Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment

Abstract

We report on an experimental investigation of the dynamics of entanglement between a single qubit and its environment, as well as for pairs of qubits interacting independently with individual environments, using photons obtained from parametric down-conversion. The qubits are encoded in the polarizations of single photons, while the interaction with the environment is implemented by coupling the polarization of each photon with its momentum. A convenient Sagnac interferometer allows for the implementation of several decoherence channels and for the continuous monitoring of the environment. For an initially-entangled photon pair, one observes the vanishing of entanglement before coherence disappears. For a single qubit interacting with an environment, the dynamics of complementarity relations connecting single-qubit properties and its entanglement with the environment is experimentally determined. The evolution of a single qubit under continuous monitoring of the environment is investigated, demonstrating that a qubit may decay even when the environment is found in the unexcited state. This implies that entanglement can be increased by local continuous monitoring, which is equivalent to entanglement distillation. We also present a detailed analysis of the transfer of entanglement from the two-qubit system to the two corresponding environments, between which entanglement may suddenly appear, and show instances for which no entanglement is created between dephasing environments, nor between each of them and the corresponding qubit: the initial two-qubit entanglement gets transformed into legitimate multiqubit entanglement of the Greenberger-Horne-Zeilinger (GHZ) type.

System-environment dynamics of X-type states in noninertial frames

“…There are at most d 2 independent Kraus operators, where d is the dimension of the system [31,32]. Together with Eq.…”

“…Together with Eq. (5), the dynamical evolution of the complete system-environment state can be also given by the following map [31] :…”

Dependence of Entanglement on Initial States under Amplitude Damping Channel in Non-Inertial Frames

“…Sibasish Ghosh showed that it is not possible to discriminate between any three Bell states if only a single copy is provided and if only local operations and classical communication are allowed [14]. At present most of the studies consider only one of the Bell states but ignore the other three [9][10][11][12][13]15,16] because different Bell states will give the same result without considering environment. On the other hand, Philip Walther and Anton Zeilinger realized a probabilistic for Bell state analyzer for two photonic quantum bits by use of a non-destructive controlled-NOT gate based on entirely linear optical elements [17].…”

Dynamics of Quantum Entanglement in Reservoir with Memory Effects

“…A reasonable model is considered as one open qubit S entangled with an ancillary qubit A which is isolated from a local vacuum reservoir E [34]. The decoherence process can also be obtained by the map in terms of the total system-environment state [35,36]. The evolution of the states for the total system can be obtained by…”