On the effective size of certain "Schrödinger cat'' like states

Abstract

Several experiments and experimental proposals for the production of macroscopic superpositions naturally lead to states of the general form $|{\varphi }_1{>}^{\otimes N}+|{\varphi }_2{>}^{\otimes N}$, where the number of subsystems $N$ is very large, but the states of the individual subsystems have large overlap, $|ł{\varphi }_1|{\varphi }_2{\mathring{|}}^2=1-{\epsilon }^2$. We propose two different methods for assigning an effective particle number to such states, using ideal Greenberger--Horne--Zeilinger (GHZ)-- states of the form $|0\r^{\otimes n}+|1\r^{\otimes n}$ as a standard of comparison. The two methods are based on decoherence and on a distillation protocol respectively. Both lead to an effective size $n$ of the order of $N{\epsilon }^2$.

4 pages, no figures

References in corpus (2)

• Experimental Four-photon Entanglement and High-fidelity Teleportation
• Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper box

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