1,452 research outputs found
Structure of the thermodynamic arrow of time in classical and quantum theories
In this work we analyse the structure of the thermodynamic arrow of time,
defined by transformations that leave the thermal equilibrium state unchanged,
in classical (incoherent) and quantum (coherent) regimes. We note that in the
infinite-temperature limit the thermodynamic ordering of states in both regimes
exhibits a lattice structure. This means that when energy does not matter and
the only thermodynamic resource is given by information, the thermodynamic
arrow of time has a very specific structure. Namely, for any two states at
present there exists a unique state in the past consistent with them and with
all possible joint pasts. Similarly, there also exists a unique state in the
future consistent with those states and with all possible joint futures. We
also show that the lattice structure in the classical regime is broken at
finite temperatures, i.e., when energy is a relevant thermodynamic resource.
Surprisingly, however, we prove that in the simplest quantum scenario of a
two-dimensional system, this structure is preserved at finite temperatures. We
provide the physical interpretation of these results by introducing and
analysing the history erasure process, and point out that quantum coherence may
be a necessary resource for the existence of an optimal erasure process.Comment: 14 pages, 10 figures. Published version. Expanded discussion and a
new section on history erasure process adde
Pure Nash Equilibria in Concurrent Deterministic Games
We study pure-strategy Nash equilibria in multi-player concurrent
deterministic games, for a variety of preference relations. We provide a novel
construction, called the suspect game, which transforms a multi-player
concurrent game into a two-player turn-based game which turns Nash equilibria
into winning strategies (for some objective that depends on the preference
relations of the players in the original game). We use that transformation to
design algorithms for computing Nash equilibria in finite games, which in most
cases have optimal worst-case complexity, for large classes of preference
relations. This includes the purely qualitative framework, where each player
has a single omega-regular objective that she wants to satisfy, but also the
larger class of semi-quantitative objectives, where each player has several
omega-regular objectives equipped with a preorder (for instance, a player may
want to satisfy all her objectives, or to maximise the number of objectives
that she achieves.)Comment: 72 page
Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes
Among the predictive hidden Markov models that describe a given stochastic
process, the {\epsilon}-machine is strongly minimal in that it minimizes every
R\'enyi-based memory measure. Quantum models can be smaller still. In contrast
with the {\epsilon}-machine's unique role in the classical setting, however,
among the class of processes described by pure-state hidden quantum Markov
models, there are those for which there does not exist any strongly minimal
model. Quantum memory optimization then depends on which memory measure best
matches a given problem circumstance.Comment: 14 pages, 14 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/uemum.ht
Transformations among Pure Multipartite Entangled States via Local Operations Are Almost Never Possible
Local operations assisted by classical communication (LOCC) constitute the
free operations in entanglement theory. Hence, the determination of LOCC
transformations is crucial for the understanding of entanglement. We
characterize here almost all LOCC transformations among pure multipartite
multilevel states. Combined with the analogous results for qubit states shown
by Gour \emph{et al.} [J. Math. Phys. 58, 092204 (2017)], this gives a
characterization of almost all local transformations among multipartite pure
states. We show that nontrivial LOCC transformations among generic, fully
entangled, pure states are almost never possible. Thus, almost all multipartite
states are isolated. They can neither be deterministically obtained from
local-unitary-inequivalent (LU-inequivalent) states via local operations, nor
can they be deterministically transformed to pure, fully entangled
LU-inequivalent states. In order to derive this result, we prove a more general
statement, namely, that, generically, a state possesses no nontrivial local
symmetry. We discuss further consequences of this result for the
characterization of optimal, probabilistic single copy and probabilistic
multi-copy LOCC transformations and the characterization of LU-equivalence
classes of multipartite pure states.Comment: 13 pages main text + 10 pages appendix, 1 figure; close to published
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