Quantum processes which do not use coherence

A major signature of quantum mechanics beyond classical physics is coherence, the existence of superposition states. The recently developed resource theory of quantum coherence allows the formalisation of incoherent operations -- those operations which cannot create coherence. We identify the set of operations which additionally do not use coherence. These are such that coherence cannot be exploited by a classical observer, who measures incoherent properties of the system, to go beyond classical dynamics. We give a physical interpretation in terms of interferometry and prove a dilation theorem, showing how these operations can always be constructed by interacting the system in an incoherent way with an ancilla. Such a physical justification is not known for the incoherent operations, thus our results lead to a physically well-motivated resource theory of coherence. Next, we investigate the implications for coherence in multipartite systems. We show that quantum correlations can be defined naturally with respect to a fixed basis, providing a link between coherence and quantum discord. We demonstrate the interplay between these two quantities under our studied operations, and suggest implications for the theory of quantum discord by relating the studied operations to those which cannot create discord.Comment: 15 pages, 6 figures, comments are welcome. Revised presentation and added Result 7. Close to published version (accepted for publication in Physical Review X

Quantifying memory capacity as a quantum thermodynamic resource

The information-carrying capacity of a memory is known to be a thermodynamic resource facilitating the conversion of heat to work. Szilard's engine explicates this connection through a toy example involving an energy-degenerate two-state memory. We devise a formalism to quantify the thermodynamic value of memory in general quantum systems with nontrivial energy landscapes. Calling this the thermal information capacity, we show that it converges to the non-equilibrium Helmholtz free energy in the thermodynamic limit. We compute the capacity exactly for a general two-state (qubit) memory away from the thermodynamic limit, and find it to be distinct from known free energies. We outline an explicit memory--bath coupling that can approximate the optimal qubit thermal information capacity arbitrarily well.Comment: 6 main + 7 appendix pages; 5 main + 2 appendix figure

Two Topics on Local Theta Correspondence

Ph.DDOCTOR OF PHILOSOPH