Entanglement and dephasing of quantum dissipative systems (7 pages)

Alireza Seif, Yu-Xin Wang, Aashish A. Clerk

Understanding whether dissipation in an open quantum system is truly quantum is a question of both fundamental and practical interest. We consider n qubits subject to correlated Markovian dephasing and present a sufficient condition for when bath-induced dissipation can generate system entanglement and hence must be considered quantum. Surprisingly, we find that the presence or absence of time-reversal symmetry plays a crucial role: broken time-reversal symmetry is required for dissipative entanglement generation. Further, simply having nonzero bath susceptibilities is not enough for the dissipation to be quantum. We also present an explicit experimental protocol for identifying truly quantum dephasing dissipation and lay the groundwork for studying more complex dissipative systems and finding optimal noise mitigating strategies.

Tobias Brandes, Clive Emary, Neill Lambert

A.K Rajagopal, R.W Rendell

Lin Zhang

The presence of symmetries can lead to nontrivial dynamics of operator entanglement in open quantum many-body systems, which characterizes the cost of a matrix product density operator representation of the density matrix in tensor-network methods and provides insights into the corresponding classical simulability. One example is $\mathrm{U}(1)$-symmetric open quantum systems with dephasing, in which the operator entanglement increases logarithmically at late times instead of being suppressed by the dephasing. Here we numerically study the far-from-equilibrium dynamics of operator entanglement in a dissipative quantum many-body system with the more complicated $\mathrm{SU}(2)$ symmetry and dissipations beyond dephasing. We show that after the initial rise and fall, the operator entanglement increases again in a logarithmic manner at late times in the $\mathrm{SU}(2)$-symmetric case. We find that this behavior can be fully understood from the corresponding $\mathrm{U}(1)$ subsymmetry by considering the symmetry-resolved operator entanglement. Especially, the probability distribution of different $\mathrm{U}(1)$ sectors also follows the Gaussian distribution observed in the $\mathrm{U}(1)$-symmetric case with dephasing, with the variance growing as a power law. But unlike the latter, both the classical Shannon entropy associated with the probabilities for the half system to be in different symmetry sectors and the corresponding symmetry-resolved operator entanglement now make nontrivial contributions to the late-time logarithmic growth of operator entanglement in our $\mathrm{SU}(2)$-symmetric case. Our results show evidence that the logarithmic growth of operator entanglement at long times is a generic behavior of dissipative quantum many-body dynamics with $\mathrm{U}(1)$ as the symmetry or subsymmetry and for broader dissipations beyond dephasing, although more analytical and numerical proof from future studies is still required for this conjecture. By breaking the $\mathrm{SU}(2)$ symmetry of our quantum many-body dynamics to $\mathrm{U}(1)$, we also show that the latter property---the logarithmic growth behavior of operator entanglement for broader dissipations beyond dephasing---is valid even for open quantum systems with only $\mathrm{U}(1)$ symmetry.

Helen McAneney

Ali Bourizk

We study the entanglement entropy of Hawking radiation using the open quantum systems framework. For a vacuum with a spectral gap ΔΔ, the radiation entropy saturates at a sub-maximal value, leaving a residual visibility (η(0)≈0.9000) that protects quantum information. This provides an analytical description of the rising Page curve.