Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMeasurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization
61
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Here we focus on the measurement induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an obvious operational meaning, can tackle the noncontractivity of the measurement induced nonlocality and has analytic expressions for many quantum states. Most importantly, an inverse approximate joint diagonalization algorithm, due to its simplicity, high efficiency, stability, and state independence, is presented to provide almost analytic expressions for any quantum state, which can also shed light on other aspects in physics.
rate research
Read More
We present a generic method to construct a product basis exhibiting Nonlocality Without Entanglement with $n$ parties each holding a system of dimension at least $n-1$. This basis is generated via a quantum circuit made of control-Discrete Fourier Transform gates acting on the computational basis. The simplicity of our quantum circuit allows for an intuitive understanding of this new type of nonlocality. We also show how this circuit can be used to construct Unextendible Product Bases and their associated Bound Entangled States. To our knowledge, this is the first method which, given a general Hilbert space $bigotimes_{i=1}^n {cal H}_{d_i}$ with $d_ile n-1$, makes it possible to construct (i) a basis exhibiting Nonlocality Without Entanglement, (ii) an Unextendible Product Basis, and (iii) a Bound Entangled state.
Incompatibility of observables, or measurements, is one of the key features of quantum mechanics, related, among other concepts, to Heisenbergs uncertainty relations and Bell nonlocality. In this manuscript we show, however, that even though incompatible measurements are necessary for the violation of any Bell inequality, some relevant Bell-like inequalities may be obtained if compatibility relations are assumed between the local measurements of one (or more) of the parties. Hence, compatibility of measurements is not necessarily a drawback and may, however, be useful for the detection of Bell nonlocality and device-independent certification of entanglement.
We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of $d$-dimensional quantum systems. It maximizes the entanglement of formation contained in the two copies of any maximally-entangled input state, while preserving the separability of unentangled input states. Moreover, it cannot increase the entanglement of formation of all isotropic states. For large $d$, the entanglement of formation of each clone tends to one half the entanglement of the input state, which corresponds to a classical behavior. Finally, we investigate a local entanglement cloner, which yields entangled clones with one fourth the input entanglement in the large-$d$ limit.
In this article, we propose measurement-induced nonlocality (MIN) quantified by Hellinger distance using von Neumann projective measurement. The proposed MIN is a bonafide measure of nonlocal correlation and is resistant to local ancilla problem. We obtain an analytical expression of the Hellinger distance MIN for general pure and $2 otimes n$ mixed states. In addition to comparing with similar measures, we explore the role of weak measurement in capturing nonlocal correlation.
We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest in estimating the geometric mean of a SPD matrix set in the manifold of SPD matrices endowed with the Fisher information metric. The resulting mean has several important invariance properties and has proven very useful in diverse engineering applications such as biomedical and image data processing. While for two SPD matrices the mean has an algebraic closed form solution, for a set of more than two SPD matrices it can only be estimated by iterative algorithms. However, none of the existing iterative algorithms feature at the same time fast convergence, low computational complexity per iteration and guarantee of convergence. For this reason, recently other definitions of geometric mean based on symmetric divergence measures, such as the Bhattacharyya divergence, have been considered. The resulting means, although possibly useful in practice, do not satisfy all desirable invariance properties. In this paper we consider geometric means of co-variance matrices estimated on high-dimensional time-series, assuming that the data is generated according to an instantaneous mixing model, which is very common in signal processing. We show that in these circumstances we can approximate the Fisher information geometric mean by employing an efficient AJD algorithm. Our approximation is in general much closer to the Fisher information geometric mean as compared to its competitors and verifies many invariance properties. Furthermore, convergence is guaranteed, the computational complexity is low and the convergence rate is quadratic. The accuracy of this new geometric mean approximation is demonstrated by means of simulations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
