[Show abstract][Hide abstract] ABSTRACT: Living organisms capitalize on their ability to predict their environment to
maximize their available free energy, and invest this energy in turn to create
new complex structures. Is there a preferred method by which this manipulation
of structure should be done? Our intuition is "simpler is better," but this is
only a guiding principal. Here, we substantiate this claim through
thermodynamic reasoning. We present a new framework for the manipulation of
patterns (structured sequences of data) by predictive devices. We identify the
dissipative costs and how they can be minimized by the choice of memory in
these predictive devices. For pattern generation, we see that simpler is indeed
better. However, contrary to intuition, when it comes to extracting work from a
pattern, any device capable of making statistically accurate predictions can
recover all available energy.
[Show abstract][Hide abstract] ABSTRACT: 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.
New Journal of Physics 09/2015; 17(9). DOI:10.1088/1367-2630/17/9/095003 · 3.56 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more interesting quantity in general. We show that an expression that quantifies majorization determines the optimal guaranteed work. We argue it should therefore be the central quantity of statistical mechanics, rather than the von Neumann entropy. In the limit of many identical and independent subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered but in the non-equilbrium regime the optimal guaranteed work can be radically different to the optimal average. Moreover our measure of majorization governs which evolutions can be realized via thermal interactions, whereas the non-decrease of the von Neumann entropy is not sufficiently restrictive. Our results are inspired by single-shot information theory.
New Journal of Physics 07/2015; 17(7). DOI:10.1088/1367-2630/17/7/073001 · 3.56 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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, one between
quantum states, and one between probability distributions over possible values
of work. We derive one-shot analogs of all three equations, demonstrating that
the order-infinity R\'enyi divergence is proportional to the maximum 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.
[Show abstract][Hide abstract] ABSTRACT: The tunneling experiment is a key technique for detecting Majorana fermion (MF) in solid state systems. We use Keldysh non-equilibrium Green function method to study two-lead tunneling in superconducting nanowire with Rashba and Dresselhaus spin-orbit couplings. A zero-bias dc conductance peak appears in our setup which signifies the existence of MF and is in accordance with previous experimental results on InSb nanowire. Interestingly, due to the exotic property of MF, there exists a hole transmission channel which makes the currents asymmetric at the left and right leads. The ac current response mediated by MF is also studied here. To discuss the impacts of Coulomb interaction and disorder on the transport property of Majorana nanowire, we use the renormalization group method to study the phase diagram of the wire. It is found that there is a topological phase transition under the interplay of superconductivity and disorder. We find that the Majorana transport is preserved in the superconducting-dominated topological phase and destroyed in the disorder-dominated non-topological insulator phase.
[Show abstract][Hide abstract] ABSTRACT: We suggest that quantum macroscopicity should be quantified in terms of
coherence, and propose a set of conditions that should be satisfied by any
measure of macroscopic coherence. We show that this enables a rigorous
justification of a previously proposed measure of macroscopicity based on the
quantum Fisher information, while another measure does not satisfy important
monotonicity criteria.
[Show abstract][Hide abstract] ABSTRACT: We derive an equality for non-equilibrium statistical mechanics. The equality
concerns the worst-case work output of a time-dependent Hamiltonian protocol in
the presence of a Markovian heat bath. It 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. We apply the equality to an electron box.
[Show abstract][Hide abstract] ABSTRACT: Entanglement can be well quantified by R\'{e}nyi $\alpha$-entropy which is a
generalization of the standard von Neumann entropy. Here we study the measure
of entanglement R\'{e}nyi $\alpha$-entropy for arbitrary two-qubit states. We
show that entanglement of two states may be incomparable, contrary to other
well-accepted entanglement measures. These facts impose constraint on the
convertibility of entangled states by local operations and classical
communication. We find that when $\alpha $ is larger than a critical value, the
entanglement measure by R\'{e}nyi $\alpha$-entropy is determined solely by
concurrence which is a well accepted measure of entanglement. When $\alpha $ is
small, the entanglement R\'{e}nyi $\alpha$-entropy of Werner state is obtained.
Interestingly, we show that entanglement R\'{e}nyi $\alpha$-entropy of Werner
state is always less than any pure entangled state when $\alpha $ is close to
zero, even this Werner state is close to a maximally entangled state and the
concurrence is larger. We also conclude that the optimal decomposition of a
general mixed state cannot be the same for all $\alpha $.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: We investigate the notion of quantumness based on the non-commutativity of
the algebra of observables and introduce a measure of quantumness based on the
mutual incompatibility of quantum states. Since it relies on the full algebra
of observables, our measure for composed systems is partition independent and
witnesses the global quantum nature of a state. We show that such quantity can
be experimentally measured with an interferometric setup and that, when an
arbitrary bipartition is introduced, it detects the one-way quantum
correlations restricted to one of the two subsystems. We finally show that, by
combining only two projective measurements and carrying out the interference
procedure, our measure becomes an efficient universal witness of quantum
discord and non-classical correlations.
[Show abstract][Hide abstract] ABSTRACT: In general relativity, closed timelike curves can break causality with
remarkable and unsettling consequences. At the classical level, they induce
causal paradoxes disturbing enough to motivate conjectures that explicitly
prevent their existence. At the quantum level, resolving such paradoxes induce
radical benefits - from cloning unknown quantum states to solving problems
intractable to quantum computers. Instinctively, one expects these benefits to
vanish if causality is respected. Here we show that in harnessing entanglement,
we can efficiently solve NP-complete problems and clone arbitrary quantum
states - even when all time-travelling systems are completely isolated from the
past. Thus, the many defining benefits of closed timelike curves can still be
harnessed, even when causality is preserved. Our results unveil the subtle
interplay between entanglement and general relativity, and significantly
improve the potential of probing the radical effects that may exist at the
interface between relativity and quantum theory.
[Show abstract][Hide abstract] ABSTRACT: Maxwell's daemon is a popular personification of a principle connecting information gain and extractable work in thermodynamics. A Szilard Engine is a particular hypothetical realization of Maxwell's daemon, which is able to extract work from a single thermal reservoir by measuring the position of particle(s) within the system. Here we investigate the role of particle statistics in the whole process; namely, how the extractable work changes if instead of classical particles fermions or bosons are used as the working medium. We give a unifying argument for the optimal work in the different cases: the extractable work is determined solely by the information gain of the initial measurement, as measured by the mutual information, regardless of the number and type of particles which constitute the working substance.
[Show abstract][Hide abstract] ABSTRACT: We investigate the thermodynamical properties of quantum fields in curved
spacetime. Our approach is to consider quantum fields in curved spacetime as a
quantum system undergoing an out-of-equilibrium transformation. The
non-equilibrium features are studied by using a formalism which has been
developed to derive fluctuation relations and emergent irreversible features
beyond the linear response regime. We apply these ideas to an expanding
universe scenario, therefore avoiding assumptions on the relation between
entropy and quantum matter. We provide a fluctuation theorem which allows us to
understand particle production due to the expansion of the universe as an
entropic increase. Our results pave the way towards a different understanding
of the thermodynamics of relativistic and quantum systems in our universe.
[Show abstract][Hide abstract] ABSTRACT: Fluctuation-dissipation relations, such as Crooks' Theorem and Jarzynski's
Equality, are powerful tools in quantum and classical nonequilibrium
statistical mechanics. We link these relations to a newer approach known as
"one-shot statistical mechanics." Rooted in one-shot information theory,
one-shot statistical mechanics concerns statements true of every implementation
of a protocol, not only of averages. We show that two general models for work
extraction in the presence of heat baths obey fluctuation relations and
one-shot results. We demonstrate the usefulness of this bridge between
frameworks in several ways. Using Crooks' Theorem, we derive a bound on
one-shot work quantities. These bounds are tighter, in certain parameter
regimes, than a bound in the fluctuation literature and a bound in the one-shot
literature. Our bounds withstand tests by numerical simulations of an
information-theoretic Carnot engine. By analyzing data from DNA-hairpin
experiments, we show that experiments used to test fluctuation theorems also
test one-shot results. Additionally, we derive one-shot analogs of a known
equality between a relative entropy and the average work dissipated as heat.
Our unification of experimentally tested fluctuation relations with one-shot
statistical mechanics is intended to bridge one-shot theory to applications.
[Show abstract][Hide abstract] ABSTRACT: Recently, a novel operational strategy to access quantum correlation
functions of the form Tr[A rho B] was provided in [F. Buscemi, M. Dall'Arno, M.
Ozawa, and V. Vedral, arXiv:1312.4240]. Here we propose a realization scheme,
that we call partial expectation values, implementing such strategy in terms of
a unitary interaction with an ancillary system followed by the measurement of
an observable on the ancilla. Our scheme is universal, being independent of
rho, A, and B, and it is optimal in a statistical sense. Our scheme is suitable
for implementation with present quantum optical technology, and provides a new
way to test uncertainty relations.
International Journal of Quantum Information 09/2014; 12(07n08). DOI:10.1142/S0219749915600023 · 0.88 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present arguments to the effect that time and temperature can be viewed as
a form of quantum entanglement. Furthermore, if temperature is thought of as
arising from the quantum mechanical tunneling probability this then offers us a
way of dynamically "converting" time into temperature based on the entanglement
between the transmitted and reflected modes. We then show how similar
entanglement-based logic can be applied to the dynamics of cosmological
inflation and discuss the possibility of having observable effects of the early
gravitational entanglement at the level of the universe.
[Show abstract][Hide abstract] ABSTRACT: The quantum uncertainty principle stipulates that when one observable is predictable there must be some other observables that are unpredictable. The principle is viewed as holding the key to many quantum phenomena and understanding it deeper is of great interest in the study of the foundations of quantum theory. Here we show that apart from being restrictive, the principle also plays a positive role as the enabler of non-classical dynamics in an interferometer. First we note that instantaneous action at a distance should not be possible. We show that for general probabilistic theories this heavily curtails the non-classical dynamics. We prove that there is a trade-off with the uncertainty principle that allows theories to evade this restriction. On one extreme, non-classical theories with maximal certainty have their non-classical dynamics absolutely restricted to only the identity operation. On the other extreme, quantum theory minimizes certainty in return for maximal non-classical dynamics.
[Show abstract][Hide abstract] ABSTRACT: There have recently been a number of proposals for measures to describe the
extent to which the quantum behaviour of a system extends to the macroscopic
scale. We argue that measures for systems of qubits should be extended to
classify a larger set of states (including two-dimensional cluster states and
certain topological states) as macroscopically quantum. This is motivated by
the ability to use local measurements to distil a Schroedinger's cat state from
states which are not macroscopically quantum according to current measures. We
also investigate the role played by imperfect measurements.
[Show abstract][Hide abstract] ABSTRACT: A generic and intuitive model for coherent energy transport in multiple
minima systems coupled to a quantum mechanical bath is shown. Using a simple
spin-boson system, we illustrate how a generic donor-acceptor system can be
brought into resonance using a narrow band of vibrational modes, such that the
transfer efficiency of an electron-hole pair (exciton) is made arbitrarily
high. Coherent transport phenomena in nature are of renewed interest since the
discovery that a photon captured by the light-harvesting complex (LHC) in
photosynthetic organisms can be conveyed to a chemical reaction centre with
near-perfect efficiency. Classical explanations of the transfer use stochastic
diffusion to model the hopping motion of a photo-excited exciton. This accounts
inadequately for the speed and efficiency of the energy transfer measured in a
series of recent landmark experiments. Taking a quantum mechanical perspective
can help capture the salient features of the efficient part of that transfer.
To show the versatility of the model, we extend it to a multiple minima system
comprising seven-sites, reminiscent of the widely studied Fenna-Matthews-Olson
(FMO) light-harvesting complex. We show that an idealised transport model for
multiple minima coupled to a narrow-band phonon can transport energy with
arbitrarily high efficiency.