395 research outputs found
State convertibility in the von Neumann algebra framework
We establish a generalisation of the fundamental state convertibility theorem
in quantum information to the context of bipartite quantum systems modelled by
commuting semi-finite von Neumann algebras. Namely, we establish a
generalisation to this setting of Nielsen's theorem on the convertibility of
quantum states under local operations and classical communication (LOCC)
schemes. Along the way, we introduce an appropriate generalisation of LOCC
operations and connect the resulting notion of approximate convertibility to
the theory of singular numbers and majorisation in von Neumann algebras. As an
application of our result in the setting of -factors, we show that the
entropy of the singular value distribution relative to the unique tracial state
is an entanglement monotone in the sense of Vidal, thus yielding a new way to
quantify entanglement in that context. Building on previous work in the
infinite-dimensional setting, we show that trace vectors play the role of
maximally entangled states for general -factors. Examples are drawn from
infinite spin chains, quasi-free representations of the CAR, and discretised
versions of the CCR.Comment: 36 pages, v2: journal version, 38 page
A method to find quantum noiseless subsystems
We develop a structure theory for decoherence-free subspaces and noiseless
subsystems that applies to arbitrary (not necessarily unital) quantum
operations. The theory can be alternatively phrased in terms of the
superoperator perspective, or the algebraic noise commutant formalism. As an
application, we propose a method for finding all such subspaces and subsystems
for arbitrary quantum operations. We suggest that this work brings the
fundamental passive technique for error correction in quantum computing an
important step closer to practical realization.Comment: 5 pages, to appear in Physical Review Letter
Black hole evaporation with separated fermions
In models with a low quantum gravity scale, a well-motivated reason to expect
quark and lepton fields are localized but physically separated is to avoid
proton decay. This could happen in a ``fat-brane'' or in an additional,
orthogonal 1/TeV sized dimension in which the gauge and Higgs fields live
throughout. Black holes with masses of order the quantum gravity scale are
therefore expected to evaporate non-universally, preferentially radiating
directly into quarks or leptons but not both. Should black holes be copiously
produced at a future hadron collider, we find the ratio of final state jets to
charged leptons to photons is 113:8:1, which differs from previous analyses
that assumed all standard model fields live at the same point in the extra
dimensional space.Comment: 5 pages, REVTe
Corrections to Gravity due to a Sol Manifold Extra Dimensional Space
The corrections to the gravitational potential due to a Sol extra dimensional
compact manifold, denoted as , are studied. The total spacetime is of
the form . The range of the Sol corrections is investigated
and compared to the range of the corrections.Comment: 13 pages, 10 figures, published versio
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