selective measurement cannot be realized. In order for such a system $M$ to exist, we show that in one selective measurement of an observable of a quantum system $S_0$ of particles in $S$, there exists a negative entropy transfer from $M$ to $S$ that can be directly transformed into an amount of Helmholtz free energy of $k_BT$ where $T$ is the thermodynamic temperature of the system $S$. Equivalently, an extra amount of work, $k_BT$, is required to be done by the system $M$.

Diederik Aerts