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arXiv:quant-ph/9701020

Cooperative loss and decoherence in quantum computation and commuication

L.-M. Duan, Guang‐Can Guo

Published Jan 16, 1997• 1 citation
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Abstract

Cooperative effects in the loss (the amplitude damping) and decoherence (the phase damping) of the qubits (two-state quantum systems) due to the inevitable coupling to the same environment are investigated. It is found that the qubits undergo the dissipation coherently in this case. In particular, for a special kind of input states (called the coherence-preserving states), whose form depends on the type of the coupling, loss and decoherence in quantum memory are much reduced. Based on this phenomenon, a scheme by encoding the general input states of the qubits into the corresponding coherence-preserving states is proposed for reducing the cooperative loss and decoherence in quantum computation or communication.

DOI
10.48550/arxiv.quant-ph/9701020

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Cooperative effects in the loss (the amplitude damping) and decoherence (the phase damping) of the qubits (two-state quantum systems) due to the inevitable coupling to the same environment are investigated. It is found that the qubits undergo the dissipation coherently in this case. In particular, for a special kind of input states (called the coherence-preserving states), whose form depends on the type of the coupling, loss and decoherence in quantum memory are much reduced. Based on this phenomenon, a scheme by encoding the general input states of the qubits into the corresponding coherence-preserving states is proposed for reducing the cooperative loss and decoherence in quantum computation or communication.
A scheme for protecting quantum states from both independent and cooperative decoherence is proposed. The scheme operates by pairing each qubit (two-state quantum system) with an ancilla qubit and by encoding the states of the qubits into corresponding coherence-preserving states of qubit pairs. In this scheme, amplitude damping (loss of energy) as well as phase damping (dephasing) is prevented by a strategy called ``free-Hamiltonian elimination.'' We further extend the scheme to include quantum gate operations and show that loss and decoherence during such operations can also be prevented.
This article presents a comprehensive study of the impact of decoherence on the average correlation for pure quantum states. We explore two primary mechanisms of decoherence: phase damping and amplitude damping, each having distinct effects on quantum systems. Phase damping, which describes the loss of quantum coherence without energy loss, primarily affects the phase relationships between the components of a quantum system while amplitude damping involves energy dissipation and also affects the state's occupation probabilities. We show that the average correlation follows a predictable decaying pattern in both scenarios. Our analysis can be understood in the context of quantum computing, by focusing on how phase damping influences the entanglement and correlation between qubits, key factors in quantum computational efficiency and error correction protocols.
Decoherence in quantum-computer memory due to the inevitable coupling to the external environment is examined. We make the assumption that all quantum bits (qubits) interact with the same environment rather than the assumption of separate environments for different qubits. It is found that the qubits decohere collectively. For some kinds of entangled input states, no decoherence occurs at all in the memory, even if the qubits are interacting with the environment. Based on this phenomenon, a scheme is proposed for reducing the collective decoherence. We also discuss possible implications of this decoherence model for quantum measurements.
We study the behavior of cooperative multiplayer quantum games [Q. Chen, Y. Wang, J.T. Liu, and K.L. Wang, Phys. Lett. A 327 (2004) 98; A.P. Flitney and L.C.L. Hollenberg, Quantum Inf. Comput. 7 (2007) 111] in the presence of decoherence using different quantum channels such as amplitude damping, depolarizing and phase damping. It is seen that the outcomes of the games for the two damping channels with maximum values of decoherence reduce to same value. However, in comparison to phase damping channel, the payoffs of cooperators are strongly damped under the influence amplitude damping channel for the lower values of decoherence parameter. In the case of depolarizing channel, the game is a no-payoff game irrespective of the degree of entanglement in the initial state for the larger values of decoherence parameter. The decoherence gets the cooperators worse off.
We study the behavior of cooperative multiplayer quantum games [35,36] in the presence of decoherence using different quantum channels such as amplitude damping, depolarizing and phase damping. It is seen that the outcomes of the games for the two damping channels with maximum values of decoherence reduce to same value. However, in comparison to phase damping channel, the payoffs of cooperators are strongly damped under the influence\ amplitude damping channel for\ the lower values of decoherence parameter. In the case of depolarizing channel, the game is a no-payoff game irrespective of the degree of entanglement in the initial state for the larger values of decoherence parameter. The decoherence gets the cooperators worse off.
If quantum bits (qubits) couple to the same environment, it has been found the qubits decohere coherently. An interesting result from this phenomenon is that, for a kind of input states, i.e., the coherence-preserving states, coherence of the qubits can be preserved perfectly in quantum memory. In this paper, we propose a feasible scheme to transform an arbitrary unknown input state to the corresponding coherence-preserving state. The transformed state undergoes no decoherence in the noisy memory and, after that, it can be transformed back into the original state with decoherence much reduced. This scheme involves the use of an analogy of the ideas of quantum teleportation.