38 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
Tunneling transfer protocol in a quantum dot chain immune to inhomogeneity
We propose a quantum dot (QD) implementation of a quantum state transfer
channel. The proposed channel consists of N vertically stacked QDs with the
nearest neighbor tunnel coupling, placed in an axial electric field. We show
that the system supports high-fidelity transfer of the state of a terminal dot
both by free evolution and by adiabatic transfer. The protocol is to a large
extent insensitive to inhomogeneity of the energy parameters of the dots and
requires only a global electric field.Comment: 3 pages, 6 figure
Quantum-state transfer in spin chains via isolated resonance of terminal spins
We propose a quantum-state transfer protocol in a spin chain that requires
only the control of the spins at the ends of the quantum wire. The protocol is
to a large extent insensitive to inhomogeneity caused by local magnetic fields
and perturbation of exchange couplings. Moreover, apart from the free evolution
regime, it allows one to induce an adiabatic spin transfer, which provides the
possibility of performing the transfer on demand. We also show that the amount
of information leaking into the central part of the chain is small throughout
the whole transfer process (which protects the information sent from being
eavesdropped) and can be controlled by the magnitude of the external magnetic
field.Comment: 7 pages, 5 figures. Published versio
Beyond the thermodynamic limit: finite-size corrections to state interconversion rates
Thermodynamics is traditionally constrained to the study of macroscopic
systems whose energy fluctuations are negligible compared to their average
energy. Here, we push beyond this thermodynamic limit by developing a
mathematical framework to rigorously address the problem of thermodynamic
transformations of finite-size systems. More formally, we analyse state
interconversion under thermal operations and between arbitrary
energy-incoherent states. We find precise relations between the optimal rate at
which interconversion can take place and the desired infidelity of the final
state when the system size is sufficiently large. These so-called second-order
asymptotics provide a bridge between the extreme cases of single-shot
thermodynamics and the asymptotic limit of infinitely large systems. We
illustrate the utility of our results with several examples. We first show how
thermodynamic cycles are affected by irreversibility due to finite-size
effects. We then provide a precise expression for the gap between the
distillable work and work of formation that opens away from the thermodynamic
limit. Finally, we explain how the performance of a heat engine gets affected
when one of the heat baths it operates between is finite. We find that while
perfect work cannot generally be extracted at Carnot efficiency, there are
conditions under which these finite-size effects vanish. In deriving our
results we also clarify relations between different notions of approximate
majorisation.Comment: 31 pages, 10 figures. Final version, to be published in Quantu
Distinguishing classically indistinguishable states and channels
We investigate an original family of quantum distinguishability problems,
where the goal is to perfectly distinguish between quantum states that
become identical under a completely decohering map. Similarly, we study
distinguishability of quantum channels that cannot be distinguished when
one is restricted to decohered input and output states. The studied problems
arise naturally in the presence of a superselection rule, allow one to quantify
the amount of information that can be encoded in phase degrees of freedom
(coherences), and are related to time-energy uncertainty relation. We present a
collection of results on both necessary and sufficient conditions for the
existence of perfectly distinguishable states (channels) that are
classically indistinguishable.Comment: 22 pages, 8 figures. Published versio
Coherifying quantum channels
Is it always possible to explain random stochastic transitions between states
of a finite-dimensional system as arising from the deterministic quantum
evolution of the system? If not, then what is the minimal amount of randomness
required by quantum theory to explain a given stochastic process? Here, we
address this problem by studying possible coherifications of a quantum channel
, i.e., we look for channels that induce the same
classical transitions , but are "more coherent". To quantify the coherence
of a channel we measure the coherence of the corresponding
Jamio{\l}kowski state . We show that the classical transition matrix
can be coherified to reversible unitary dynamics if and only if is
unistochastic. Otherwise the Jamio{\l}kowski state of
the optimally coherified channel is mixed, and the dynamics must necessarily be
irreversible. To assess the extent to which an optimal process
is indeterministic we find explicit bounds on the entropy
and purity of , and relate the latter to the unitarity of
. We also find optimal coherifications for several classes
of channels, including all one-qubit channels. Finally, we provide a
non-optimal coherification procedure that works for an arbitrary channel
and reduces its rank (the minimal number of required Kraus operators) from
to .Comment: 20 pages, 8 figures. Published versio
Resource engines
In this paper we aim to push the analogy between thermodynamics and quantum
resource theories one step further. Previous inspirations were based on
thermodynamic considerations concerning scenarios with a single heat bath,
neglecting an important part of thermodynamics that studies heat engines
operating between two baths at different temperatures. Here, we investigate the
performance of resource engines, which replace the access to two heat baths at
different temperatures with two arbitrary constraints on state transformations.
The idea is to imitate the action of a two--stroke heat engine, where the
system is sent to two agents (Alice and Bob) in turns, and they can transform
it using their constrained sets of free operations. We raise and address
several questions, including whether or not a resource engine can generate a
full set of quantum operations or all possible state transformations, and how
many strokes are needed for that. We also explain how the resource engine
picture provides a natural way to fuse two or more resource theories, and we
discuss in detail the fusion of two resource theories of thermodynamics with
two different temperatures, and two resource theories of coherence with respect
to two different bases.Comment: 25 pages, 4 figures, comments welcom
Thermal recall: Memory-assisted Markovian thermal processes
We develop a resource-theoretic framework that allows one to bridge the gap
between two approaches to quantum thermodynamics based on Markovian thermal
processes (which model memoryless dynamics) and thermal operations (which model
arbitrarily non-Markovian dynamics). Our approach is built on the notion of
memory-assisted Markovian thermal processes, where memoryless thermodynamic
processes are promoted to non-Markovianity by explicitly modelling ancillary
memory systems initialised in thermal equilibrium states. Within this setting,
we propose a family of protocols composed of sequences of elementary two-level
thermalisations that approximate all transitions between energy-incoherent
states accessible via thermal operations. We prove that, as the size of the
memory increases, these approximations become arbitrarily good for all
transitions in the infinite temperature limit, and for a subset of transitions
in the finite temperature regime. Furthermore, we present solid numerical
evidence for the convergence of our protocol to any transition at finite
temperatures. We also explain how our framework can be used to quantify the
role played by memory effects in thermodynamic protocols such as work
extraction. Finally, our results show that elementary control over two energy
levels at a given time is sufficient to generate all energy-incoherent
transitions accessible via thermal operations if one allows for ancillary
thermal systems.Comment: 20 pages, 14 figures. Substantially extended results with new
sections and application. Published versio