81 research outputs found
Entanglement Typicality
We provide a summary of both seminal and recent results on typical
entanglement. By typical values of entanglement, we refer here to values of
entanglement quantifiers that (given a reasonable measure on the manifold of
states) appear with arbitrarily high probability for quantum systems of
sufficiently high dimensionality. We work within the Haar measure framework for
discrete quantum variables, where we report on results concerning the average
von Neumann and linear entropies as well as arguments implying the typicality
of such values in the asymptotic limit. We then proceed to discuss the
generation of typical quantum states with random circuitry. Different phases of
entanglement, and the connection between typical entanglement and
thermodynamics are discussed. We also cover approaches to measures on the
non-compact set of Gaussian states of continuous variable quantum systems.Comment: Review paper with two quotes and minimalist figure
Teleportation fidelities of squeezed states from thermodynamical state space measures.
Published versio
The work value of information
We present quantitative relations between work and information that are valid
both for finite sized and internally correlated systems as well in the
thermodynamical limit. We suggest work extraction should be viewed as a game
where the amount of work an agent can extract depends on how well it can guess
the micro-state of the system. In general it depends both on the agent's
knowledge and risk-tolerance, because the agent can bet on facts that are not
certain and thereby risk failure of the work extraction. We derive strikingly
simple expressions for the extractable work in the extreme cases of effectively
zero- and arbitrary risk tolerance respectively, thereby enveloping all cases.
Our derivation makes a connection between heat engines and the smooth entropy
approach. The latter has recently extended Shannon theory to encompass finite
sized and internally correlated bit strings, and our analysis points the way to
an analogous extension of statistical mechanics.Comment: 5 pages, 4 figure
Guaranteed energy-efficient bit reset in finite time
Landauer's principle states that it costs at least kTln2 of work to reset one
bit in the presence of a heat bath at temperature T. The bound of kTln2 is
achieved in the unphysical infinite-time limit. Here we ask what is possible if
one is restricted to finite-time protocols. We prove analytically that it is
possible to reset a bit with a work cost close to kTln2 in a finite time. We
construct an explicit protocol that achieves this, which involves changing the
system's Hamiltonian avoiding quantum coherences, and thermalising. Using
concepts and techniques pertaining to single-shot statistical mechanics, we
further develop the limit on the work cost, proving that the heat dissipated is
close to the minimal possible not just on average, but guaranteed with high
confidence in every run. Moreover we exploit the protocol to design a quantum
heat engine that works near the Carnot efficiency in finite time.Comment: 5 pages + 5 page technical appendix. 5 figures. Author accepted
versio
Maximum one-shot dissipated work from Renyi divergences
Thermodynamics describes large-scale, slowly evolving systems. Two modern
approaches generalize thermodynamics: fluctuation theorems, which concern
finite-time nonequilibrium processes, and one-shot statistical mechanics, which
concerns small scales and finite numbers of trials. Combining these approaches,
we calculate a one-shot analog of the average dissipated work defined in
fluctuation contexts: the cost of performing a protocol in finite time instead
of quasistatically. The average dissipated work has been shown to be
proportional to a relative entropy between phase-space densities, to a relative
entropy between quantum states, and to a relative entropy between probability
distributions over possible values of work. We derive one-shot analogs of all
three equations, demonstrating that the order-infinity Renyi divergence is
proportional to the maximum possible dissipated work in each case. These
one-shot analogs of fluctuation-theorem results contribute to the unification
of these two toolkits for small-scale, nonequilibrium statistical physics.Comment: 8 pages. Close to published versio
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