345 research outputs found
Different instances of time as different quantum modes: quantum states across space-time for continuous variables
Space-time is one of the most essential, yet most mysterious concepts in
physics. In quantum mechanics it is common to understand time as a marker of
instances of evolution and define states around all the space but at one time;
while in general relativity space-time is taken as a combinator, curved around
mass. Here we present a unified approach on both space and time in quantum
theory, and build quantum states across spacetime instead of only on spatial
slices. We no longer distinguish measurements on the same system at different
times with measurements on different systems at one time and construct
spacetime states upon these measurement statistics. As a first step towards
non-relativistic quantum field theory, we consider how to approach this in the
continuous-variable multi-mode regime. We propose six possible definitions for
spacetime states in continuous variables, based on four different measurement
processes: quadratures, displaced parity operators, position measurements and
weak measurements. The basic idea is to treat different instances of time as
different quantum modes. They are motivated by the pseudo-density matrix
formulation among indefinite causal structures and the path integral formalism.
We show that these definitions lead to desirable properties, and raise the
differences and similarities between spatial and temporal correlations. An
experimental proposal for tomography is presented, construing the operational
meaning of the spacetime states.Comment: 28 pages, comments welcom
Entanglement Typicality
We provide a summary of both seminal and recent results on typical
entanglement. By typical values of entanglement, we refer here to values of
entanglement quantifiers that (given a reasonable measure on the manifold of
states) appear with arbitrarily high probability for quantum systems of
sufficiently high dimensionality. We work within the Haar measure framework for
discrete quantum variables, where we report on results concerning the average
von Neumann and linear entropies as well as arguments implying the typicality
of such values in the asymptotic limit. We then proceed to discuss the
generation of typical quantum states with random circuitry. Different phases of
entanglement, and the connection between typical entanglement and
thermodynamics are discussed. We also cover approaches to measures on the
non-compact set of Gaussian states of continuous variable quantum systems.Comment: Review paper with two quotes and minimalist figure
The work value of information
We present quantitative relations between work and information that are valid
both for finite sized and internally correlated systems as well in the
thermodynamical limit. We suggest work extraction should be viewed as a game
where the amount of work an agent can extract depends on how well it can guess
the micro-state of the system. In general it depends both on the agent's
knowledge and risk-tolerance, because the agent can bet on facts that are not
certain and thereby risk failure of the work extraction. We derive strikingly
simple expressions for the extractable work in the extreme cases of effectively
zero- and arbitrary risk tolerance respectively, thereby enveloping all cases.
Our derivation makes a connection between heat engines and the smooth entropy
approach. The latter has recently extended Shannon theory to encompass finite
sized and internally correlated bit strings, and our analysis points the way to
an analogous extension of statistical mechanics.Comment: 5 pages, 4 figure
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