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arXiv:quant-ph/0503120 · Physical Review A

Limitations of practical multiphoton decoherence-free states

Yong-Sheng Zhang, Chuan‐Feng Li, Yun‐Feng Huang, Guang‐Can Guo

Published Jul 11, 2005• 7 citations
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Abstract

It is shown that the decoherence-free subspace (DFS) of practical multiphoton polarization cannot avoid exponential decoherence even in the same extra environment if the photons are frequency anticorrelated. The reason lies in the fact that the condition of collective decoherence is not satisfied in this case. As an example, the evolution of a biphoton decoherence-free state is given. A possible solution for a feasible multiphoton DFS state is also given.

DOI
10.1103/physreva.72.012308

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It is shown that the decoherence-free subspace (DFS) of practical multiphoton polarization cannot avoid exponential decoherence even in the same extra environment if the photons are frequency anticorrelated. The reason lies in the fact that the condition of collective decoherence is not satisfied in this case. As an example, the evolution of a biphoton decoherence-free state is given. A possible solution for a feasible multiphoton DFS state is also given.
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Decoherence free subspaces (DFS) is a theoretical tool towards experimental implementation of quantum information storage and processing. However, they represent an experimental challenge, since conditions for their existence are very stringent. This work explores the situation in which a system of NNN oscillators coupled to a bath of harmonic oscillators is close to satisfy the conditions for the existence of DFS. We show, in the Born-Markov limit and for small deviations from separability and degeneracy conditions, that there are {\emph{weak decoherence subspaces}} which resemble the original notion of DFS.
A quantum key distribution with decoherence-free subspaces has been proposed to overcome collective noise to the polarization modes of photons flying in quantum channels. Prototypes of this scheme have also been achieved with a parametric down-conversion source. However, the photon-number-splitting attack we propose will make practical implementations of this scheme insecure since the parametric down-conversion source may occasionally emit multiphoton pairs. We propose a decoy-state method to make these implementations immune to this attack. With this decoy-state method, both the security distance and key bit rate will be increased.
The cause of decoherence in a quantum system can be traced back to the interaction with the environment. As it has been pointed out by Dicke, in a system of N two-level atoms, where each of the atoms is individually dipole coupled to the environment, there are collective, subradiant states, that have no dipole coupling to photon modes, and therefore, they are expected to decay slower. This property also implies that these type of states decohere slower. We propose a scheme which will create such states. First, the two-level atoms are placed in a strongly detuned cavity and one of the atoms, called the control atom is excited. The time evolution of the coupled atom-cavity system leads to an appropriately entangled state of the atoms. By the aid of a suitable single-atom phase transformation, it is possible to drive the atomic state into the subradiant, i.e., decoherence-free subspace. Up to a certain average number of photons, the result is independent of the state of the cavity. The analysis of the conditions shows that this scheme is feasible with present day techniques achieved in atom-cavity interaction experiments.