Knowledge of the relationships among different features of quantumness, like entanglement and state purity, is important from both fundamental and practical viewpoints. Yet, this issue remains little explored in dynamical contexts for open quantum systems. We address this problem by studying the dynamics of entanglement and purity for two-qubit systems using paradigmatic models of radiation-matter interaction, with a qubit being isolated from the environment (spectator configuration). We show the effects of the corresponding local quantum channels on an initial two-qubit pure entangled state in the concurrence–purity diagram and find the conditions which enable dynamical closed formulas of concurrence, used to quantify entanglement, as a function of purity. We finally discuss the usefulness of these relations in assessing entanglement and purity thresholds which allow noisy quantum teleportation. Our results provide new insights about how different properties of composite open quantum systems behave and relate each other during quantum evolutions.
We investigate the dynamics of non-classical correlations and quantum coherence in open quantum systems by employing metrics like local quantum Fisher information, local quantum uncertainty, and quantum Jensen-Shannon divergence. Our focus here is on a system of two qubits in two distinct physical situations: the first one when the two qubits are coupled to a cavity field whether the system is closed or open, while the second consists of two qubits immersed in dephasing reservoirs. Our study places significant emphasis on how the evolution of these quantum criterion is influenced by the initial state's purity (whether pure or mixed) and the nature of the environment (whether Markovian or non-Markovian). We observe that a decrease in the initial state's purity corresponds to a reduction in both quantum correlations and quantum coherence, whereas higher purity enhances these quantumness. Furthermore, we establish a quantum teleportation strategy based on the two different physical scenarios. In this approach, the resulting state of the two qubits functions as a quantum channel integrated into a quantum teleportation protocol. We also analyze how the purity of the initial state and the Markovian or non-Markovian regimes impact the quantum teleportation process.
Using simple models of radiation-matter interaction we study the reduced dynamics of a quantum central system formed by two qubits under the spectator configuration. Purity and concurrence as measures of decoherence and entanglement are evaluated in analytical form. Interestingly in these systems, entanglement sudden death is found despite having less complex dynamics than models used in previous studies. Furthermore, we have analysed the associated local quantum operations generated by the dynamics and how their action on an initial Bell state is characterized in the concurrence-purity diagram.
We investigate the dynamics of non-classical correlations and quantum coherence in open quantum systems by employing metrics like local quantum Fisher information, local quantum uncertainty, and quantum Jensen-Shannon divergence. Our focus here is on a system of two qubits in two distinct physical situations: the first one when the two qubits are coupled to a single-mode cavity, while the second consists of two qubits immersed in dephasing reservoirs. Our study places significant emphasis on how the evolution of these quantum criterion is influenced by the initial state's purity (whether pure or mixed) and the nature of the environment (whether Markovian or non-Markovian). We observe that a decrease in the initial state's purity corresponds to a reduction in both quantum correlations and quantum coherence, whereas higher purity enhances these quantumness. Furthermore, we establish a quantum teleportation strategy based on the two different physical scenarios. In this approach, the resulting state of the two qubits functions as a quantum channel integrated into a quantum teleportation protocol. We also analyze how the purity of the initial state and the Markovian or non-Markovian regimes impact the quantum teleportation process.
We study decoherence of one, two, and
n non-interacting qubits. Decoherence, measured in terms of purity, is calculated in linear response approximation, making use of the spectator configuration. The environment and its interaction with the qubits are modelled by random matrices. For two qubits, numerical studies reveal a simple one to one correspondence between its decoherence and its internal entanglement decay. Using this relation we are able to give a formula for concurrence decay. For large environments the evolution induces a unital channel in the two qubits, providing a partial explanation for the relation above. Using a kicked Ising spin network, we study the exact evolution of two non-interacting qubits in the presence of a spin bath. We find that the entanglement (as measured by concurrence) of the two qubits has a close relation to the purity of the pair, and closely follows an analytic relation derived for Werner states. As a collateral result we find that an integrable environment causes quadratic decay of concurrence as well as of purity, while a chaotic environment causes linear decay. Both quantities display recurrences in some integrable environments. Good agreement with the results found using random matrix theory is obtained. Finally, we analyze decoherence of a quantum register in the absence of non-local operations. The problem is solved in terms of a sum rule which implies linear scaling in the number of qubits. Each term involves a single qubit and its entanglement with the remaining ones. Two conditions are essential: decoherence must be small and the coupling of different qubits must be uncorrelated in the interaction picture. We apply the result to the random matrix model, and illustrate its reach considering a GHZ state coupled to a spin bath.
We investigate the dynamical relations among entanglement, mixedness, and nonlocality, quantified by concurrence
C, purity
P, and maximum Bell function
B, respectively, in a system of two qubits in a common structured reservoir. To this aim we introduce the
C-
P-
B parameter space and analyze the time evolution of the point representative of the system state in such a space. The dynamical interplay among entanglement, mixedness, and nonlocality strongly depends on the initial state of the system. For a two-excitation Bell state the representative point draws a multibranch curve in the
C-
P-
B space and we show that a closed relation among these quantifiers does not hold. By extending the known relation between
C and
B for pure states, we give an expression among the three quantifiers for mixed states. In this equation we introduce a quantity, vanishing for pure states, which in general does not have a closed form in terms of
C,
P and
B. Finally, we demonstrate that for an initial one-excitation Bell state, a closed
C-
P-
B relation instead exists and the system evolves, remaining always a maximally entangled mixed state.
Purity as a quantifier of an impact of environment on an open quantum system is studied for a qubit dephasingly interacting with its environment. We analyze how time evolution of the purity depends on initial states of the composite system both in the case of infinite and finite environments. It is shown that for a certain class of initial preparations, the purity of an evolving qubit state initially correlated with infinite environment can be greater than in the case of uncorrelated qubit-environment initial preparations. We identify a class of initial states leading to such desired outcome.