# Quantum teleportation through noisy channels with multi-qubit GHZ states

Quantum teleportation through noisy channels with multi-qubit GHZ states We investigate two-party quantum teleportation through noisy channels for multi-qubit Greenberger–Horne–Zeilinger (GHZ) states and find which state loses less quantum information in the process. The dynamics of states is described by the master equation with the noisy channels that lead to the quantum channels to be mixed states. We analytically solve the Lindblad equation for $$n$$ n -qubit GHZ states $$n\in \{4,5,6\}$$ n ∈ { 4 , 5 , 6 } where Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Using the average fidelity, we show that 3GHZ state is more robust than $$n$$ n GHZ state under most noisy channels. However, $$n$$ n GHZ state preserves same quantum information with respect to Einstein–Podolsky–Rosen and 3GHZ states where the noise is in $$x$$ x direction in which the fidelity remains unchanged. We explicitly show that Jung et al.’s conjecture (Phys Rev A 78:012312, 2008), namely “average fidelity with same-axis noisy channels is in general larger than average fidelity with different-axes noisy channels,” is not valid for 3GHZ and 4GHZ states. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Quantum teleportation through noisy channels with multi-qubit GHZ states

, Volume 13 (8) – Jun 18, 2014
23 pages

/lp/springer_journal/quantum-teleportation-through-noisy-channels-with-multi-qubit-ghz-Wz0MTgSbOU
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-014-0766-2
Publisher site
See Article on Publisher Site

### Abstract

We investigate two-party quantum teleportation through noisy channels for multi-qubit Greenberger–Horne–Zeilinger (GHZ) states and find which state loses less quantum information in the process. The dynamics of states is described by the master equation with the noisy channels that lead to the quantum channels to be mixed states. We analytically solve the Lindblad equation for $$n$$ n -qubit GHZ states $$n\in \{4,5,6\}$$ n ∈ { 4 , 5 , 6 } where Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Using the average fidelity, we show that 3GHZ state is more robust than $$n$$ n GHZ state under most noisy channels. However, $$n$$ n GHZ state preserves same quantum information with respect to Einstein–Podolsky–Rosen and 3GHZ states where the noise is in $$x$$ x direction in which the fidelity remains unchanged. We explicitly show that Jung et al.’s conjecture (Phys Rev A 78:012312, 2008), namely “average fidelity with same-axis noisy channels is in general larger than average fidelity with different-axes noisy channels,” is not valid for 3GHZ and 4GHZ states.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Jun 18, 2014

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