81 research outputs found
Facial structures for various notions of positivity and applications to the theory of entanglement
In this expository note, we explain facial structures for the convex cones
consisting of positive linear maps, completely positive linear maps,
decomposable positive linear maps between matrix algebras, respectively. These
will be applied to study the notions of entangled edge states with positive
partial transposes and optimality of entanglement witnesses.Comment: An expository note. Section 7 and Section 8 have been enlarge
De Finetti theorem on the CAR algebra
The symmetric states on a quasi local C*-algebra on the infinite set of
indices J are those invariant under the action of the group of the permutations
moving only a finite, but arbitrary, number of elements of J. The celebrated De
Finetti Theorem describes the structure of the symmetric states (i.e.
exchangeable probability measures) in classical probability. In the present
paper we extend De Finetti Theorem to the case of the CAR algebra, that is for
physical systems describing Fermions. Namely, after showing that a symmetric
state is automatically even under the natural action of the parity
automorphism, we prove that the compact convex set of such states is a Choquet
simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of
permutations previously described) are precisely the product states in the
sense of Araki-Moriya. In order to do that, we also prove some ergodic
properties naturally enjoyed by the symmetric states which have a
self--containing interest.Comment: 23 pages, juornal reference: Communications in Mathematical Physics,
to appea
Structure and mechanism of acetolactate decarboxylase
Acetolactate decarboxylase catalyzes the conversion of both enantiomers of acetolactate to the (R)-enantiomer of acetoin, via a mechanism that has been shown to involve a prior rearrangement of the non-natural (R)-enantiomer substrate to the natural (S)-enantiomer. In this paper, a series of crystal structures of ALDC complex with designed transition state mimics are reported. These structures, coupled with inhibition studies and site-directed mutagenesis provide an improved understanding of the molecular processes involved in the stereoselective decarboxylation/protonation events. A mechanism for the transformation of each enantiomer of acetolactate is proposed
Faithful Squashed Entanglement
Squashed entanglement is a measure for the entanglement of bipartite quantum
states. In this paper we present a lower bound for squashed entanglement in
terms of a distance to the set of separable states. This implies that squashed
entanglement is faithful, that is, strictly positive if and only if the state
is entangled. We derive the bound on squashed entanglement from a bound on
quantum conditional mutual information, which is used to define squashed
entanglement and corresponds to the amount by which strong subadditivity of von
Neumann entropy fails to be saturated. Our result therefore sheds light on the
structure of states that almost satisfy strong subadditivity with equality. The
proof is based on two recent results from quantum information theory: the
operational interpretation of the quantum mutual information as the optimal
rate for state redistribution and the interpretation of the regularised
relative entropy of entanglement as an error exponent in hypothesis testing.
The distance to the set of separable states is measured by the one-way LOCC
norm, an operationally-motivated norm giving the optimal probability of
distinguishing two bipartite quantum states, each shared by two parties, using
any protocol formed by local quantum operations and one-directional classical
communication between the parties. A similar result for the Frobenius or
Euclidean norm follows immediately. The result has two applications in
complexity theory. The first is a quasipolynomial-time algorithm solving the
weak membership problem for the set of separable states in one-way LOCC or
Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show
that multiple provers are not more powerful than a single prover when the
verifier is restricted to one-way LOCC operations thereby providing a new
characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published
version, claims have been weakened from the LOCC norm to the one-way LOCC
nor
Frobenius structures over Hilbert C*-modules
We study the monoidal dagger category of Hilbert C*-modules over a
commutative C*-algebra from the perspective of categorical quantum mechanics.
The dual objects are the finitely presented projective Hilbert C*-modules.
Special dagger Frobenius structures correspond to bundles of uniformly
finite-dimensional C*-algebras. A monoid is dagger Frobenius over the base if
and only if it is dagger Frobenius over its centre and the centre is dagger
Frobenius over the base. We characterise the commutative dagger Frobenius
structures as finite coverings, and give nontrivial examples of both
commutative and central dagger Frobenius structures. Subobjects of the tensor
unit correspond to clopen subsets of the Gelfand spectrum of the C*-algebra,
and we discuss dagger kernels.Comment: 35 page
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