We devise a method to certify nonclassical features via correlations of phase-space distributions by unifying the notions of quasiprobabilities and matrices of correlation functions. Our approach complements and extends recent results that were based on Chebyshev's integral inequality \cite{BA19}. The method developed here correlates arbitrary phase-space functions at arbitrary points in phase space, including multimode scenarios and higher-order correlations. Furthermore, our approach provides necessary and sufficient nonclassicality criteria, applies to phase-space functions beyond s -parametrized ones, and is accessible in experiments. To demonstrate the power of our technique, the quantum characteristics of discrete- and continuous-variable, single- and multimode, as well as pure and mixed states are certified only employing second-order correlations and Husimi functions, which always resemble a classical probability distribution. Moreover, nonlinear generalizations of our approach are studied. Therefore, a versatile and broadly applicable framework is devised to uncover quantum properties in terms of matrices of phase-space distributions.We devise a method to certify nonclassical features via correlations of phase-space distributions by unifying the notions of quasiprobabilities and matrices of correlation functions. Our approach complements and extends recent results that were based on Chebyshev's integral inequality \cite{BA19}. The method developed here correlates arbitrary phase-space functions at arbitrary points in phase space, including multimode scenarios and higher-order correlations. Furthermore, our approach provides necessary and sufficient nonclassicality criteria, applies to phase-space functions beyond s -parametrized ones, and is accessible in experiments. To demonstrate the power of our technique, the quantum characteristics of discrete- and continuous-variable, single- and multimode, as well as pure and mixed states are certified only employing second-order correlations and Husimi functions, which always resemble a classical probability distribution. Moreover, nonlinear generalizations of our approach are studied. Therefore, a versatile and broadly applicable framework is devised to uncover quantum properties in terms of matrices of phase-space distributions.

arXiv:2003.11031QuantumOct 15, 202031 citations

Dynamical correlation functions for linear spin chains

Gerhard Müller, H. Beck

Physica B+CJan 1, 19771 citation

Extended coupled-cluster treatment of correlations in quantum magnets

J. Rosenfeld, N.E. Ligterink, R. F. Bishop

The spin-half $\mathrm{XXZ}$ model on the linear chain and the square lattice are examined with the extended coupled-cluster method (ECCM) of quantum many-body theory. We are able to describe both the Ising-Heisenberg phase and the $\mathrm{XY}$ -Heisenberg phase, starting from known wave functions in the Ising limit and at the phase transition point between the $\mathrm{XY}$ -Heisenberg and ferromagnetic phases, respectively, and by systematically incorporating correlations on top of them. The ECCM yields good numerical results via a diagrammatic approach, which makes the numerical implementation of higher-order truncation schemes feasible. In particular, the best nonextrapolated coupled-cluster result for the sublattice magnetization is obtained, which indicates the employment of an improved wave function. Furthermore, the ECCM finds the expected qualitatively different behaviors of the linear-chain and square-lattice cases.The spin-half $\mathrm{XXZ}$ model on the linear chain and the square lattice are examined with the extended coupled-cluster method (ECCM) of quantum many-body theory. We are able to describe both the Ising-Heisenberg phase and the $\mathrm{XY}$-Heisenberg phase, starting from known wave functions in the Ising limit and at the phase transition point between the $\mathrm{XY}$-Heisenberg and ferromagnetic phases, respectively, and by systematically incorporating correlations on top of them. The ECCM yields good numerical results via a diagrammatic approach, which makes the numerical implementation of higher-order truncation schemes feasible. In particular, the best nonextrapolated coupled-cluster result for the sublattice magnetization is obtained, which indicates the employment of an improved wave function. Furthermore, the ECCM finds the expected qualitatively different behaviors of the linear-chain and square-lattice cases.

arXiv:cond-mat/9901183Physical review. B, Condensed matterAug 1, 199912 citations

Dynamic SCF approximation for spin correlation functions

В. П. Калашников, N.V. Kozhevnikov

Physics Letters AOct 1, 19780 citations

Interferometric scheme for direct measurement of moments of transverse spatial variables of photons

S. Machado, P. Milman, Stephen Patrick Walborn

We propose an interferometric method for the direct measurement of the moments of the transverse spatial variables of an optical field. The key elements are spatial light modulators, used to imprint a transverse phase on the field. We show that our measurement scheme can be used to measure the spatial correlation functions of a two-photon state directly, which allows for the identification of spatial entanglement without the need for partial state reconstruction. Our method can also be extended to $N$ -photon states. We show that the method is more efficient than the measurement of marginal probability distributions, and that it can be made resilient to small alignment errors.We propose an interferometric method for the direct measurement of the moments of the transverse spatial variables of an optical field. The key elements are spatial light modulators, used to imprint a transverse phase on the field. We show that our measurement scheme can be used to measure the spatial correlation functions of a two-photon state directly, which allows for the identification of spatial entanglement without the need for partial state reconstruction. Our method can also be extended to $N$-photon states. We show that the method is more efficient than the measurement of marginal probability distributions, and that it can be made resilient to small alignment errors.

Physical Review AMay 24, 20136 citations

New method of computing correlation functions. I

Raoul Rashidovich Nigmatullin

Russian Physics JournalOct 1, 19770 citations

The spin-half

\mathrm{XXZ}

model on the linear chain and the square lattice are examined with the extended coupled-cluster method (ECCM) of quantum many-body theory. We are able to describe both the Ising-Heisenberg phase and the

\mathrm{XY}

-Heisenberg phase, starting from known wave functions in the Ising limit and at the phase transition point between the

\mathrm{XY}

-Heisenberg and ferromagnetic phases, respectively, and by systematically incorporating correlations on top of them. The ECCM yields good numerical results via a diagrammatic approach, which makes the numerical implementation of higher-order truncation schemes feasible. In particular, the best nonextrapolated coupled-cluster result for the sublattice magnetization is obtained, which indicates the employment of an improved wave function. Furthermore, the ECCM finds the expected qualitatively different behaviors of the linear-chain and square-lattice cases.

N

-photon states. We show that the method is more efficient than the measurement of marginal probability distributions, and that it can be made resilient to small alignment errors.