712 research outputs found
The possibility of a British earned income tax credit
The possibility of an earned income tax credit, based on the US model, is currently high up the British political agenda. This paper examines the strengths and weaknesses of the current British system of in-work benefits, before reviewing the effectiveness of the US Earned Income Tax Credit (EITC) scheme. The British and US systems are then directly compared in terms of the net income delivered and the effective tax rate (net benefit deduction rate). Although the evidence in favour of a US-style EITC is weak, two possible variants are considered. The paper concludes that the only future for an EITC is probably as a partial scheme, linked to the amalgamation of in-work and out-of-work benefits, which removes wage subsidisation from the sphere of social security by means of a semi-individualised tax credit. Even so, the same goals could be achieved through the benefit system.
Concepts of quantum non-Markovianity: a hierarchy
Markovian approximation is a widely-employed idea in descriptions of the
dynamics of open quantum systems (OQSs). Although it is usually claimed to be a
concept inspired by classical Markovianity, the term quantum Markovianity is
used inconsistently and often unrigorously in the literature. In this report we
compare the descriptions of classical stochastic processes and quantum
stochastic processes (as arising in OQSs), and show that there are inherent
differences that lead to the non-trivial problem of characterizing quantum
non-Markovianity. Rather than proposing a single definition of quantum
Markovianity, we study a host of Markov-related concepts in the quantum regime.
Some of these concepts have long been used in quantum theory, such as quantum
white noise, factorization approximation, divisibility, Lindblad master
equation, etc.. Others are first proposed in this report, including those we
call past-future independence, no (quantum) information backflow, and
composability. All of these concepts are defined under a unified framework,
which allows us to rigorously build hierarchy relations among them. With
various examples, we argue that the current most often used definitions of
quantum Markovianity in the literature do not fully capture the memoryless
property of OQSs. In fact, quantum non-Markovianity is highly
context-dependent. The results in this report, summarized as a hierarchy
figure, bring clarity to the nature of quantum non-Markovianity.Comment: Clarifications and references added; discussion of the related
classical hierarchy significantly improved. To appear in Physics Report
Quantum phenomena modelled by interactions between many classical worlds
We investigate whether quantum theory can be understood as the continuum
limit of a mechanical theory, in which there is a huge, but finite, number of
classical 'worlds', and quantum effects arise solely from a universal
interaction between these worlds, without reference to any wave function. Here
a `world' means an entire universe with well-defined properties, determined by
the classical configuration of its particles and fields. In our approach each
world evolves deterministically; probabilities arise due to ignorance as to
which world a given observer occupies; and we argue that in the limit of
infinitely many worlds the wave function can be recovered (as a secondary
object) from the motion of these worlds. We introduce a simple model of such a
'many interacting worlds' approach and show that it can reproduce some generic
quantum phenomena---such as Ehrenfest's theorem, wavepacket spreading, barrier
tunneling and zero point energy---as a direct consequence of mutual repulsion
between worlds. Finally, we perform numerical simulations using our approach.
We demonstrate, first, that it can be used to calculate quantum ground states,
and second, that it is capable of reproducing, at least qualitatively, the
double-slit interference phenomenon.Comment: Published version (including further discussion of interpretation and
quantum limit
Stochastic Heisenberg limit: Optimal estimation of a fluctuating phase
The ultimate limits to estimating a fluctuating phase imposed on an optical
beam can be found using the recently derived continuous quantum Cramer-Rao
bound. For Gaussian stationary statistics, and a phase spectrum scaling
asymptotically as 1/omega^p with p>1, the minimum mean-square error in any
(single-time) phase estimate scales as N^{-2(p-1)/(p+1)}, where N is the photon
flux. This gives the usual Heisenberg limit for a constant phase (as the limit
p--> infinity) and provides a stochastic Heisenberg limit for fluctuating
phases. For p=2 (Brownian motion), this limit can be attained by phase
tracking.Comment: 5+4 pages, to appear in Physical Review Letter
On the dynamics of initially correlated open quantum systems: theory and applications
We show that the dynamics of any open quantum system that is initially
correlated with its environment can be described by a set of (or less)
completely positive maps, where d is the dimension of the system. Only one such
map is required for the special case of no initial correlations. The same maps
describe the dynamics of any system-environment state obtained from the initial
state by a local operation on the system. The reduction of the system dynamics
to a set of completely positive maps allows known numerical and analytic tools
for uncorrelated initial states to be applied to the general case of initially
correlated states, which we exemplify by solving the qubit dephasing model for
such states, and provides a natural approach to quantum Markovianity for this
case. We show that this set of completely positive maps can be experimentally
characterised using only local operations on the system, via a generalisation
of noise spectroscopy protocols. As further applications, we first consider the
problem of retrodicting the dynamics of an open quantum system which is in an
arbitrary state when it becomes accessible to the experimenter, and explore the
conditions under which retrodiction is possible. We also introduce a related
one-sided or limited-access tomography protocol for determining an arbitrary
bipartite state, evolving under a sufficiently rich Hamiltonian, via local
operations and measurements on just one component. We simulate this protocol
for a physical model of particular relevance to nitrogen-vacancy centres, and
in particular show how to reconstruct the density matrix of a set of three
qubits, interacting via dipolar coupling and in the presence of local magnetic
fields, by measuring and controlling only one of them.Comment: 19 pages. Comments welcom
The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation
We propose quantum versions of the Bell-Ziv-Zakai lower bounds on the error
in multiparameter estimation. As an application we consider measurement of a
time-varying optical phase signal with stationary Gaussian prior statistics and
a power law spectrum , with . With no other
assumptions, we show that the mean-square error has a lower bound scaling as
, where is the time-averaged mean photon
flux. Moreover, we show that this accuracy is achievable by sampling and
interpolation, for any . This bound is thus a rigorous generalization of
the Heisenberg limit, for measurement of a single unknown optical phase, to a
stochastically varying optical phase.Comment: 18 pages, 6 figures, comments welcom
Ground states in the Many Interacting Worlds approach
Recently the Many-Interacting-Worlds (MIW) approach to a quantum theory
without wave functions was proposed. This approach leads quite naturally to
numerical integrators of the Schr\"odinger equation. It has been suggested that
such integrators may feature advantages over fixed-grid methods for higher
numbers of degrees of freedom. However, as yet, little is known about concrete
MIW models for more than one spatial dimension and/or more than one particle.
In this work we develop the MIW approach further to treat arbitrary degrees of
freedom, and provide a systematic study of a corresponding numerical
implementation for computing one-particle ground and excited states in one
dimension, and ground states in two spatial dimensions. With this step towards
the treatment of higher degrees of freedom we hope to stimulate their further
study.Comment: 16 pages, 8 figure
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