3,695 research outputs found
Characterization of four-qubit states via Bell inequalities
A set of Bell inequalities classifying the quantum entanglement of four-qubit
states is presented. These inequalities involve only two measurement settings
per observer and can characterize fully separable, bi-separable and
tri-separable quantum states. In addition, a quadratic inequality of the Bell
operators for four-qubit systems is derived
Dirac nodal line metal for topological antiferromagnetic spintronics
Topological antiferromagnetic (AFM) spintronics is an emerging field of
research, which exploits the N\'eel vector to control the topological
electronic states and the associated spin-dependent transport properties. A
recently discovered N\'eel spin-orbit torque has been proposed to electrically
manipulate Dirac band crossings in antiferromagnets; however, a reliable AFM
material to realize these properties in practice is missing. Here, we predict
that room temperature AFM metal MnPd allows the electrical control of the
Dirac nodal line by the N\'eel spin-orbit torque. Based on first-principles
density functional theory calculations, we show that reorientation of the
N\'eel vector leads to switching between the symmetry-protected degenerate
state and the gapped state associated with the dispersive Dirac nodal line at
the Fermi energy. The calculated spin Hall conductivity strongly depends on the
N\'eel vector orientation and can be used to experimentally detect the
predicted effect using a proposed spin-orbit torque device. Our results
indicate that AFM Dirac nodal line metal MnPd represents a promising
material for topological AFM spintronics
On the Approximation and Complexity of Deep Neural Networks to Invariant Functions
Recent years have witnessed a hot wave of deep neural networks in various
domains; however, it is not yet well understood theoretically. A theoretical
characterization of deep neural networks should point out their approximation
ability and complexity, i.e., showing which architecture and size are
sufficient to handle the concerned tasks. This work takes one step on this
direction by theoretically studying the approximation and complexity of deep
neural networks to invariant functions. We first prove that the invariant
functions can be universally approximated by deep neural networks. Then we show
that a broad range of invariant functions can be asymptotically approximated by
various types of neural network models that includes the complex-valued neural
networks, convolutional neural networks, and Bayesian neural networks using a
polynomial number of parameters or optimization iterations. We also provide a
feasible application that connects the parameter estimation and forecasting of
high-resolution signals with our theoretical conclusions. The empirical results
obtained on simulation experiments demonstrate the effectiveness of our method
Constructing mutually unbiased bases from unextendible maximally entangled bases
We study mutually unbiased bases (MUBs) in which all the bases are
unextendible maximally entangled ones. We first present a necessary and
sufficient condition of constructing a pair of MUBs in . Based
on this condition, an analytical and necessary condition for constructing MUBs
is given. Moreover we illustrate our approach by some detailed examples in . The results are generalized to and
a concrete example in is given.Comment: 14 page
Projection based lower bounds of concurrence for multipartite quantum systems
We study the concurrence of arbitrary-dimensional multipartite quantum
states. Analytical lower bounds of concurrence for tripartite quantum states
are derived by projecting high-dimensional states to
substates. The results are then generalized to arbitrary multipartite quantum
systems. Furthermore, the scheme enables us obtain lower bounds of concurrence
for arbitrary four-partite quantum states by projecting high-dimensional states
to arbitrary given lower dimensional substates. By detailed examples we show
that our results improve the existing lower bounds of concurrence.Comment: 13pages, 2figure
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