Stable Macroscopic Quantum Superpositions

We study the stability of superpositions of macroscopically distinct quantum states under decoherence. We introduce a class of quantum states with entanglement features similar to Greenberger-Horne-Zeilinger (GHZ) states, but with an inherent stability against noise and decoherence. We show that in contrast to GHZ states, these so-called concatenated GHZ states remain multipartite entangled even for macroscopic numbers of particles and can be used for quantum metrology in noisy environments. We also propose a scalable experimental realization of these states using existing ion-trap setups.

Figure 1

(a) Relative negativity $\mathcal{N}({\rho }_{{\varphi }_C})/{\mathcal{N}}_0$ for the bipartition one logical qubit vs rest for fixed noise parameter $p=0.9$ as a function of system size $N$, where the negativity of the initial state ${\mathcal{N}}_0=0.5$ for all $m$ and $N$. (b) Fisher information ${\mathcal{F}}_A({\rho }_{{\varphi }_C})$ for fixed noise parameter $p=0.9$ and $A=\sum _k({\sigma }_x^{\otimes m}{)}^k$, as a function of system size $N$ for different block sizes $m$. For comparison, the region between the standard quantum limit and the Heisenberg limit is shaded.