Microscopic analysis of the microscopic reversibility in quantum systems

We investigate the robustness of the microscopic reversibility in open quantum systems which is discussed by Monnai [arXiv:1106.1982 (2011)]. We derive an exact relation between the forward transition probability and the reversed transition probability in the case of a general measurement basis. We show that the microscopic reversibility acquires some corrections in general and discuss the physical meaning of the corrections. Under certain processes, some of the correction terms vanish and we numerically confirmed that the remaining correction term becomes negligible; the microscopic reversibility almost holds even when the local system cannot be regarded as macroscopic.Comment: 12 pages, 10 figure

Toward an Energy Efficient Language and Compiler for (Partially) Reversible Algorithms

We introduce a new programming language for expressing reversibility, Energy-Efficient Language (Eel), geared toward algorithm design and implementation. Eel is the first language to take advantage of a partially reversible computation model, where programs can be composed of both reversible and irreversible operations. In this model, irreversible operations cost energy for every bit of information created or destroyed. To handle programs of varying degrees of reversibility, Eel supports a log stack to automatically trade energy costs for space costs, and introduces many powerful control logic operators including protected conditional, general conditional, protected loops, and general loops. In this paper, we present the design and compiler for the three language levels of Eel along with an interpreter to simulate and annotate incurred energy costs of a program.Comment: 17 pages, 0 additional figures, pre-print to be published in The 8th Conference on Reversible Computing (RC2016

General Reversibility

The first and the second author introduced reversible ccs (rccs) in order to model concurrent computations where certain actions are allowed to be reversed. Here we show that the core of the construction can be analysed at an abstract level, yielding a theorem of pure category theory which underlies the previous results. This opens the way to several new examples; in particular we demonstrate an application to Petri nets.

Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production

The solution to nonlinear Fokker-Planck equation is constructed in terms of the minimal Markov semigroup generated by the equation. The semigroup is obtained by a purely functional analytical method via Hille-Yosida theorem. The existence of the positive invariant measure with density is established and a weak form of Foguel alternative proven. We show the equivalence among self-adjoint of the elliptic operator, time-reversibility, and zero entropy production rate of the stationary diffusion process. A thermodynamic theory for diffusion processes emerges.Comment: 23 page

A product form for the general stochastic matching model

We consider a stochastic matching model with a general compatibility graph, as introduced in \cite{MaiMoy16}. We show that the natural necessary condition of stability of the system is also sufficient for the natural matching policy 'First Come, First Matched' (FCFM). For doing so, we derive the stationary distribution under a remarkable product form, by using an original dynamic reversibility property related to that of \cite{ABMW17} for the bipartite matching model

Local reversibility and entanglement structure of many-body ground states

The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area law for entanglement entropy and the exponential decay of correlations between spatially separated observables. In this letter we present a novel characterization of locality in quantum states, which we call `local reversibility'. It characterizes the type of operations that are needed to reverse the action of a general disturbance on the state. We prove that unique ground states of gapped local Hamiltonian are locally reversible. This way, we identify new fundamental features of many-body ground states, which cannot be derived from the aforementioned properties. We use local reversibility to distinguish between states enjoying microscopic and macroscopic quantum phenomena. To demonstrate the potential of our approach, we prove specific properties of ground states, which are relevant both to critical and non-critical theories.Comment: 12 revtex pages, 2 pdf figs; minor changes, typos corrected. To be published in Quantum Science and Technolog