1,649 research outputs found
Reformulating the Quantum Uncertainty Relation
Uncertainty principle is one of the cornerstones of quantum theory. In the
literature, there are two types of uncertainty relations, the operator form
concerning the variances of physical observables and the entropy form related
to entropic quantities. Both these forms are inequalities involving pairwise
observables, and are found to be nontrivial to incorporate multiple
observables. In this work we introduce a new form of uncertainty relation which
may give out complete trade-off relations for variances of observables in pure
and mixed quantum systems. Unlike the prevailing uncertainty relations, which
are either quantum state dependent or not directly measurable, our bounds for
variances of observables are quantum state independent and immune from the
"triviality" problem of having zero expectation values. Furthermore, the new
uncertainty relation may provide a geometric explanation for the reason why
there are limitations on the simultaneous determination of different
observables in -dimensional Hilbert space.Comment: 15 pages, 2 figures; published in Scientific Report
A Necessary and Sufficient Criterion for the Separability of Quantum State
Quantum entanglement has been regarded as one of the key physical resources
in quantum information sciences. However, the determination of whether a mixed
state is entangled or not is generally a hard issue, even for the bipartite
system. In this work we propose an operational necessary and sufficient
criterion for the separability of an arbitrary bipartite mixed state, by virtue
of the multiplicative Horn's problem. The work follows the work initiated by
Horodecki {\it et. al.} and uses the Bloch vector representation introduced to
the separability problem by J. De Vicente. In our criterion, a complete and
finite set of inequalities to determine the separability of compound system is
obtained, which may be viewed as trade-off relations between the quantumness of
subsystems. We apply the obtained result to explicit examples, e.g. the
separable decomposition of arbitrary dimension Werner state and isotropic
state.Comment: 33 pages; published in Scientific Report
Separable Decompositions of Bipartite Mixed States
We present a practical scheme for the decomposition of a bipartite mixed
state into a sum of direct products of local density matrices, using the
technique developed in Li and Qiao (Sci. Rep. 8: 1442, 2018). In the scheme,
the correlation matrix which characterizes the bipartite entanglement is first
decomposed into two matrices composed of the Bloch vectors of local states.
Then we show that the symmetries of Bloch vectors are consistent with that of
the correlation matrix, and the magnitudes of the local Bloch vectors are lower
bounded by the correlation matrix. Concrete examples for the separable
decompositions of bipartite mixed states are presented for illustration.Comment: 22 pages; published in Quantum Inf. Proces
Equivalence theorem of uncertainty relations
We present an equivalence theorem to unify the two classes of uncertainty
relations, i.e., the variance-based ones and the entropic forms, which shows
that the entropy of an operator in a quantum system can be built from the
variances of a set of commutative operators. That means an uncertainty relation
in the language of entropy may be mapped onto a variance-based one, and vice
versa. Employing the equivalence theorem, alternative formulations of entropic
uncertainty relations stronger than existing ones in the literature are
obtained for qubit system, and variance based uncertainty relations for spin
systems are reached from the corresponding entropic uncertainty relations.Comment: 18 pages, 1 figure; published in J. Phys. A: Math. Theo
Generation of Einstein-Podolsky-Rosen State via Earth's Gravitational Field
Although various physical systems have been explored to produce entangled
states involving electromagnetic, strong, and weak interactions, the gravity
has not yet been touched in practical entanglement generation. Here, we propose
an experimentally feasible scheme for generating spin entangled neutron pairs
via the Earth's gravitational field, whose productivity can be one pair in
every few seconds with the current technology. The scheme is realized by
passing two neutrons through a specific rectangular cavity, where the gravity
adjusts the neutrons into entangled state. This provides a simple and practical
way for the implementation of the test of quantum nonlocality and statistics in
gravitational field.Comment: 12 pages, 9 figure
Connection between Measurement Disturbance Relation and Multipartite Quantum Correlation
It is found that the measurement disturbance relation (MDR) determines the
strength of quantum correlation and hence is one of the essential facets of the
nature of quantum nonlocality. In reverse, the exact form of MDR may be
ascertained through measuring the correlation function. To this aim, an optical
experimental scheme is proposed. Moreover, by virtue of the correlation
function, we find that the quantum entanglement, the quantum non-locality, and
the uncertainty principle can be explicitly correlated.Comment: 27 pages, 7 figures; published in Phys. Rev.
State-independent Uncertainty Relations and Entanglement Detection
The uncertainty relation is one of the key ingredients of quantum theory.
Despite the great efforts devoted to this subject, most of the variance-based
uncertainty relations are state-dependent and suffering from the triviality
problem of zero lower bounds. Here we develop a method to get uncertainty
relations with state-independent lower bounds. The method works by exploring
the eigenvalues of a Hermitian matrix composed by Bloch vectors of incompatible
observables and is applicable for both pure and mixed states and for arbitrary
number of N- dimensional observables. The uncertainty relation for incompatible
observables can be explained by geometric relations related to the parallel
postulate and the inequalities in Horn's conjecture on Hermitian matrix sum.
Practical entanglement criteria are also presented based on the derived
uncertainty relations.Comment: 15 pages, no figure
Ascertaining the Uncertainty Relations via Quantum Correlations
We propose a new scheme to express the uncertainty principle in form of
inequality of the bipartite correlation functions for a given multipartite
state, which provides an experimentally feasible and model-independent way to
verify various uncertainty and measurement disturbance relations. By virtue of
this scheme the implementation of experimental measurement on the measurement
disturbance relation to a variety of physical systems becomes practical. The
inequality in turn also imposes a constraint on the strength of correlation,
i.e. it determines the maximum value of the correlation function for two-body
system and a monogamy relation of the bipartite correlation functions for
multipartite system.Comment: 18 pages, 2 figures; published in J. Phys. A: Math. Theo
S-PowerGraph: Streaming Graph Partitioning for Natural Graphs by Vertex-Cut
One standard solution for analyzing large natural graphs is to adopt
distributed computation on clusters. In distributed computation, graph
partitioning (GP) methods assign the vertices or edges of a graph to different
machines in a balanced way so that some distributed algorithms can be adapted
for. Most of traditional GP methods are offline, which means that the whole
graph has been observed before partitioning. However, the offline methods often
incur high computation cost. Hence, streaming graph partitioning (SGP) methods,
which can partition graphs in an online way, have recently attracted great
attention in distributed computation. There exist two typical GP strategies:
edge-cut and vertex-cut. Most SGP methods adopt edge-cut, but few vertex-cut
methods have been proposed for SGP. However, the vertex-cut strategy would be a
better choice than the edge-cut strategy because the degree of a natural graph
in general follows a highly skewed power-law distribution. Thus, we propose a
novel method, called S-PowerGraph, for SGP of natural graphs by vertex-cut. Our
S-PowerGraph method is simple but effective. Experiments on several large
natural graphs and synthetic graphs show that our S-PowerGraph can outperform
the state-of-the-art baselines
A New Relaxation Approach to Normalized Hypergraph Cut
Normalized graph cut (NGC) has become a popular research topic due to its
wide applications in a large variety of areas like machine learning and very
large scale integration (VLSI) circuit design. Most of traditional NGC methods
are based on pairwise relationships (similarities). However, in real-world
applications relationships among the vertices (objects) may be more complex
than pairwise, which are typically represented as hyperedges in hypergraphs.
Thus, normalized hypergraph cut (NHC) has attracted more and more attention.
Existing NHC methods cannot achieve satisfactory performance in real
applications. In this paper, we propose a novel relaxation approach, which is
called relaxed NHC (RNHC), to solve the NHC problem. Our model is defined as an
optimization problem on the Stiefel manifold. To solve this problem, we resort
to the Cayley transformation to devise a feasible learning algorithm.
Experimental results on a set of large hypergraph benchmarks for clustering and
partitioning in VLSI domain show that RNHC can outperform the state-of-the-art
methods
- …