11,636 research outputs found
Towards a unified approach to information-disturbance tradeoffs in quantum measurements
We show that the global balance of information dynamics for general quantum
measurements given in [F. Buscemi, M. Hayashi, and M. Horodecki, Phys.Rev.Lett.
100, 210504 (2008)] makes it possible to unify various and generally
inequivalent approaches adopted in order to derive information-disturbance
tradeoffs in quantum theory. We focus in particular on those tradeoffs,
constituting the vast majority of the literature on the subject, where
disturbance is defined either in terms of average output fidelity or of
entanglement fidelity
Efficiency bounds for nonequilibrium heat engines
We analyze the efficiency of thermal engines (either quantum or classical)
working with a single heat reservoir like atmosphere. The engine first gets an
energy intake, which can be done in arbitrary non-equilibrium way e.g.
combustion of fuel. Then the engine performs the work and returns to the
initial state. We distinguish two general classes of engines where the working
body first equilibrates within itself and then performs the work (ergodic
engine) or when it performs the work before equilibrating (non-ergodic engine).
We show that in both cases the second law of thermodynamics limits their
efficiency. For ergodic engines we find a rigorous upper bound for the
efficiency, which is strictly smaller than the equivalent Carnot efficiency.
I.e. the Carnot efficiency can be never achieved in single reservoir heat
engines. For non-ergodic engines the efficiency can be higher and can exceed
the equilibrium Carnot bound. By extending the fundamental thermodynamic
relation to nonequilibrium processes, we find a rigorous thermodynamic bound
for the efficiency of both ergodic and non-ergodic engines and show that it is
given by the relative entropy of the non-equilibrium and initial equilibrium
distributions.These results suggest a new general strategy for designing more
efficient engines. We illustrate our ideas by using simple examples.Comment: updated version, 16 pages, 3 figure
Converse bounds for private communication over quantum channels
This paper establishes several converse bounds on the private transmission
capabilities of a quantum channel. The main conceptual development builds
firmly on the notion of a private state, which is a powerful, uniquely quantum
method for simplifying the tripartite picture of privacy involving local
operations and public classical communication to a bipartite picture of quantum
privacy involving local operations and classical communication. This approach
has previously led to some of the strongest upper bounds on secret key rates,
including the squashed entanglement and the relative entropy of entanglement.
Here we use this approach along with a "privacy test" to establish a general
meta-converse bound for private communication, which has a number of
applications. The meta-converse allows for proving that any quantum channel's
relative entropy of entanglement is a strong converse rate for private
communication. For covariant channels, the meta-converse also leads to
second-order expansions of relative entropy of entanglement bounds for private
communication rates. For such channels, the bounds also apply to the private
communication setting in which the sender and receiver are assisted by
unlimited public classical communication, and as such, they are relevant for
establishing various converse bounds for quantum key distribution protocols
conducted over these channels. We find precise characterizations for several
channels of interest and apply the methods to establish several converse bounds
on the private transmission capabilities of all phase-insensitive bosonic
channels.Comment: v3: 53 pages, 3 figures, final version accepted for publication in
IEEE Transactions on Information Theor
The Role of Relative Entropy in Quantum Information Theory
Quantum mechanics and information theory are among the most important
scientific discoveries of the last century. Although these two areas initially
developed separately it has emerged that they are in fact intimately related.
In this review I will show how quantum information theory extends traditional
information theory by exploring the limits imposed by quantum, rather than
classical mechanics on information storage and transmission. The derivation of
many key results uniquely differentiates this review from the "usual"
presentation in that they are shown to follow logically from one crucial
property of relative entropy. Within the review optimal bounds on the speed-up
that quantum computers can achieve over their classical counter-parts are
outlined using information theoretic arguments. In addition important
implications of quantum information theory to thermodynamics and quantum
measurement are intermittently discussed. A number of simple examples and
derivations including quantum super-dense coding, quantum teleportation,
Deutsch's and Grover's algorithms are also included.Comment: 40 pages, 11 figure
Testing quantum mechanics: a statistical approach
As experiments continue to push the quantum-classical boundary using
increasingly complex dynamical systems, the interpretation of experimental data
becomes more and more challenging: when the observations are noisy, indirect,
and limited, how can we be sure that we are observing quantum behavior? This
tutorial highlights some of the difficulties in such experimental tests of
quantum mechanics, using optomechanics as the central example, and discusses
how the issues can be resolved using techniques from statistics and insights
from quantum information theory.Comment: v1: 2 pages; v2: invited tutorial for Quantum Measurements and
Quantum Metrology, substantial expansion of v1, 19 pages; v3: accepted; v4:
corrected some errors, publishe
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