76 research outputs found
Beyond heat baths II: Framework for generalized thermodynamic resource theories
Thermodynamics, which describes vast systems, has been reconciled with small
scales, relevant to single-molecule experiments, in resource theories. Resource
theories have been used to model exchanges of energy and information. Recently,
particle exchanges were modeled; and an umbrella family of thermodynamic
resource theories was proposed to model diverse baths, interactions, and free
energies. This paper motivates and details the family's structure and
prospective applications. How to model electrochemical, gravitational,
magnetic, and other thermodynamic systems is explained. Szilard's engine and
Landauer's Principle are generalized, as resourcefulness is shown to be
convertible not only between information and gravitational energy, but also
among diverse degrees of freedom. Extensive variables are associated with
quantum operators that might fail to commute, introducing extra nonclassicality
into thermodynamic resource theories. An early version of this paper partially
motivated the later development of noncommutative thermalization. This
generalization expands the theories' potential for modeling realistic systems
with which small-scale statistical mechanics might be tested experimentally.Comment: Minor updates (contributions clarified, material restored from v1,
references updated). 18 pages (including 2 figures) + appendice
Quantum information in the Posner model of quantum cognition
Matthew Fisher recently postulated a mechanism by which quantum phenomena
could influence cognition: Phosphorus nuclear spins may resist decoherence for
long times, especially when in Posner molecules. The spins would serve as
biological qubits. We imagine that Fisher postulates correctly. How adroitly
could biological systems process quantum information (QI)? We establish a
framework for answering. Additionally, we construct applications of biological
qubits to quantum error correction, quantum communication, and quantum
computation. First, we posit how the QI encoded by the spins transforms as
Posner molecules form. The transformation points to a natural computational
basis for qubits in Posner molecules. From the basis, we construct a quantum
code that detects arbitrary single-qubit errors. Each molecule encodes one
qutrit. Shifting from information storage to computation, we define the model
of Posner quantum computation. To illustrate the model's quantum-communication
ability, we show how it can teleport information incoherently: A state's
weights are teleported. Dephasing results from the entangling operation's
simulation of a coarse-grained Bell measurement. Whether Posner quantum
computation is universal remains an open question. However, the model's
operations can efficiently prepare a Posner state usable as a resource in
universal measurement-based quantum computation. The state results from
deforming the Affleck-Kennedy-Lieb-Tasaki (AKLT) state and is a projected
entangled-pair state (PEPS). Finally, we show that entanglement can affect
molecular-binding rates, boosting a binding probability from 33.6% to 100% in
an example. This work opens the door for the QI-theoretic analysis of
biological qubits and Posner molecules.Comment: Published versio
Quantum voting and violation of Arrow's Impossibility Theorem
We propose a quantum voting system, in the spirit of quantum games such as
the quantum Prisoner's Dilemma. Our scheme enables a constitution to violate a
quantum analog of Arrow's Impossibility Theorem. Arrow's Theorem is a claim
proved deductively in economics: Every (classical) constitution endowed with
three innocuous-seeming properties is a dictatorship. We construct quantum
analogs of constitutions, of the properties, and of Arrow's Theorem. A quantum
version of majority rule, we show, violates this Quantum Arrow Conjecture. Our
voting system allows for tactical-voting strategies reliant on entanglement,
interference, and superpositions. This contribution to quantum game theory
helps elucidate how quantum phenomena can be harnessed for strategic advantage.Comment: Version accepted by Phys. Rev. A. Added background and references
about game theory and about Arrow's Theorem. Added an opportunity for further
research. For citation purposes: The second author's family name is "Yunger
Halpern" (not "Halpern"
Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices
We describe the formation of highly degenerate, Landau-level-like amplified
states in a strained photonic honeycomb lattice in which amplification breaks
the sublattice symmetry. As a consequence of the parity anomaly, the zeroth
Landau level is localized on a single sublattice and possesses an enhanced or
reduced amplification rate. The spectral properties of the higher Landau levels
are constrained by a generalized time-reversal symmetry. In the setting of
two-dimensional photonic crystal lasers, the anomaly directly affects the mode
selection and lasing threshold while in three-dimensional photonic lattices it
can be probed via beam dynamics.Comment: 5 pages, 2 figures, submitted to journal in May 2012. v2: final
version, including supplemental material (5+2 pages, 2+3 figures
Number of trials required to estimate a free-energy difference, using fluctuation relations
The difference Delta F between free energies has applications in biology,
chemistry, and pharmacology. The value of Delta F can be estimated from
experiments or simulations, via fluctuation theorems developed in statistical
mechanics. Calculating the error in a Delta F estimate is difficult. Worse,
atypical trials dominate estimates. How many trials one should perform was
estimated roughly in [Jarzynski, Phys. Rev. E 73, 046105 (2006)]. We enhance
the approximation with information-theoretic strategies: We quantify
"dominance" with a tolerance parameter chosen by the experimenter or simulator.
We bound the number of trials one should expect to perform, using the
order-infinity Renyi entropy. The bound can be estimated if one implements the
"good practice" of bidirectionality, known to improve estimates of Delta F.
Estimating Delta F from this number of trials leads to an error that we bound
approximately. Numerical experiments on a weakly interacting dilute classical
gas support our analytical calculations.Comment: 7 pages (5 figures). Published version. Added fail-safety analysis,
discussion of quantum and classical settings, and comparisons with previous
work
Fundamental limitations on photoisomerization from thermodynamic resource theories
Small, out-of-equilibrium, and quantum systems defy simple thermodynamic
expressions. Such systems are exemplified by molecular switches, which exchange
heat with a bath. These molecules can photoisomerize, or change conformation,
or switch, upon absorbing light. The photoisomerization probability depends on
kinetic details that couple the molecule's energetics to its dissipation.
Therefore, a simple, general, thermodynamic-style bound on the
photoisomerization probability seems out of reach. We derive such a bound using
a resource theory. The resource-theory framework is a set of mathematical
tools, developed in quantum information theory, used to generalize
thermodynamics to small and quantum settings. From this toolkit has been
derived a generalization of the second law, the thermomajorization preorder. We
use thermomajorization to upper-bound the photoisomerization probability. Then,
we compare the bound with an equilibrium prediction and with a Lindbladian
model. We identify a realistic parameter regime in which the Lindbladian
evolution saturates the thermomajorization bound. We also quantify the energy
coherence in the electronic degree of freedom, and we argue that this coherence
cannot promote photoisomerization. This work illustrates how
quantum-information-theoretic thermodynamics can elucidate complex quantum
processes in nature, experiments, and synthetics.Comment: 8.5 pages. Published versio
The quasiprobability behind the out-of-time-ordered correlator
Two topics, evolving rapidly in separate fields, were combined recently: The
out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in
many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents
operators in quantum optics. The OTOC has been shown to equal a moment of a
summed quasiprobability. That quasiprobability, we argue, is an extension of
the KD distribution. We explore the quasiprobability's structure from
experimental, numerical, and theoretical perspectives. First, we simplify and
analyze the weak-measurement and interference protocols for measuring the OTOC
and its quasiprobability. We decrease, exponentially in system size, the number
of trials required to infer the OTOC from weak measurements. We also construct
a circuit for implementing the weak-measurement scheme. Next, we calculate the
quasiprobability (after coarse-graining) numerically and analytically: We
simulate a transverse-field Ising model first. Then, we calculate the
quasiprobability averaged over random circuits, which model chaotic dynamics.
The quasiprobability, we find, distinguishes chaotic from integrable regimes.
We observe nonclassical behaviors: The quasiprobability typically has negative
components. It becomes nonreal in some regimes. The onset of scrambling breaks
a symmetry that bifurcates the quasiprobability, as in classical-chaos
pitchforks. Finally, we present mathematical properties. The quasiprobability
obeys a Bayes-type theorem, for example, that exponentially decreases the
memory required to calculate weak values, in certain cases. A time-ordered
correlator analogous to the OTOC, insensitive to quantum-information
scrambling, depends on a quasiprobability closer to a classical probability.
This work not only illuminates the OTOC's underpinnings, but also generalizes
quasiprobability theory and motivates immediate-future weak-measurement
challenges.Comment: Close to published versio
Entropic uncertainty relations for quantum information scrambling
How violently do two quantum operators disagree? Different fields of physics
feature different measures of incompatibility: (i) In quantum information
theory, entropic uncertainty relations constrain measurement outcomes. (ii) In
condensed matter and high-energy physics, the out-of-time-ordered correlator
(OTOC) signals scrambling, the spread of information through many-body
entanglement. We unite these measures, proving entropic uncertainty relations
for scrambling. The entropies are of distributions over weak and strong
measurements' possible outcomes. The weak measurements ensure that the OTOC
quasiprobability (a nonclassical generalization of a probability, which
coarse-grains to the OTOC) governs terms in the uncertainty bound. The
quasiprobability causes scrambling to strengthen the bound in numerical
simulations of a spin chain. This strengthening shows that entropic uncertainty
relations can reflect the type of operator disagreement behind scrambling.
Generalizing beyond scrambling, we prove entropic uncertainty relations
satisfied by commonly performed weak-measurement experiments. We unveil a
physical significance of weak values (conditioned expectation values): as
governing terms in entropic uncertainty bounds.Comment: Close to published version, but has more-pedagogical formatting. 13
pages, including 4 figure
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