3,343,214 research outputs found
Superadditivity of quantum relative entropy for general states
The property of superadditivity of the quantum relative entropy states that,
in a bipartite system ,
for every density operator one has . In
this work, we provide an extension of this inequality for arbitrary density
operators . More specifically, we prove that holds for all bipartite states
and , where .Comment: 14 pages. v3: Final version. The main theorem has been improved,
adding a fourth step to its proof and also some remarks. v2: There was a flaw
in the proof of the previous version. This has been corrected in this
version. The constant appearing in the main Theorem has changed accordingl
Symmetric Extension of Two-Qubit States
Quantum key distribution uses public discussion protocols to establish shared
secret keys. In the exploration of ultimate limits to such protocols, the
property of symmetric extendibility of underlying bipartite states
plays an important role. A bipartite state is symmetric extendible
if there exits a tripartite state , such that the marginal
state is identical to the marginal state, i.e. .
For a symmetric extendible state , the first task of the public
discussion protocol is to break this symmetric extendibility. Therefore to
characterize all bi-partite quantum states that possess symmetric extensions is
of vital importance. We prove a simple analytical formula that a two-qubit
state admits a symmetric extension if and only if
\tr(\rho_B^2)\geq \tr(\rho_{AB}^2)-4\sqrt{\det{\rho_{AB}}}. Given the
intimate relationship between the symmetric extension problem and the quantum
marginal problem, our result also provides the first analytical necessary and
sufficient condition for the quantum marginal problem with overlapping
marginals.Comment: 10 pages, no figure. comments are welcome. Version 2: introduction
rewritte
Sherrington-Kirkpatrick model near : expanding around the Replica Symmetric Solution
An expansion for the free energy functional of the Sherrington-Kirkpatrick
(SK) model, around the Replica Symmetric SK solution is investigated. In particular, when the
expansion is truncated to fourth order in. . The
Full Replica Symmetry Broken (FRSB) solution is explicitly found but it turns
out to exist only in the range of temperature , not
including T=0. On the other hand an expansion around the paramagnetic solution
up to fourth order yields a FRSB solution
that exists in a limited temperature range .Comment: 18 pages, 3 figure
On the structure of the new electromagnetic conservation laws
New electromagnetic conservation laws have recently been proposed: in the
absence of electromagnetic currents, the trace of the Chevreton superenergy
tensor, is divergence-free in four-dimensional (a) Einstein spacetimes
for test fields, (b) Einstein-Maxwell spacetimes. Subsequently it has been
pointed out, in analogy with flat spaces, that for Einstein spacetimes the
trace of the Chevreton superenergy tensor can be rearranged in the
form of a generalised wave operator acting on the energy momentum
tensor of the test fields, i.e., . In this
letter we show, for Einstein-Maxwell spacetimes in the full non-linear theory,
that, although, the trace of the Chevreton superenergy tensor can
again be rearranged in the form of a generalised wave operator
acting on the electromagnetic energy momentum tensor, in this case the result
is also crucially dependent on Einstein's equations; hence we argue that the
divergence-free property of the tensor has
significant independent content beyond that of the divergence-free property of
Perspective on gravitational self-force analyses
A point particle of mass moving on a geodesic creates a perturbation
, of the spacetime metric , that diverges at the particle.
Simple expressions are given for the singular part of and its
distortion caused by the spacetime. This singular part h^\SS_{ab} is
described in different coordinate systems and in different gauges. Subtracting
h^\SS_{ab} from leaves a regular remainder . The
self-force on the particle from its own gravitational field adjusts the world
line at \Or(\mu) to be a geodesic of ; this adjustment
includes all of the effects of radiation reaction. For the case that the
particle is a small non-rotating black hole, we give a uniformly valid
approximation to a solution of the Einstein equations, with a remainder of
\Or(\mu^2) as .
An example presents the actual steps involved in a self-force calculation.
Gauge freedom introduces ambiguity in perturbation analysis. However,
physically interesting problems avoid this ambiguity.Comment: 40 pages, to appear in a special issue of CQG on radiation reaction,
contains additional references, improved notation for tensor harmonic
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