20,252 research outputs found
Negativity Bounds for Weyl-Heisenberg Quasiprobability Representations
The appearance of negative terms in quasiprobability representations of
quantum theory is known to be inevitable, and, due to its equivalence with the
onset of contextuality, of central interest in quantum computation and
information. Until recently, however, nothing has been known about how much
negativity is necessary in a quasiprobability representation. Zhu proved that
the upper and lower bounds with respect to one type of negativity measure are
saturated by quasiprobability representations which are in one-to-one
correspondence with the elusive symmetric informationally complete quantum
measurements (SICs). We define a family of negativity measures which includes
Zhu's as a special case and consider another member of the family which we call
"sum negativity." We prove a sufficient condition for local maxima in sum
negativity and find exact global maxima in dimensions and . Notably, we
find that Zhu's result on the SICs does not generally extend to sum negativity,
although the analogous result does hold in dimension . Finally, the Hoggar
lines in dimension make an appearance in a conjecture on sum negativity.Comment: 21 pages. v2: journal version, added reference
Topological Kondo effect with Majorana fermions
The Kondo effect is a striking consequence of the coupling of itinerant
electrons to a quantum spin with degenerate energy levels. While degeneracies
are commonly thought to arise from symmetries or fine-tuning of parameters, the
recent emergence of Majorana fermions has brought to the fore an entirely
different possibility: a "topological degeneracy" which arises from the
nonlocal character of Majorana fermions. Here we show that nonlocal quantum
spins formed from these degrees of freedom give rise to a novel "topological
Kondo effect". This leads to a robust non-Fermi liquid behavior, known to be
difficult to achieve in the conventional Kondo context. Focusing on mesoscopic
superconductor devices, we predict several unique transport signatures of this
Kondo effect, which would demonstrate the non-local quantum dynamics of
Majorana fermions, and validate their potential for topological quantum
computation
On the Brauer groups of symmetries of abelian Dijkgraaf-Witten theories
Symmetries of three-dimensional topological field theories are naturally
defined in terms of invertible topological surface defects. Symmetry groups are
thus Brauer-Picard groups. We present a gauge theoretic realization of all
symmetries of abelian Dijkgraaf-Witten theories. The symmetry group for a
Dijkgraaf-Witten theory with gauge group a finite abelian group , and with
vanishing 3-cocycle, is generated by group automorphisms of , by
automorphisms of the trivial Chern-Simons 2-gerbe on the stack of -bundles,
and by partial e-m dualities.
We show that transmission functors naturally extracted from extended
topological field theories with surface defects give a physical realization of
the bijection between invertible bimodule categories of a fusion category and
braided auto-equivalences of its Drinfeld center. The latter provides the
labels for bulk Wilson lines; it follows that a symmetry is completely
characterized by its action on bulk Wilson lines.Comment: 21 pages, 9 figures. v2: Minor changes, typos corrected and
references added. v3: Typos correcte
Nonorthogonal Quantum States Maximize Classical Information Capacity
I demonstrate that, rather unexpectedly, there exist noisy quantum channels
for which the optimal classical information transmission rate is achieved only
by signaling alphabets consisting of nonorthogonal quantum states.Comment: 5 pages, REVTeX, mild extension of results, much improved
presentation, to appear in Physical Review Letter
Two qubit copying machine for economical quantum eavesdropping
We study the mapping which occurs when a single qubit in an arbitrary state
interacts with another qubit in a given, fixed state resulting in some unitary
transformation on the two qubit system which, in effect, makes two copies of
the first qubit. The general problem of the quality of the resulting copies is
discussed using a special representation, a generalization of the usual Schmidt
decomposition, of an arbitrary two-dimensional subspace of a tensor product of
two 2-dimensional Hilbert spaces. We exhibit quantum circuits which can
reproduce the results of any two qubit copying machine of this type. A simple
stochastic generalization (using a ``classical'' random signal) of the copying
machine is also considered. These copying machines provide simple embodiments
of previously proposed optimal eavesdropping schemes for the BB84 and B92
quantum cryptography protocols.Comment: Minor changes. 26 pages RevTex including 7 PS figure
Deformations of modules of differential forms
We study non-trivial deformations of the natural action of the Lie algebra
on the space of differential forms on . We calculate abstractions for integrability of infinitesimal
multi-parameter deformations and determine the commutative associative algebra
corresponding to the miniversal deformation in the sense of \cite{ff}.Comment: Published by JNMP at http://www.sm.luth.se/math/JNM
Exceptional quantum subgroups for the rank two Lie algebras B2 and G2
Exceptional modular invariants for the Lie algebras B2 (at levels 2,3,7,12)
and G2 (at levels 3,4) can be obtained from conformal embeddings. We determine
the associated alge bras of quantum symmetries and discover or recover, as a
by-product, the graphs describing exceptional quantum subgroups of type B2 or
G2 which encode their module structure over the associated fusion category.
Global dimensions are given.Comment: 33 pages, 27 color figure
Maximization of capacity and p-norms for some product channels
It is conjectured that the Holevo capacity of a product channel \Omega
\otimes \Phi is achieved when product states are used as input. Amosov, Holevo
and Werner have also conjectured that the maximal p-norm of a product channel
is achieved with product input states. In this paper we establish both of these
conjectures in the case that \Omega is arbitrary and \Phi is a CQ or QC channel
(as defined by Holevo). We also establish the Amosov, Holevo and Werner
conjecture when \Omega is arbitrary and either \Phi is a qubit channel and p=2,
or \Phi is a unital qubit channel and p is integer. Our proofs involve a new
conjecture for the norm of an output state of the half-noisy channel I \otimes
\Phi, when \Phi is a qubit channel. We show that this conjecture in some cases
also implies additivity of the Holevo capacity
- âŠ