Gaussian states and channels with mathematical rigor

The extremality of Gaussian states is exploited to show that Gaussian states are the most robust, among all possible bipartite continuous-variable states at fixed energy, against disentanglement due to noisy evolutions in Markovian Gaussian channels involving dissipation and thermal hopping. This proves a conjecture raised recently [M. Allegra, P. Giorda, and M. G. A. Paris, Phys. Rev. Lett. 105, 100503 (2010)], providing a rigorous validation of the conclusions of that work. The problem of identifying continuous-variable states with maximum resilience to entanglement damping in more general bosonic open-system dynamical evolutions, possibly including correlated noise and non-Markovian effects, remains open.The extremality of Gaussian states is exploited to show that Gaussian states are the most robust, among all possible bipartite continuous-variable states at fixed energy, against disentanglement due to noisy evolutions in Markovian Gaussian channels involving dissipation and thermal hopping. This proves a conjecture raised recently [M. Allegra, P. Giorda, and M. G. A. Paris, Phys. Rev. Lett. 105, 100503 (2010)], providing a rigorous validation of the conclusions of that work. The problem of identifying continuous-variable states with maximum resilience to entanglement damping in more general bosonic open-system dynamical evolutions, possibly including correlated noise and non-Markovian effects, remains open.

arXiv:1102.2356Physical Review AFeb 9, 201120 citations

Quantum mechanics and gaussian channels

Kenjiro Yanagi

Physics Letters AFeb 1, 19823 citations

A control problem for gaussian states

Masahiro Yanagisawa, Hidenori Kimura

Springer eBooksOct 2, 20075 citations

Efficient impurity-bath trial states from superposed Slater determinants

Izak Snyman, Serge Florens

The representation of ground states of fermionic quantum impurity problems as superpositions of Gaussian states has recently been given a rigorous mathematical foundation [S. Bravyi and D. Gosset, Commun. Math. Phys. 356, 451 (2017)]. It is natural to ask how many parameters are required for an efficient variational scheme based on this representation. An upper bound is $O({N}^{2})$ , where $N$ is the system size, which corresponds to the number parameters needed to specify an arbitrary Gaussian state. We provide an alternative representation, with more favorable scaling, only requiring $O(N)$ parameters, that we illustrate for the interacting resonant-level model. We achieve the reduction by associating mean-field-like parent Hamiltonians with the individual terms in the superposition, using physical insight to retain only the most relevant channels in each parent Hamiltonian. We benchmark our variational ansatz against the numerical renormalization group, and compare our results to other variational schemes of a similar nature to ours. Apart from the ground-state energy, we also study the spectrum of the covariance matrix---a very stringent measure of accuracy. Our approach outperforms some existing variational schemes and remains quantitatively accurate in the numerically challenging near-critical regime.The representation of ground states of fermionic quantum impurity problems as superpositions of Gaussian states has recently been given a rigorous mathematical foundation [S. Bravyi and D. Gosset, Commun. Math. Phys. 356, 451 (2017)]. It is natural to ask how many parameters are required for an efficient variational scheme based on this representation. An upper bound is $O({N}^{2})$, where $N$ is the system size, which corresponds to the number parameters needed to specify an arbitrary Gaussian state. We provide an alternative representation, with more favorable scaling, only requiring $O(N)$ parameters, that we illustrate for the interacting resonant-level model. We achieve the reduction by associating mean-field-like parent Hamiltonians with the individual terms in the superposition, using physical insight to retain only the most relevant channels in each parent Hamiltonian. We benchmark our variational ansatz against the numerical renormalization group, and compare our results to other variational schemes of a similar nature to ours. Apart from the ground-state energy, we also study the spectrum of the covariance matrix---a very stringent measure of accuracy. Our approach outperforms some existing variational schemes and remains quantitatively accurate in the numerically challenging near-critical regime.

arXiv:2106.14027Physical review. B./Physical review. BNov 19, 20215 citations

Gaussian states as minimum uncertainty states

Shuangshuang Fu, Shunlong Luo, Yue Zhang

Physics Letters AOct 8, 201917 citations

Gaussian entanglement in the turbulent atmosphere

Martin Bohmann, А. А. Семенов, Jan Sperling +1 more

We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a nontrivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in principle, renders it possible to transfer the Gaussian entanglement through any turbulent channel over arbitrary distances. Therefore, our approach provides the theoretical foundation for advanced applications of Gaussian entanglement in free-space quantum communication.We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a nontrivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in principle, renders it possible to transfer the Gaussian entanglement through any turbulent channel over arbitrary distances. Therefore, our approach provides the theoretical foundation for advanced applications of Gaussian entanglement in free-space quantum communication.

arXiv:1603.02828Physical Review AJul 21, 201640 citations

O({N}^{2})

, where

N

is the system size, which corresponds to the number parameters needed to specify an arbitrary Gaussian state. We provide an alternative representation, with more favorable scaling, only requiring

O(N)

parameters, that we illustrate for the interacting resonant-level model. We achieve the reduction by associating mean-field-like parent Hamiltonians with the individual terms in the superposition, using physical insight to retain only the most relevant channels in each parent Hamiltonian. We benchmark our variational ansatz against the numerical renormalization group, and compare our results to other variational schemes of a similar nature to ours. Apart from the ground-state energy, we also study the spectrum of the covariance matrix---a very stringent measure of accuracy. Our approach outperforms some existing variational schemes and remains quantitatively accurate in the numerically challenging near-critical regime.