We apply quantum model inspired on the classical Bayesian method also called mutual information to study the multipartite correlation in quantum images by using the flexible representation of quantum images (FRQI). This can be reflected by considering von Neumann entropy. The results are compared between two images of size $2\times 2$ and $8\times 8$ from different classical and quantum methods. We find that the classical joint entropy is invariant under transformation of change of color but the quantum entropy is sensitive to this change. It is shown that the total correlation $I_T$ could arrive to the double amount of the classical joint entropy.We apply quantum model inspired on the classical Bayesian method also called mutual information to study the multipartite correlation in quantum images by using the flexible representation of quantum images (FRQI). This can be reflected by considering von Neumann entropy. The results are compared between two images of size $2\times 2$ and $8\times 8$ from different classical and quantum methods. We find that the classical joint entropy is invariant under transformation of change of color but the quantum entropy is sensitive to this change. It is shown that the total correlation $I_T$ could arrive to the double amount of the classical joint entropy.

arXiv:1812.11053Dec 21, 20183 citations

Spatiotemporal multipartite entanglement

Mikhail I. Kolobov, Giuseppe Patera

In this Rapid Communication, we propose, following the spirit of quantum imaging, to generalize the theory of multipartite entanglement for the continuous-variable Gaussian states by considering, instead of the global covariance matrix, the local correlation matrix at two different spatiotemporal points $(\mathrm{\ensuremath{\rho}P\vec},t)$ and $(\mathrm{\ensuremath{\rho}P\vec} {}^{'},{t}^{'})$, with $\mathrm{\ensuremath{\rho}P\vec}$ being the transverse coordinate. Our approach makes it possible to introduce the characteristic spatial length and the characteristic time of the multipartite entanglement, which in general depend on the number of ``parties'' in the system. As an example, we consider tripartite entanglement in spontaneous parametric down-conversion with a spatially structured pump. We investigate spatiotemporal properties of such entanglement and calculate its characteristic spatial length and time.In this Rapid Communication, we propose, following the spirit of quantum imaging, to generalize the theory of multipartite entanglement for the continuous-variable Gaussian states by considering, instead of the global covariance matrix, the local correlation matrix at two different spatiotemporal points $(\mathrm{\ensuremath{\rho}P\vec},t)$ and $(\mathrm{\ensuremath{\rho}P\vec} {}^{'},{t}^{'})$, with $\mathrm{\ensuremath{\rho}P\vec}$ being the transverse coordinate. Our approach makes it possible to introduce the characteristic spatial length and the characteristic time of the multipartite entanglement, which in general depend on the number of ``parties'' in the system. As an example, we consider tripartite entanglement in spontaneous parametric down-conversion with a spatially structured pump. We investigate spatiotemporal properties of such entanglement and calculate its characteristic spatial length and time.

Physical Review AMay 11, 20119 citations

Complementary quantum correlations among multipartite systems

Zhi‐Xiang Jin, Shao-Ming Fei, Cong‐Feng Qiao

arXiv:2002.04456Quantum Information ProcessingFeb 4, 202017 citations

Partial correlations in multipartite quantum systems

Zhihua Guo, Huaixin Cao, Shixian Qu

Information SciencesAug 19, 201419 citations

Spatio-temporal properties of multipartite entanglement

Giuseppe Patera, Mikhail I. Kolobov

Quantum multipartite entanglement is a striking phenomenon predicted by quantum mechanics when several parts of a physical system share the same quantum state that cannot be factorized into the states of individual subsystems. The Gaussian quantum states are usually characterized by the covariance matrix of the quadrature components. A powerful formalism for treating the Gaussian states is that of the symplectic eigenvalues. In particular, a quantitative measure of multipartite entanglement is the so-called logarithmic negativity, related to the symplectic eigenvalues of the partially transposed covariance matrix. Considering only global variances of the field quadratures one completely neglects the spatiotemporal properties of the electromagnetic field. We propose, following the spirit of quantum imaging, to generalize the theory of multipartite entanglement for the continuous variable Gaussian states by considering the local correlation matrix at two different spatiotemporal points [see manuscript for characters] and [see manuscript for characters] with [see manuscript for characters] being the transverse coordinate. For stationary and homogeneous systems one can also introduce the spatiotemporal Fourier components of the correlation matrix. The formalism of the global symplectic eigenvalues can be straightforwardly generalized to the frequency-dependent symplectic eigenvalues. This generalized theory allows, in particular, to introduce the characteristic spatial area and time of the multipartite entanglement, which in general depend on the number of "parties" in the system. As an example we consider multipartite entanglement in spontaneous parametric down-conversion with spatially-structured pump. We investigate spatial properties of such entanglement and calculate its characteristic spatial length.Quantum multipartite entanglement is a striking phenomenon predicted by quantum mechanics when several parts of a physical system share the same quantum state that cannot be factorized into the states of individual subsystems. The Gaussian quantum states are usually characterized by the covariance matrix of the quadrature components. A powerful formalism for treating the Gaussian states is that of the symplectic eigenvalues. In particular, a quantitative measure of multipartite entanglement is the so-called logarithmic negativity, related to the symplectic eigenvalues of the partially transposed covariance matrix. Considering only global variances of the field quadratures one completely neglects the spatiotemporal properties of the electromagnetic field. We propose, following the spirit of quantum imaging, to generalize the theory of multipartite entanglement for the continuous variable Gaussian states by considering the local correlation matrix at two different spatiotemporal points [see manuscript for characters] and [see manuscript for characters] with [see manuscript for characters] being the transverse coordinate. For stationary and homogeneous systems one can also introduce the spatiotemporal Fourier components of the correlation matrix. The formalism of the global symplectic eigenvalues can be straightforwardly generalized to the frequency-dependent symplectic eigenvalues. This generalized theory allows, in particular, to introduce the characteristic spatial area and time of the multipartite entanglement, which in general depend on the number of "parties" in the system. As an example we consider multipartite entanglement in spontaneous parametric down-conversion with spatially-structured pump. We investigate spatial properties of such entanglement and calculate its characteristic spatial length.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEApr 30, 20100 citations

2\times 2

and

8\times 8

from different classical and quantum methods. We find that the classical joint entropy is invariant under transformation of change of color but the quantum entropy is sensitive to this change. It is shown that the total correlation

I_T

could arrive to the double amount of the classical joint entropy.