6 research outputs found
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
Noise in Quantum Information Processing
Quantum phenomena such as superposition and entanglement imbue quantum systems with information processing power in excess of their classical counterparts. These properties of quantum states are, however, highly fragile. As we enter the era of noisy intermediate-scale quantum (NISQ) devices, this vulnerability to noise is a major hurdle to the experimental realisation of quantum technologies. In this thesis we explore the role of noise in quantum information processing from two different perspectives. In Part I we consider noise from the perspective of quantum error correcting codes. Error correcting codes are often analysed with respect to simplified toy models of noise, such as iid depolarising noise. We consider generalising these techniques for analysing codes under more realistic noise models, including features such as biased or correlated errors. We also consider designing customised codes which not only take into account and exploit features of the underlying physical noise. Considering such tailored codes will be of particular importance for NISQ applications in which finite-size effects can be significant. In Part II we apply tools from information theory to study the finite-resource effects which arise in the trade-offs between resource costs and error rates for certain quantum information processing tasks. We start by considering classical communication over quantum channels, providing a refined analysis of the trade-off between communication rate and error in the regime of a finite number of channel uses. We then extend these techniques to the problem of resource interconversion in theories such as quantum entanglement and quantum thermodynamics, studying finite-size effects which arise in resource-error trade-offs. By studying this effect in detail, we also show how detrimental finite-size effects in devices such as thermal engines may be greatly suppressed by carefully engineering the underlying resource interconversion processes
Quantum dichotomies and coherent thermodynamics beyond first-order asymptotics
We address the problem of exact and approximate transformation of quantum
dichotomies in the asymptotic regime, i.e., the existence of a quantum channel
mapping into with an
error (measured by trace distance) and into
exactly, for a large number . We derive
second-order asymptotic expressions for the optimal transformation rate
in the small, moderate, and large deviation error regimes, as well as the
zero-error regime, for an arbitrary pair of initial states
and a commuting pair of final states. We also prove that
for and given by thermal Gibbs states, the derived
optimal transformation rates in the first three regimes can be attained by
thermal operations. This allows us, for the first time, to study the
second-order asymptotics of thermodynamic state interconversion with fully
general initial states that may have coherence between different energy
eigenspaces. Thus, we discuss the optimal performance of thermodynamic
protocols with coherent inputs and describe three novel resonance phenomena
allowing one to significantly reduce transformation errors induced by
finite-size effects. What is more, our result on quantum dichotomies can also
be used to obtain, up to second-order asymptotic terms, optimal conversion
rates between pure bipartite entangled states under local operations and
classical communication.Comment: 51 pages, 6 figures, comments welcom
Catalysis of entanglement and other quantum resources
In chemistry, a catalyst is a substance which enables a chemical reaction or
increases its rate, while remaining unchanged in the process. Instead of
chemical reactions, quantum catalysis enhances our ability to convert quantum
states into each other under physical constraints. The nature of the
constraints depends on the problem under study, and can arise, e.g., from
energy preservation. In this article we review the most recent developments of
quantum catalysis, and give also a historical overview of this research
direction. We focus on catalysis of quantum entanglement and coherence, and
also discuss this phenomenon in quantum thermodynamics and general quantum
resource theories. We review applications of quantum catalysis, and discuss
also the recent efforts on universal catalysis, where the quantum state of the
catalyst does not depend on the states to be transformed. Catalytic embezzling
is also considered, a phenomenon which occurs if the state of the catalyst can
change in the transition.Comment: 38 pages, 3 figures, comments and additional references are welcom
Moderate deviation analysis of majorisation-based resource interconversion
© 2019 IEEE. We consider the problem of interconverting a finite amount of resources within all theories whose single-shot transformation rules are based on a majorisation relation, e.g. the resource theories of entanglement and coherence (for pure state transformations), as well as thermodynamics (for energy-incoherent transformations). When only finite resources are available we expect to see a non-trivial trade-off between the rate rn at which n copies of a resource state ρ can be transformed into nrn copies of another resource state σ, and the error level ϵn of the interconversion process, as a function of n. In this work we derive the optimal trade-off in the so-called moderate deviation regime, where the rate of interconversion rn approaches its optimum in the asymptotic limit of unbounded resources (n → ∞), while the error ϵn vanishes in the same limit. We find that the moderate deviation analysis exhibits a resonance behaviour which implies that certain pairs of resource states can be interconverted at the asymptotically optimal rate with negligible error, even in the finite n regime