Superconducting rings, superselection rules and quantum measurement problems

Timothy P. Spiller, Terrence D. Clark

F. E. Harrison, K. Kong Wan

Using a Hilbert space formalism we present axiomatic models of both a current-fed thick superconducting ring and a dc SQUID (superconducting quantum interference device) as quantum systems possessing superselection rules. A method of quantization by parts is introduced to establish a quantum theory of a system having a circuit configuration. This involves separate quantization of parts of a circuit: the whole system is then recovered by adding these separately quantized parts together. Our models make clear the difference between standard quantum interference and the interference effects exhibited by SQUIDs. They lead us to question a commonly accepted definition of a classical system, and also clarify the properties required of measuring apparatus in the quantum and classical realms.

Fiona E. Harrison

C. J. P. M. Harmans, Johan E. Mooij

Timothee Hoffreumon, Mischa P. Woods

In a previous work, we showed that real quantum theory (RQT) cannot be experimentally distinguished from ordinary quantum theory (QT). In this paper, we investigate whether this indistinguishability survives two natural extensions of the setting: allowing separated measurements to be represented by commuting rather than tensor-product observables, and imposing superselection rules, as in fermionic information theory. We show that it does in both cases. Our first result is a positive answer to the Tsirelson problem in RQT: commuting and tensor-product measurements generate the same finite-dimensional correlations. This is surprisingly not a trivial consequence of the standard complex proof, as it does not carry over to the reals. The proof obstruction becomes particularly relevant in the presence of superselection rules, which is why we first establish the equivalence in RQT before extending the framework to superselected RQT. Our second result is a local, real quantum formulation of superselected theories. We extend the RQT framework to accommodate a representation of superselection over the reals and show, in particular, that it admits a fermionic version whose predictions are experimentally indistinguishable from those of fermionic information theory. More generally, the construction extends to all superselected QTs.

Sahel Ashhab