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Ukrainian Journal of Physics

Teleportation of Quantum Entangled Two-Photon States in the Presence of Noise

I.S. Dotsenko, R.S. Korobka

Published Mar 1, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.15407/ujpe58.03.0268

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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.
In this paper, an accelerated two-qubit system initially prepared in maximum or partial entangled state, which interacts locally with white/color or white-color noises, is considered. Due to the acceleration process and the noise effect, the entanglement degraded. Therefore, the effect of noise strength, initial state settings and the acceleration on the survival entanglement are investigated by means of the concurrence. Moreover, the initial parameters that describe this system are estimated by using the quantum Fisher information, where two forms are considered, namely by using a single and two-qubit forms. It is shown that, by using the two-qubit form, the estimation degree of these parameters is larger than that displayed by using a single-qubit form.
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 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.
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.
In this manuscript, we investigate the effect of the white and color noise on a accelerated two-qubit system, where different initial state setting are considered. The behavior of the survival amount of entanglement is quantified for this accelerated system by means of the concurrence. We show that, the color noise enhances the generated entanglement between the two particles even for small values of the initial purity of the accelerated state. However, the larger values of the white noise strength improve the generated entanglement. The initial parameters that describe this system are estimated by using Fisher information, where two forms are considered, namely by using a single and two-qubit forms. It is shown that, by using the two-qubit form, the estimation degree of these parameters is larger than that displayed by using a single-qubit form.