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Communications in Theoretical Physics

Entanglement Swapping in the Presence of White and Color Noise

I.S. Dotsenko, R.S. Korobka

Published Feb 1, 2018• 6 citations
Publisher

Abstract

Abstract The influence of white and color noise on the outcome of the entanglement swapping process is investigated in a four-qubit system. Critical degree of noise in initial state, that could destroy entanglement in a result state is presented. The entanglement characteristics, such as concurrence, tangle, etc. are compared. Results could be helpful for experiments regarding entanglement swapping as conditions for initial quantum entangled states, to obtain entangled result state.

DOI
10.1088/0253-6102/69/2/143

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Abstract The influence of white and color noise on the outcome of the entanglement swapping process is investigated in a four-qubit system. Critical degree of noise in initial state, that could destroy entanglement in a result state is presented. The entanglement characteristics, such as concurrence, tangle, etc. are compared. Results could be helpful for experiments regarding entanglement swapping as conditions for initial quantum entangled states, to obtain entangled result state.
On the basis of a system of four qubits, the influence of white and colored noises in the states of initially prepared entangled qubit pairs on the final state obtained as a result of the entanglement swapping has been considered. The corresponding density matrices are obtained, and the redistribution of fractions for the pure state and white and colored noises is analyzed. Conditions for the entanglement preservation and destruction in the course of the transition from the initial to the final state are determined. A comparison between the von Neumann entropy for the initial and final states of qubits is carried out.
Entanglement swapping is gaining widespread attention due to its application in entanglement distribution among different parts of quantum appliances. We investigate the entanglement swapping for pure and noisy systems, and argue different entanglement quantifiers for quantum states. We explore the relationship between the entanglement of initial states and the average entanglement of final states in terms of concurrence and negativity. We find that if initial quantum states are maximally entangled and we make measurements in the Bell basis, then average concurrence and average negativity of final states give similar results. In this case, we simply obtain the average concurrence (average negativity) of the final states by taking the product of concurrences (negativities) of the initial states. However, the measurement in non-maximally entangled basis during entanglement swapping degrades the average swapped entanglement. Further, the product of the entanglement of the initial mixed states provides an upper bound to the average swapped entanglement of final states obtained after entanglement swapping. The negativity work well for weak entangled noisy states but concurrence gives better results for relatively strong entanglement regimes. We also discuss how successfully the output state can be used as a channel for the teleportation of an unknown qubit.
The nonlocal correlations between quantum states in an entangled system are essential to many quantum communications applications. A basic quantum operation, which permits the distribution of entanglement between two initially uncorrelated systems, is entanglement swapping. Here we present a rigorous formulation of entanglement swapping of any two partially mixed two-qubit states without limiting ourselves to any specific type of state or noise. Further, for two important classes of the input states, Bell diagonal and pure states, we describe how the concurrence of the final state is related to the concurrence of the initial states. First, we consider Bell diagonal states, and find bounds on the concurrence of the final state in terms of the concurrences of the initial states. These bounds are important for communications applications because polarization mode dispersion in fibers produces Bell diagonal states up to a local unitary rotation. Second, we show that swapping pure states occasionally results in a state of higher concurrence than either of the initial states. In addition, we find that two pure states are most likely to be capable of swapping to a state of increased concurrence when the two initial states have similar concurrences. Our analysis offers a completely general framework for investigating the behavior of any pair of two-qubit states when used for entanglement swapping.
Abstract We investigate the entanglement swapping under phase damping global noise and amplitude damping global noise. The two qubits the intermediate user holds during the entanglement swapping process first suffer from a global noise before the Bell measurement is carried out. Based on this assumption, the influence of global phase damping noise and global amplitude damping noise on the output entanglement of entanglement swapping is investigated, respectively. Our findings imply that the output entanglement is completely independent of the phase damping global noise and determined by the input entanglement when entanglement swapping is performed in a global phase damping noise environment. In addition, when entanglement swapping is executed in an amplitude damping environment, the output entanglement oscillates periodically with time, and the output entanglement may disappear at some points and reappear at others. In this case, we need not only to improve the input entanglement but also to control the evolution time of the amplitude damping global noise to ensure the optimal output entanglement. Our findings may help experimentalists to avoid and utilize environmental noise in entanglement swapping.
We consider entanglement swapping, a key component of quantum network operations and entanglement distribution. Pure entangled states, which are the desired input to the swapping protocol, are typically mixed by environmental interactions, causing a reduction in their degree of entanglement. Thus an understanding of entanglement swapping with partially mixed states is of importance. Here we present a general analytical solution for entanglement swapping of arbitrary two-qubit states. Our result provides a comprehensive method for analyzing entanglement swapping in quantum networks. First, we show that the concurrence of a partially mixed state is conserved when this state is swapped with a Bell state. Then, we find upper and lower bounds on the concurrence of the state resulting from entanglement swapping for various classes of input states. Finally, we determine a general relationship between the ranks of the initial states and the rank of the final state after swapping.
The basic entanglement-swapping scheme can be seen as a process which allows one to redistribute the Bell states properties between different pairs of a four-qubit system. We analyze a similar scheme by performing a Bell--von Neumann measurement over two local qubits, each one initially correlated through an XXX state with a spatially distant qubit. This process swaps the XXX feature without conditions, whereas the input entanglement is partially distributed in the four possible outcome states under certain conditions. Specifically, we obtain two threshold values for the entanglement of formation of the input XXX states in order for the outcome states to be nonseparable.