Dynamics of entanglement in systems of identical fermions undergoing decoherence

Information that is stored in quantum-mechanical systems can be easily lost because of the interaction with the environment in a process known as decoherence. Possible physical implementations of many processes in quantum information theory involve systems of identical particles, whence comprehension of the dynamics of entanglement induced by decoherence processes in identical-particle open systems becomes relevant. Here we study the effects and concomitant entanglement evolution arising from the interaction between a system of two identical fermions and the environment for two paradigmatic quantum channels. Entanglement measures are introduced to quantify the entanglement between the different parties, and a study of the dynamics of entanglement for some particular examples is carried out. Our analysis, which includes also the evolution of an entanglement indicator based on an entropic criteria, offers insights into the dynamics of entanglement in open systems of identical particles, involving the emergence of multipartite genuine entanglement. The results improve our understanding of the phenomenon of decoherence and will provide strategies to control it.

Figure 1

Entanglement evolution for the initial state (29) under the amplitude-damping decoherence channel. Evolution of the entanglement between the fermions (orange solid line), evolution of the entanglement between the environment and the pair of fermions (violet dotted line), and evolution of the entanglement between one fermion and the rest of the system (green dashed line). (Inset) Evolution of the negativity of the reduced state of one fermion and the environment. All depicted quantities are dimensionless.

Figure 2

Entanglement evolution for the initial state (34) with $\alpha =\beta =1/\sqrt{2}$ under the amplitude-damping decoherence channel. Evolution of the entanglement between the fermions (orange solid line), evolution of the entanglement between the environment and the two fermions (violet dotted line), and evolution of the entanglement between one fermion and the rest of the system (green dashed line). (Inset) Evolution of the negativity of the reduced state of one fermion and the environment. All depicted quantities are dimensionless.

Figure 3

Entanglement evolution for the initial state (39) with $\delta =1/\sqrt{2},\gamma =-i\delta$ under the phase-damping decoherence channel. Evolution of the entanglement between the fermions (orange solid line), evolution of the entanglement between the environment and the two fermions (violet dotted line), and evolution of the entanglement between one fermion and the rest of the system (green dashed line). All depicted quantities are dimensionless.

Figure 4

Entropic entanglement indicator evolution (dashed line) and evolution of the fermionic concurrence (solid line) for the initial state (29) under ADC. (Inset) Evolution of the entropic entanglement indicator (dashed line) and fermionic concurrence dynamics (solid line) for the initial state (34) with $\alpha =\beta =1/\sqrt{2}$ under ADC. The logarithms in the entropic entanglement indicator are taken to the base 2 and all depicted quantities are dimensionless.