658 research outputs found
A class of genuinely high-dimensionally entangled states with a positive partial transpose
Entangled states with a positive partial transpose (so-called PPT states) are
central to many interesting problems in quantum theory. On one hand, they are
considered to be weakly entangled, since no pure state entanglement can be
distilled from them. On the other hand, it has been shown recently that some of
these PPT states exhibit genuinely high-dimensional entanglement, i.e. they
have a high Schmidt number. Here we investigate dimensional PPT
states for discussed recently by Sindici and Piani, and by
generalizing their methods to the calculation of Schmidt numbers we show that a
linear scaling of its Schmidt number in the local dimension can be
attained.Comment: 8 page
Hysteretic optimization for the Sherrington-Kirkpatrick spin glass
Hysteretic optimization is a heuristic optimization method based on the
observation that magnetic samples are driven into a low energy state when
demagnetized by an oscillating magnetic field of decreasing amplitude. We show
that hysteretic optimization is very good for finding ground states of
Sherrington-Kirkpatrick spin glass systems. With this method it is possible to
get good statistics for ground state energies for large samples of systems
consisting of up to about 2000 spins. The way we estimate error rates may be
useful for some other optimization methods as well. Our results show that both
the average and the width of the ground state energy distribution converges
faster with increasing size than expected from earlier studies.Comment: Physica A, accepte
Multisetting Bell-type inequalities for detecting genuine tripartite entanglement
In a recent paper, Bancal et al. put forward the concept of
device-independent witnesses of genuine multipartite entanglement. These
witnesses are capable of verifying genuine multipartite entanglement produced
in a lab without resorting to any knowledge of the dimension of the state space
or of the specific form of the measurement operators. As a by-product they
found a three-party three-setting Bell inequality which enables to detect
genuine tripartite entanglement in a noisy 3-qubit Greenberger-Horne-Zeilinger
(GHZ) state for visibilities as low as 2/3 in a device-independent way. In this
paper, we generalize this inequality to an arbitrary number of settings,
demonstrating a threshold visibility of 2/pi~0.6366 for number of settings
going to infinity. We also present a pseudo-telepathy Bell inequality achieving
the same threshold value. We argue that our device-independent witnesses are
optimal in the sense that the above value cannot be beaten with
three-party-correlation Bell inequalities.Comment: 7 page
Maximal violation of the I3322 inequality using infinite dimensional quantum systems
The I3322 inequality is the simplest bipartite two-outcome Bell inequality
beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three
two-outcome measurements per party. In case of the CHSH inequality the maximal
quantum violation can already be attained with local two-dimensional quantum
systems, however, there is no such evidence for the I3322 inequality. In this
paper a family of measurement operators and states is given which enables us to
attain the largest possible quantum value in an infinite dimensional Hilbert
space. Further, it is conjectured that our construction is optimal in the sense
that measuring finite dimensional quantum systems is not enough to achieve the
true quantum maximum. We also describe an efficient iterative algorithm for
computing quantum maximum of an arbitrary two-outcome Bell inequality in any
given Hilbert space dimension. This algorithm played a key role to obtain our
results for the I3322 inequality, and we also applied it to improve on our
previous results concerning the maximum quantum violation of several bipartite
two-outcome Bell inequalities with up to five settings per party.Comment: 9 pages, 3 figures, 1 tabl
Platonic Bell inequalities for all dimensions
In this paper we study the Platonic Bell inequalities for all possible
dimensions. There are five Platonic solids in three dimensions, but there are
also solids with Platonic properties (also known as regular polyhedra) in four
and higher dimensions. The concept of Platonic Bell inequalities in the
three-dimensional Euclidean space was introduced by Tavakoli and Gisin [Quantum
4, 293 (2020)]. For any three-dimensional Platonic solid, an arrangement of
projective measurements is associated where the measurement directions point
toward the vertices of the solids. For the higher dimensional regular
polyhedra, we use the correspondence of the vertices to the measurements in the
abstract Tsirelson space. We give a remarkably simple formula for the quantum
violation of all the Platonic Bell inequalities, which we prove to attain the
maximum possible quantum violation of the Bell inequalities, i.e. the Tsirelson
bound. To construct Bell inequalities with a large number of settings, it is
crucial to compute the local bound efficiently. In general, the computation
time required to compute the local bound grows exponentially with the number of
measurement settings. We find a method to compute the local bound exactly for
any bipartite two-outcome Bell inequality, where the dependence becomes
polynomial whose degree is the rank of the Bell matrix. To show that this
algorithm can be used in practice, we compute the local bound of a 300-setting
Platonic Bell inequality based on the halved dodecaplex. In addition, we use a
diagonal modification of the original Platonic Bell matrix to increase the
ratio of quantum to local bound. In this way, we obtain a four-dimensional
60-setting Platonic Bell inequality based on the halved tetraplex for which the
quantum violation exceeds the ratio.Comment: 24 pages, 2 figures, 3 tables. Accepted for publication in Quantu
The ground state energy of the Edwards-Anderson spin glass model with a parallel tempering Monte Carlo algorithm
We study the efficiency of parallel tempering Monte Carlo technique for
calculating true ground states of the Edwards-Anderson spin glass model.
Bimodal and Gaussian bond distributions were considered in two and
three-dimensional lattices. By a systematic analysis we find a simple formula
to estimate the values of the parameters needed in the algorithm to find the GS
with a fixed average probability. We also study the performance of the
algorithm for single samples, quantifying the difference between samples where
the GS is hard, or easy, to find. The GS energies we obtain are in good
agreement with the values found in the literature. Our results show that the
performance of the parallel tempering technique is comparable to more powerful
heuristics developed to find the ground state of Ising spin glass systems.Comment: 30 pages, 17 figures. A new section added. Accepted for publication
in Physica
Closing the detection loophole in multipartite Bell tests using GHZ states
We investigate the problem of closing the detection loophole in multipartite
Bell tests, and show that the required detection efficiencies can be
significantly lowered compared to the bipartite case. In particular, we present
Bell tests based on n-qubit Greenberger-Horne-Zeilinger states, which can
tolerate efficiencies as low as 38% for a reasonable number of parties and
measurements. Even in the presence of a significant amount of noise,
efficiencies below 50% can be tolerated, which is encouraging given recent
experimental progress. Finally we give strong evidence that, for a sufficiently
large number of parties and measurements, arbitrarily small efficiencies can be
tolerated, even in the presence of an arbitrary large amount of noise.Comment: 5 pages, 3 figure
Bound entangled singlet-like states for quantum metrology
Bipartite entangled quantum states with a positive partial transpose (PPT),
i.e., PPT entangled states, are usually considered very weakly entangled. Since
no pure entanglement can be distilled from them, they are also called bound
entangled. In this paper we present two classes of ()-dimensional
PPT entangled states for any which outperform all separable states in
metrology significantly. We present strong evidence that our states provide the
maximal metrological gain achievable by PPT states for a given system size.
When the dimension goes to infinity, the metrological gain of these states
becomes maximal and equals the metrological gain of a pair of maximally
entangled qubits. Thus, we argue that our states could be called "PPT
singlets."Comment: 17 pages including 3 figures, revtex4.2; v2: presentation improved,
some further results added, links to MATLAB programs generating the bound
entangled states added; v3: published versio
Self-testing in prepare-and-measure scenarios and a robust version of Wigner's theorem
We consider communication scenarios where one party sends quantum states of
known dimensionality , prepared with an untrusted apparatus, to another,
distant party, who probes them with uncharacterized measurement devices. We
prove that, for any ensemble of reference pure quantum states, there exists one
such prepare-and-measure scenario and a linear functional on its observed
measurement probabilities, such that can only be maximized if the
preparations coincide with the reference states, modulo a unitary or an
anti-unitary transformation. In other words, prepare-and-measure scenarios
allow one to "self-test" arbitrary ensembles of pure quantum states. Arbitrary
extreme -dimensional quantum measurements, or sets thereof, can be similarly
self-tested. Our results rely on a robust generalization of Wigner's theorem, a
known result in particle physics that characterizes physical symmetries.Comment: 26 page
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