Pure-state dynamics of a pair of charge qubits in a random environment (12 pages)

Marco Lucamarini, Simone Paganelli

Nikola Burić

A pair of charge qubits in a random electromagnetic environment is studied, using the description of the random dynamics of its pure-state vector as given by quantum-state diffusion theory. It is shown by numerical computations that the pure-state dynamics provides a more detailed description than the density-matrix picture of the main effects such as phase dumping and depolarization.

Koji Yamaguchi

The notion of typicality in statistical mechanics is essential to characterize a macroscopic system. An overwhelming majority of the pure state looks almost identical if we neglect macroscopic non-local correlations, suggesting that thermal equilibrium is the collection of the typical properties. Quantum entanglement, which characterizes a non-local correlation, also has a typical behavior in equilibrium systems. However, it remains elusive whether there is a typical behavior of entanglement in dynamical non-equilibrium systems. To investigate the typicality, we consider a situation where a system in a pure state starts to share entanglement with its environment system due to the interaction between them. Assuming the initial state is randomly chosen from an ensemble of pure states, a criteria for the typicality of the Rényi entropies is presented. In addition, it is analytically proven that the second Rényi entropy has a typical behavior in two cases. The first one is an energy dissipation process in a multiple-qubit system which is initially in a random pure state in an energy shell. Since the typical behavior is qualitatively the same as the prediction of the Page curve conjecture, it gives the first proof of the Page curve conjecture in a dynamical process. In the second case, the typicality is proven for any dynamics described by a multiple-product of a single-qudit channel when the system is initially in a pure state randomly chosen from the whole Hilbert space. This result shows that entanglement typicality is not a specific feature of energy dissipating processes.

J. Stehlik

Gaurav Sarmah, Ramakrishna Podila

Finite quantum environments can relax local probes without acting as canonical baths. We study this distinction for a probe qubit coupled to a programmable bath of ($N$) qubits under excitation-number-conserving dynamics. The conserved charge partitions the Hilbert space into sectors. We characterize probe-level bath emergence using the sector-resolved late-time population ($p_e^{(q)}$), the sector-memory variance ($M_N$), and a global Gibbs-fit error ($Δ_G^{\mathrm{global}}$). Exact simulations with Haar-random pure states in each complete fixed-charge sector yield sector-dependent populations close to the maximally mixed-sector benchmark ($p_e^{(q)}=q/(N+1)$), producing a nonzero Gibbs obstruction. We then construct charge-preserving Floquet circuits using ($R_z$) phases and ($XX+YY$) exchange gates, validate them with ideal and noisy Qiskit simulations, and implement finite-depth experiments on IBM Fez. For ($N=4$) and ($ε=0$), the hardware data give ($M_N \simeq 0.044$), ($Δ_G^{\mathrm{global}} \simeq 0.558$), and charge preservation near 0.90 after readout mitigation. A paired symmetry-breaking scan using bath ($R_x(ε)$) rotations reduces both diagnostics while increasing charge leakage, but does not erase sector ordering over the accessible depths. These results show that equilibration within constrained sectors is insufficient to produce a single sector-independent Gibbs state for the probe.

Shengyang Zhou, Enrique Pacis Blair

Models of quantum disentanglement are developed for nanometer-scale molecular charge qubits (MCQs). Two MCQs, A and B, are prepared in a Bell state and separated for negligible A–B interactions. Interactions between the local environment and each MCQ unravels A–B entanglement during coherent system+environment evolution. Three models are used for dynamics: (1) a previously developed numerical model, in which both AB and environment E are modeled explicitly; (2) an exact, semi-analytic model, in which only the dynamics of AB are calculated, and (3) an approximate model developed from the semi-analytic model and assumptions about randomness in E. In the approximate model, the non-zero coherences of the density operator for AB decay with a Gaussian time dependence. This provides a time scale for system dynamics in the exact models as well. This time scale is related directly to the strength of AB–E interaction. This time scale describes cases where environmental interaction with one target MCQ is dominant, generalizing a previous time scale applicable only when both MCQs have roughly the same strength of interaction with the local environment. Entanglement is measured using two-qubit correlation functions, the dynamics of which are used to demonstrate the effectiveness of the time scale. The early-time decay of coherences and the loss of entanglement are well-characterized as Gaussian, a behavior that Markovian models for memoryless environments cannot capture. The approximate Gaussian model may be used to describe the dynamics of MCQ disentanglement under the influence of environments modeled here, as well as other environments where randomness is present.