Background

Recent experiments [1][2][3] have explored quantum versions of the Maxwell demon. There is a fundamental difference between classical and quantum measurement: Classical measurements are passive, at least in principle, and information about the measured system is transferred to the measurement device without changing or disturbing the state of the system. Quantum measurements are active and the state of the system after the measurement is in general different from the state before the measurement. This means that the analysis of quantum Maxwell demons has a fundamental difference as compared to classical. Several papers have discussed the quantum Maxwell demon, the classic papers being by Zurek[4] and Lloyd[5]. The models considered are different, and the conclusions reached are at least superficially contradictory. However, this may be a result of differences in assumptions rather than actual disagreements in the analysis. Lloyd considered a two-state system and concluded that the measurement process induces extra entropy

production, thereby degrading the performance of a quantum demon compared to a classical one. Zurek considered a more exact quantum duplicate of the classical Szilard engine, with one quantum particle in a box where a dividing wall is introduced to isolate the particle in one of the two halves. He found that as long as there was good thermal contact with a heat bath during the entire operation, the quantum version would give the same results as the classical. His analysis was recently criticised[6], and it was pointed out that contrary to the classical case, the insertion of the dividing wall will have an energy cost in quantum theory. However, the entropy production in a quantum measurement was not discussed in this situation, and the relation to the results of Lloyd remain unclear.

The main objective of the master project is to provide a clear understanding of the various versions of the quantum Maxwell demon and its implication for the understanding of quantum measurements. This is important for several reasons. First, it is of principal interest to have a clear understanding of a model problem for quantum feedback operation of a information processing device. Second, this is connected to the understanding of quantum measurements and their difference from classical, which still is the most important unsolved problem in the foundations of quantum mechanics. Third, with the advent of new experiments, it is important to have a general theoretical framework in which to place the different versions of operation, as well as to motivate and explore novel experimental variants. .

Plan for the project

We can distinguish several types of quantum Maxwell demons. First, the system that is measured is a quantum system, while the demon itself is classical. This means that the demons measurement is a quantum measurement, collapsing the wave function and giving a well defined classical measurement outcome. Second, both the measured system and the demon itself are quantum systems, and the measurement process is described fully quantum mechanically, as an interaction leading to entanglement between the two. The system can be initially prepared in some (possibly mixed) state, and then decoupled from the environment during measurement and feedback. Or the system can be in thermal equilibrium during the whole process, in which environmental decoherence will affect the system state. In this project, we want to reach a unified theoretical understanding of the different types of quantum Maxwell's demons by constructing models that will interpolate between those studied previously. In this way we can continuously change between measurements in different bases, with different degree of environmental decoherence and with measurements being projective or entangling to various degrees. At present time, it is also not clear where in this set of models the current experiments are to be placed. We plan to make a critical review of existing and proposed experiments to see where they fall in the general picture.

[1] N. Cottet, S. Jezouin, L. Bretheau, P. Campagne-Ibarcq, Q. Ficheux, J. Anders, A. Auffèves, R. Azouit, P. Rouchon, B.

Huard, Observing a quantum Maxwell demon at work, 2017

[2] Patrice A. Camati, John P. S. Peterson,Tiago B. Batalhão, Kaonan Micadei, Alexandre M. Souza, Roberto S. Sarthour,

Ivan S. Oliveira, and Roberto M. Serra, Experimental Rectification of Entropy Production by Maxwell’s Demonin a

Quantum System, 2016

[3] J. P. S. Peterson, R. S. Sarthour, A. M. Souza,I. S. Oliveira, J. Goold, K. Modi,D. O. Soares-Pinto,and L. C. C eleri,

Experimental demonstration of information to energy conversion in a quantum system at the Landauer Limit, 2016

[4] Wojciech Hubert Zurek, MAXWELL’S DEMON, SZILARD’S ENGINE AND QUANTUMMEASUREMENTS, 2003

[5] Seth Lloyd, Quantum-mechanical Maxwell’s demon, 1997

[6] Sang Wook Kim, Takahiro Sagawa, Simone De Liberato, and Masahito Ueda, Quantum Szilard Engine, 2011