9,272 research outputs found
Optimality of programmable quantum measurements
We prove that for a programmable measurement device that approximates every
POVM with an error , the dimension of the program space has to grow
at least polynomially with . In the case of qubits we can
improve the general result by showing a linear growth. This proves the
optimality of the programmable measurement devices recently designed in [G. M.
D'Ariano and P. Perinotti, Phys. Rev. Lett. \textbf{94}, 090401 (2005)]
A model for conservative chaos constructed from multi-component Bose-Einstein condensates with a trap in 2 dimensions
To show a mechanism leading to the breakdown of a particle picture for the
multi-component Bose-Einstein condensates(BECs) with a harmonic trap in high
dimensions, we investigate the corresponding 2- nonlinear Schr{\"o}dinger
equation (Gross-Pitaevskii equation) with use of a modified variational
principle. A molecule of two identical Gaussian wavepackets has two degrees of
freedom(DFs), the separation of center-of-masses and the wavepacket width.
Without the inter-component interaction(ICI) these DFs show independent regular
oscillations with the degenerate eigen-frequencies. The inclusion of ICI
strongly mixes these DFs, generating a fat mode that breaks a particle picture,
which however can be recovered by introducing a time-periodic ICI with zero
average. In case of the molecule of three wavepackets for a three-component
BEC, the increase of amplitude of ICI yields a transition from regular to
chaotic oscillations in the wavepacket breathing.Comment: 5 pages, 4 figure
Classifying quantum phases using Matrix Product States and PEPS
We give a classification of gapped quantum phases of one-dimensional systems
in the framework of Matrix Product States (MPS) and their associated parent
Hamiltonians, for systems with unique as well as degenerate ground states, and
both in the absence and presence of symmetries. We find that without
symmetries, all systems are in the same phase, up to accidental ground state
degeneracies. If symmetries are imposed, phases without symmetry breaking
(i.e., with unique ground states) are classified by the cohomology classes of
the symmetry group, this is, the equivalence classes of its projective
representations, a result first derived in [X. Chen, Z.-C. Gu, and X.-G. Wen,
Phys. Rev. B 83, 035107 (2011); arXiv:1008.3745]. For phases with symmetry
breaking (i.e., degenerate ground states), we find that the symmetry consists
of two parts, one of which acts by permuting the ground states, while the other
acts on individual ground states, and phases are labelled by both the
permutation action of the former and the cohomology class of the latter. Using
Projected Entangled Pair States (PEPS), we subsequently extend our framework to
the classification of two-dimensional phases in the neighborhood of a number of
important cases, in particular systems with unique ground states, degenerate
ground states with a local order parameter, and topological order. We also show
that in two dimensions, imposing symmetries does not constrain the phase
diagram in the same way it does in one dimension. As a central tool, we
introduce the isometric form, a normal form for MPS and PEPS which is a
renormalization fixed point. Transforming a state to its isometric form does
not change the phase, and thus, we can focus on to the classification of
isometric forms.Comment: v2: 21 pages, 6 figures. Significantly rewritten and extended. Now
contains a classification of phases both without and with symmetries, for
systems with both unique and degenerate ground states. v3: 24 pages. Improved
according to referees' suggestions (most notably added examples and improved
definition of phases under symmetries). Accepted at Phys. Rev.
On the frequency dependence of p-mode frequency shifts induced by magnetic activity in Kepler solar-like stars
The variations of the frequencies of the low-degree acoustic oscillations in
the Sun induced by magnetic activity show a dependence with radial order. The
frequency shifts are observed to increase towards higher-order modes to reach a
maximum of about 0.8 muHz over the 11-yr solar cycle. A comparable frequency
dependence is also measured in two other main-sequence solar-like stars, the
F-star HD49933, and the young 1-Gyr-old solar analog KIC10644253, although with
different amplitudes of the shifts of about 2 muHz and 0.5 muHz respectively.
Our objective here is to extend this analysis to stars with different masses,
metallicities, and evolutionary stages. From an initial set of 87 Kepler
solar-like oscillating stars with already known individual p-mode frequencies,
we identify five stars showing frequency shifts that can be considered reliable
using selection criteria based on Monte Carlo simulations and on the
photospheric magnetic activity proxy Sph. The frequency dependence of the
frequency shifts of four of these stars could be measured for the l=0 and l=1
modes individually. Given the quality of the data, the results could indicate
that a different physical source of perturbation than in the Sun is dominating
in this sample of solar-like stars.Comment: Accepted for publication in A&
Matrix Product States with long-range Localizable Entanglement
We derive a criterion to determine when a translationally invariant matrix
product state (MPS) has long-range localizable entanglement, where that
quantity remains finite in the thermodynamic limit. We give examples fulfilling
this criterion and eventually use it to obtain all such MPS with bond dimension
2 and 3.Comment: 8 pages, 1 figur
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