156 research outputs found
Three-by-three bound entanglement with general unextendible product bases
We discuss the subject of Unextendible Product Bases with the orthogonality
condition dropped and we prove that the lowest rank non-separable
positive-partial-transpose states, i.e. states of rank 4 in 3 x 3 systems are
always locally equivalent to a projection onto the orthogonal complement of a
linear subspace spanned by an orthogonal Unextendible Product Basis. The
product vectors in the kernels of the states belong to a non-zero measure
subset of all general Unextendible Product Bases, nevertheless they can always
be locally transformed to the orthogonal form. This fully confirms the
surprising numerical results recently reported by Leinaas et al. Parts of the
paper rely heavily on the use of Bezout's Theorem from algebraic geometry.Comment: 36 page
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
Optimal entanglement witnesses from generalized reduction and Robertson maps
We provide a generalization of the reduction and Robertson positive maps in
matrix algebras. They give rise to a new class of optimal entanglement
witnesses. Their structural physical approximation is analyzed. As a byproduct
we provide a new examples of PPT (Positive Partial Transpose) entangled states.Comment: 14 page
Quantum Bayes rule
We state a quantum version of Bayes's rule for statistical inference and give
a simple general derivation within the framework of generalized measurements.
The rule can be applied to measurements on N copies of a system if the initial
state of the N copies is exchangeable. As an illustration, we apply the rule to
N qubits. Finally, we show that quantum state estimates derived via the
principle of maximum entropy are fundamentally different from those obtained
via the quantum Bayes rule.Comment: REVTEX, 9 page
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
Entanglement purification of unknown quantum states
A concern has been expressed that ``the Jaynes principle can produce fake
entanglement'' [R. Horodecki et al., Phys. Rev. A {\bf 59}, 1799 (1999)]. In
this paper we discuss the general problem of distilling maximally entangled
states from copies of a bipartite quantum system about which only partial
information is known, for instance in the form of a given expectation value. We
point out that there is indeed a problem with applying the Jaynes principle of
maximum entropy to more than one copy of a system, but the nature of this
problem is classical and was discussed extensively by Jaynes. Under the
additional assumption that the state of the copies of the
quantum system is exchangeable, one can write down a simple general expression
for . We show how to modify two standard entanglement purification
protocols, one-way hashing and recurrence, so that they can be applied to
exchangeable states. We thus give an explicit algorithm for distilling
entanglement from an unknown or partially known quantum state.Comment: 20 pages RevTeX 3.0 + 1 figure (encapsulated Postscript) Submitted to
Physical Review
Positive maps, positive polynomials and entanglement witnesses
We link the study of positive quantum maps, block positive operators, and
entanglement witnesses with problems related to multivariate polynomials. For
instance, we show how indecomposable block positive operators relate to
biquadratic forms that are not sums of squares. Although the general problem of
describing the set of positive maps remains open, in some particular cases we
solve the corresponding polynomial inequalities and obtain explicit conditions
for positivity.Comment: 17 pages, 1 figur
Quantum Gate Fidelity in Terms of Choi Matrices
We provide new results for computing and comparing the quantum gate fidelity
of quantum channels via their Choi matrices. We extend recent work that showed
there exist non-dual pairs of quantum channels with equal gate fidelity by
providing an explicit characterization of all such channels. We use our
characterization to show that when the dimension is 2 (or 3, under slightly
stronger hypotheses), the gate fidelity of two channels is equal if and only if
their difference equals the difference of some unital map and its dual -- a
fact that has been shown to be false when the dimension is 4 or larger. We also
present a formula for the minimum gate fidelity of a channel in terms of a
well-studied norm on a compression of its Choi matrix. As a consequence,
several new ways of bounding and approximating the minimum gate fidelity
follow, including a simple semidefinite program to compute it for qubit
channels.Comment: Minor corrections and updates since v1. 16 pages, 1 figur
Construction of entangled edge states with positive partial transposes
We construct a class of entangled edge states with positive
partial transposes using indecomposable positive linear maps. This class
contains several new types of entangled edge states with respect to the range
dimensions of themselves and their partial transposes.Comment: 14 page
Quiet daytime Arctic ionospheric D region
Phase and amplitude measurements of VLF radio waves propagating sub‐ionospherically on long paths across the Arctic are used to determine the high latitude, daytime D region height and sharpness of the bottom edge of the Earth's ionosphere. The principal path used is from the 23.4 kHz transmitter, DHO, in north Germany, northwards across the Arctic passing ~2° from the North Pole, and then southwards to Nome, Alaska, thus avoiding most land and all thick ice. Significant observational support is obtained from the also nearly all‐sea path from JXN in Norway (~67° N, 16.4 kHz) across the North Pole to Nome. By suitably comparing measurements with modeling using the US Navy code LWPC, the daytime D region (Wait) height and sharpness parameters in the Arctic are found to be H' = 73.7 ± 0.7 km and ß = 0.32 ±0.02 km‐1 in the summer of 2013 ‐ i.e., at (weak) solar maximum. It is also found that, unlike at lower latitudes, VLF phase and amplitude recordings on (~1000 km) paths at high subarctic latitudes show very little change with solar zenith angle in both phase and amplitude during daytime for solar zenith angles ~300 keV for electrons) with a contribution from galactic cosmic rays, rather than by solar Lyman‐α which dominates at low and middle latitudes
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