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arXiv:0808.4045

Role of Three-Qubit Mixed-States Entanglement in Teleportation Scheme

DaeKil Park, Sayatnova Tamaryan, Jin-Woo Son

Published Aug 29, 2008• 0 citations
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Abstract

The bipartite quantum teleportation with a three-qubit mixture of GHZ and W states as a quantum channel is discussed. When the quantum channel is a mixed state consisting of the GHZ state plus small perturbed W state, the entanglement of the channel becomes zero when the average fidelity $\bar{F}_{GHZ}$ is less than 0.775. This means that the mixed state cannot play an any role as a quantum channel at $\bar{F}_{GHZ} \leq 0.775$. For the case of the mixed state consisting of the W state plus small perturbed GHZ state it turn out that this mixed state cannot play a role as a quantum channel at $\bar{F}_W \leq 0.833$.

DOI
10.48550/arxiv.0808.4045

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The bipartite quantum teleportation with a three-qubit mixture of GHZ and W states as a quantum channel is discussed. When the quantum channel is a mixed state consisting of the GHZ state plus small perturbed W state, the entanglement of the channel becomes zero when the average fidelity FˉGHZ\bar{F}_{GHZ}FˉGHZ​ is less than 0.775. This means that the mixed state cannot play an any role as a quantum channel at FˉGHZ≤0.775\bar{F}_{GHZ} \leq 0.775FˉGHZ​≤0.775. For the case of the mixed state consisting of the W state plus small perturbed GHZ state it turn out that this mixed state cannot play a role as a quantum channel at FˉW≤0.833\bar{F}_W \leq 0.833FˉW​≤0.833.
Abstract We investigate the criteria for two-qubit states that could be transmitted via W-state. The appropriate criterias are entangled states which have maximum number of terms equal to number of channel terms and maximum of two different constants. We have also shown quantum teleportation of a particular type of two-qubit state via three-qubit GHZ-like states, with Alice possesses the first qubit of the channel and the rest belongs to Bob. GHZ-like state is an entangled state which has different characteristic from GHZ state. It is stronger against particle loss than GHZ state. Furthermore, GHZ-like states which can teleport a particular type of two-qubit state are GHZ-like states which have two terms.
Quantum teleportation plays a significant role in the field of quantum communication. This paper investigates quantum teleportation through a noisy environment by using GHZ state and non-standard W state as quantum channels. We analyze the efficiency of quantum teleportation by solving analytically a master equation in Lindblad form. Following the quantum teleportation protocol, we obtain the fidelity of quantum teleportation as a function of evolution time. The calculation results show that the teleportation fidelity using non-standard W is higher in comparison to GHZ state at the same evolution time. Moreover, we consider the efficiency of teleportation with weak measurements and reverse quantum measurement under amplitude damping noise. Our analysis suggests that the teleportation fidelity using non-standard W is also more robust to noise than GHZ state in the same conditions. Interestingly, we found that weak measurement and its reverse operation have no positive effect on the efficiency of quantum teleportation by using GHZ and non-standard W state in the amplitude damping noise environment. In addition, we also demonstrate the efficiency of quantum teleportation can be improved by making minor modifications to the protocol.
The quantum teleportation with a noisy EPR state is discussed. Using an optimal decomposition technique, we compute the concurrence, entanglement of formation and Groverian measure for various noisy EPR resources. It is shown analytically that all entanglement measures reduce to zero when , where is an average fidelity between Alice and Bob. This fact indicates that the entanglement is a genuine physical resource for the teleportation process. This fact gives valuable clues to the optimal decomposition for higher-qubit mixed states. As an example, the optimal decompositions for the 3-qubit mixed states are discussed by adopting a teleportation with a W-state.
We present a mathematical formulation of old teleportation protocol (original teleportation protocol introduced by Bennett et al.) for mixed state and study in detail the role of mixedness of the two-qubit quantum channel in a teleportation protocol. We show that maximally entangled mixed state described by the density matrix of rank-4 will be useful as a two-qubit teleportation channel to teleport a single qubit mixed state when the teleportation channel parameter p1 > 1/2. Also we discuss the case when p1 ≤ 1/2.