253 research outputs found
Using quantum theory to reduce the complexity of input-output processes
All natural things process and transform information. They receive
environmental information as input, and transform it into appropriate output
responses. Much of science is dedicated to building models of such systems --
algorithmic abstractions of their input-output behavior that allow us to
simulate how such systems can behave in the future, conditioned on what has
transpired in the past. Here, we show that classical models cannot avoid
inefficiency -- storing past information that is unnecessary for correct future
simulation. We construct quantum models that mitigate this waste, whenever it
is physically possible to do so. This suggests that the complexity of general
input-output processes depends fundamentally on what sort of information theory
we use to describe them.Comment: 10 pages, 5 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
Characterization of the probabilistic models that can be embedded in quantum theory
Quantum bits can be isolated to perform useful information-theoretic tasks,
even though physical systems are fundamentally described by very
high-dimensional operator algebras. This is because qubits can be consistently
embedded into higher-dimensional Hilbert spaces. A similar embedding of
classical probability distributions into quantum theory enables the emergence
of classical physics via decoherence. Here, we ask which other probabilistic
models can similarly be embedded into finite-dimensional quantum theory. We
show that the embeddable models are exactly those that correspond to the
Euclidean special Jordan algebras: quantum theory over the reals, the complex
numbers, or the quaternions, and "spin factors" (qubits with more than three
degrees of freedom), and direct sums thereof. Among those, only classical and
standard quantum theory with superselection rules can arise from a physical
decoherence map. Our results have significant consequences for some
experimental tests of quantum theory, by clarifying how they could (or could
not) falsify it. Furthermore, they imply that all unrestricted non-classical
models must be contextual.Comment: 6 pages, 0 figure
The classical-quantum divergence of complexity in modelling spin chains
The minimal memory required to model a given stochastic process - known as
the statistical complexity - is a widely adopted quantifier of structure in
complexity science. Here, we ask if quantum mechanics can fundamentally change
the qualitative behaviour of this measure. We study this question in the
context of the classical Ising spin chain. In this system, the statistical
complexity is known to grow monotonically with temperature. We evaluate the
spin chain's quantum mechanical statistical complexity by explicitly
constructing its provably simplest quantum model, and demonstrate that this
measure exhibits drastically different behaviour: it rises to a maximum at some
finite temperature then tends back towards zero for higher temperatures. This
demonstrates how complexity, as captured by the amount of memory required to
model a process, can exhibit radically different behaviour when quantum
processing is allowed.Comment: 9 pages, 3 figures, comments are welcom
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
Introducing one-shot work into fluctuation relations
Two approaches to small-scale and quantum thermodynamics are fluctuation
relations and one-shot statistical mechanics. Fluctuation relations (such as
Crooks' Theorem and Jarzynski's Equality) relate nonequilibrium behaviors to
equilibrium quantities such as free energy. One-shot statistical mechanics
involves statements about every run of an experiment, not just about averages
over trials.
We investigate the relation between the two approaches. We show that both
approaches feature the same notions of work and the same notions of probability
distributions over possible work values. The two approaches are alternative
toolkits with which to analyze these distributions. To combine the toolkits, we
show how one-shot work quantities can be defined and bounded in contexts
governed by Crooks' Theorem. These bounds provide a new bridge from one-shot
theory to experiments originally designed for testing fluctuation theorems.Comment: 37 pages, 6 figure
Entropic equality for worst-case work at any protocol speed
We derive an equality for non-equilibrium statistical mechanics in
finite-dimensional quantum systems. The equality concerns the worst-case work
output of a time-dependent Hamiltonian protocol in the presence of a Markovian
heat bath. It has has the form "worst-case work = penalty - optimum". The
equality holds for all rates of changing the Hamiltonian and can be used to
derive the optimum by setting the penalty to 0. The optimum term contains the
max entropy of the initial state, rather than the von Neumann entropy, thus
recovering recent results from single-shot statistical mechanics. Energy
coherences can arise during the protocol but are assumed not to be present
initially. We apply the equality to an electron box.Comment: 4 page + 14 page appendix; 8 figures; AA
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