What is the significance of the Quantum Cheshire Cat to Quantum Computing? To recap, the Quantum Cheshire Cat experiment proved it was possible to separate a neutrons' spin from the neutron. Or, in other words a particle could lose its properties in special circumstances. What would the implications be to quantum computing? Does it mean measurements to the system be more accurate, as the properties of the system are isolated from external influences? When reasoning about this experiment by way of Quantum Computing, would one look at the results of the experiment with Quantum Communication (one could always look the fidelity, or even capacity of the quantum channel as enhanced) as a model or any other models would be apt to study the experiments' effects?
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4$\begingroup$ In the quantum cheshire cat experiment, the particle doesn't lose its properties. It still has them; they just happen to be in a different location than the particle. $\endgroup$– Peter ShorSep 23, 2014 at 2:18
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$\begingroup$ Is this due to the very nature of the experiment- they use post selection, that manifests the property in a different location? $\endgroup$– user3483902Sep 23, 2014 at 3:00
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1$\begingroup$ If you can use electrons and atomic nuclei to make charge 1/3 quasiparticles, is separating a neutron from its spin so surprising? $\endgroup$– Peter ShorSep 23, 2014 at 3:57
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$\begingroup$ Of course, separating spin altogether from the particle doesn't seem too far off, considering the case of charge 1/3 quasiparticles. But, in context, we have quantum channels that use quantum error correcting codes(must be the right person to ask!), when we have code transmitted over a channel, with reduced interaction with the environment, thereby reduced entropies(von Neumann entropies, for eg). So if we use a scheme where there is reduced interaction with the environment, the efforts made in error correction are reduced, is this correct? $\endgroup$– user3483902Sep 23, 2014 at 5:52
1 Answer
The quantum Cheshire Cat experiments appear to require postselection even to exhibit. Of course, postselection is itself a computational resource (and an extremely powerful one!) for "bounded" error quantum computation, and one whose power is characterised. To wit: the class PostBQP of decision problems decideable with bounded error using poly-size quantum circuits, conditioning on some single bit having the value 1 (provided that this occurs with non-zero probability) is precisely the class PP. (Recall also that PP contains NP as a subset.)
Perhaps one might ask whether quantum Cheshire cats might somehow represent a useful idiom in the design of PP algorithms for difficult problems. Alternatively, perhaps quantum Cheshire cats correspond to some intriguing feature of quantum mechanics that can be described without resorting to (anything equivalent to) postselection, and which has implications for quantum computation. However, it isn't obvious at the moment that either of these are the case.
