Based on our recently published work [Front. Phys. 21, 093201 (2026)], we extend the analysis to the density-operator evolution of a two-mode entangled quantum system subject to amplitude decay and show that the output state retains the same functional structure as the initial density operator throughout the decay. We further examine the evolutions of several quantum statistical distributions and the von Neumann entropy used to quantify entanglement during the process. This work offers a systematic approach to studying two-mode entangled open systems and yields results on the von Neumann entropy that may help facilitate entanglement measurement.
Based on our recently published work [Front. Phys. 21, 093201 (2026)], we extend the analysis to the density-operator evolution of a two-mode entangled quantum system subject to amplitude decay and show that the output state retains the same functional structure as the initial density operator throughout the decay. We further examine the evolutions of several quantum statistical distributions and the von Neumann entropy used to quantify entanglement during the process. This work offers a systematic approach to studying two-mode entangled open systems and yields results on the von Neumann entropy that may help facilitate entanglement measurement.
Extending the recent work completed by Fan et al. [ Front. Phys. 9(1), 74 (2014)] to a two-mode case, we investigate how a two-mode squeezed vacuum evolves when it undergoes a two-mode amplitude dissipative channel, with the same decay rate κ, using the continuous-variable entangled state approach. Our analytical results show that the initial pure-squeezed vacuum state evolves into a definite mixed state with entanglement and squeezing, decaying over time as a result of amplitude decay. We also investigate the time evolutions of the photon number distribution, the Wigner function, and the optical tomogram in this channel. Our results indicate that the evolved photon number distribution is related to Jacobi polynomials, the Wigner function has a standard Gaussian distribution (corresponding to the vacuum) at long periods, losing its nonclassicality due to amplitude decay, and a larger squeezing leads to a longer decay time.
Control of open quantum dynamics is of great interest for realizing quantum technologies. Therefore, it is an important task to quantify and characterize the entropy for open quantum systems under decoherence. In this paper, we study the time evolution of the von Neumann entropy for open quantum systems described by the Lindblad master equation. Note that, in particular, when the decoherence corresponds to the measurement for the observable in the system, the von Neumann entropy tends to monotonically increases as the variance becomes larger. Furthermore, we present a lower bound of the von Neumann entropy in the long-time limit. This lower bound has advantages of being straightforwardly calculated and applicable to a general Markovian open quantum system.
Quantum entanglement is a cornerstone of quantum technologies, but its susceptibility to environmental noise hinders practical implementations. This study investigates the entanglement dynamics in a two-qubit system governed by a transverse-field Ising Hamiltonian and exposed to local amplitude decoherence via the Lindblad master equation. Beginning with a maximally entangled Bell state, we numerically integrate the density matrix evolution using QuTiP. Entanglement, measured by concurrence, displays oscillatory decay influenced by the coupling J, transverse field B, and decoherence rate γ. Analytical benchmarks, including the unitary limit C(t) ≈ |cos(2Bt)| and non-interacting limit C(t) =ⅇ−2γt, corroborate the simulations. Scans across J/γ reveal that for |J|/γ > 1, entanglement lifetime (time until C < 0.5) can extend by factors of 2–10 relative to weak coupling cases, attributed to interaction-induced level splitting that mitigates damping. Bloch vectors exhibit spiraling contraction in the x-z plane toward the excited state pole, while von Neumann entropy rises in tandem with disentanglement, underscoring decoherence-driven mixing. Local observables such as 〈σ_z〉 oscillate amid relaxation to near-zero equilibrium. At finite temperature (T = 10 mK, n_th = 0.01), lifetime shortens by ~10–20% due to thermal excitations. Anchored in parameters from IBM Eagle and Google Sycamore processors, these results elucidate interaction's protective role against decoherence, offering design guidelines for resilient superconducting qubits in quantum computing and sensing. This work resolves prior inconsistencies in interaction-damping interplay and proposes testable conjectures for entanglement plateaus at specific J/γ ratios.
For a quantum state undergoing unitary Schrödinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum operator entropy, which is the Shannon entropy of the probability distribution for the eigenvalues of a Hermitian operator [R. S. Ingarden, Quantum information theory, Rep. Math. Phys. 10, 43 (1976)RMHPBE0034-487710.1016/0034-4877(76)90005-7]. These entropies characterize the missing information about a particular observable inherent in the quantum state itself. The von Neumann entropy is the quantum operator entropy for the case when the operator is the density matrix. We examine pure state unitary evolution in a simple model system composed of a set of highly interconnected topologically disordered states and a time-independent Hamiltonian. An initially confined state is subject to free expansion into available states. The time development is completely reversible with no loss of quantum information and no course graining is applied. The positional entropy increases in time in a way that is consistent with both the classical statistical mechanical entropy and the second law.
I investigate the decoherence of two-mode squeezed vacuum states by analyzing the relative entropy of entanglement. I consider two sources of decoherence: (i) the phase damping and (ii) the amplitude damping due to the coupling to the thermal environment. In particular, I give the exact value of the relative entropy of entanglement for the phase damping model. For the amplitude damping model, I give an upper bound for the relative entropy of entanglement, which turns out to be a good approximation for the entanglement measure in the usual experimental situations.
We investigate the loss of nonclassicality and non-Gaussianity of a single-mode state of the radiation field in contact with a thermal reservoir. The damped density matrix for a Fock-diagonal input is written using the Weyl expansion of the density operator. Analysis of the evolution of the quasiprobability densities reveals the existence of two successive characteristic times of the reservoir which are sufficient to assure the positivity of the Wigner function and, respectively, of the P representation. We examine the time evolution of non-Gaussianity using three recently introduced distance-type measures. They are based on the Hilbert-Schmidt metric, the relative entropy, and the Bures metric. Specifically, for an M-photon-added thermal state, we obtain a compact analytic formula of the time-dependent density matrix that is used to evaluate and compare the three non-Gaussianity measures. We find a good consistency of these measures on the sets of damped states. The explicit damped quasiprobability densities are shown to support our general findings regarding the loss of negativities of Wigner and P functions during decoherence. Finally, we point out that Gaussification of the attenuated field mode is accompanied by a nonmonotonic evolution of the von Neumann entropy of its state conditioned by the initial value of the mean photon number.