1,552 research outputs found
Optimal squeezing and entanglement from noisy Gaussian operations
We investigate the creation of squeezing via operations subject to noise and
losses and ask for the optimal use of such devices when supplemented by
noiseless passive operations. Both single and repeated uses of the device are
optimized analytically and it is proven that in the latter case the squeezing
converges exponentially fast to its asymptotic optimum, which we determine
explicitly. For the case of multiple iterations we show that the optimum can be
achieved with fixed intermediate passive operations. Finally, we relate the
results to the generation of entanglement and derive the maximal two-mode
entanglement achievable within the considered scenario.Comment: 4 pages; accepted version (minor changes), Journal-ref adde
Computational Difficulty of Computing the Density of States
We study the computational difficulty of computing the ground state
degeneracy and the density of states for local Hamiltonians. We show that the
difficulty of both problems is exactly captured by a class which we call #BQP,
which is the counting version of the quantum complexity class QMA. We show that
#BQP is not harder than its classical counting counterpart #P, which in turn
implies that computing the ground state degeneracy or the density of states for
classical Hamiltonians is just as hard as it is for quantum Hamiltonians.Comment: v2: Accepted version. 9 pages, 1 figur
The computational difficulty of finding MPS ground states
We determine the computational difficulty of finding ground states of
one-dimensional (1D) Hamiltonians which are known to be Matrix Product States
(MPS). To this end, we construct a class of 1D frustration free Hamiltonians
with unique MPS ground states and a polynomial gap above, for which finding the
ground state is at least as hard as factoring. By lifting the requirement of a
unique ground state, we obtain a class for which finding the ground state
solves an NP-complete problem. Therefore, for these Hamiltonians it is not even
possible to certify that the ground state has been found. Our results thus
imply that in order to prove convergence of variational methods over MPS, as
the Density Matrix Renormalization Group, one has to put more requirements than
just MPS ground states and a polynomial spectral gap.Comment: 5 pages. v2: accepted version, Journal-Ref adde
Quantum entanglement theory in the presence of superselection rules
Superselection rules severly constrain the operations which can be
implemented on a distributed quantum system. While the restriction to local
operations and classical communication gives rise to entanglement as a nonlocal
resource, particle number conservation additionally confines the possible
operations and should give rise to a new resource. In [Phys. Rev. Lett. 92,
087904 (2004), quant-ph/0310124] we showed that this resource can be quantified
by a single additional number, the superselection induced variance (SiV)
without changing the concept of entanglement. In this paper, we give the
results on pure states in greater detail; additionally, we provide a discussion
of mixed state nonlocality with superselection rules where we consider both
formation and distillation. Finally, we demonstrate that SiV is indeed a
resource, i.e., that it captures how well a state can be used to overcome the
restrictions imposed by the superselection rule.Comment: 16 pages, 5 figure
Supersolid Helium at High Pressure
We have measured the pressure dependence of the supersolid fraction by a
torsional oscillator technique. Superflow is found from 25.6 bar up to 136.9
bar. The supersolid fraction in the low temperature limit increases from 0.6 %
at 25.6 bar near the melting boundary up to a maximum of 1.5% near 55 bar
before showing a monotonic decrease with pressure extrapolating to zero near
170 bar.Comment: 4 pages, 4 figure
Symmetry Protected Topological Order in Open Quantum Systems
We systematically investigate the robustness of symmetry protected
topological (SPT) order in open quantum systems by studying the evolution of
string order parameters and other probes under noisy channels. We find that
one-dimensional SPT order is robust against noisy couplings to the environment
that satisfy a strong symmetry condition, while it is destabilized by noise
that satisfies only a weak symmetry condition, which generalizes the notion of
symmetry for closed systems. We also discuss "transmutation" of SPT phases into
other SPT phases of equal or lesser complexity, under noisy channels that
satisfy twisted versions of the strong symmetry condition
Matrix Product State and mean field solutions for one-dimensional systems can be found efficiently
We consider the problem of approximating ground states of one-dimensional
quantum systems within the two most common variational ansatzes, namely the
mean field ansatz and Matrix Product States. We show that both for mean field
and for Matrix Product States of fixed bond dimension, the optimal solutions
can be found in a way which is provably efficient (i.e., scales polynomially).
This implies that the corresponding variational methods can be in principle
recast in a way which scales provably polynomially. Moreover, our findings
imply that ground states of one-dimensional commuting Hamiltonians can be found
efficiently.Comment: 5 pages; v2: accepted version, Journal-ref adde
Dielectronic Resonance Method for Measuring Isotope Shifts
Longstanding problems in the comparison of very accurate hyperfine-shift
measurements to theory were partly overcome by precise measurements on
few-electron highly-charged ions. Still the agreement between theory and
experiment is unsatisfactory. In this paper, we present a radically new way of
precisely measuring hyperfine shifts, and demonstrate its effectiveness in the
case of the hyperfine shift of and in
. It is based on the precise detection of dielectronic
resonances that occur in electron-ion recombination at very low energy. This
allows us to determine the hyperfine constant to around 0.6 meV accuracy which
is on the order of 10%
Coherent states of a charged particle in a uniform magnetic field
The coherent states are constructed for a charged particle in a uniform
magnetic field based on coherent states for the circular motion which have
recently been introduced by the authors.Comment: 2 eps figure
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