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Springer eBooks

Proof of the Fermion Superselection Rule Without the Assumption of Time—Reversal Invariance

Gerhard C. Hegerfeldt, K. Kraus, Eugene Paul Wigner

Published Jan 1, 1997• 0 citations
Publisher
DOI
10.1007/978-3-662-09203-3_24

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Fermions and the Tsirelson Problem in Real Quantum Theory

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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.

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Comment on 'Reasonable fermionic quantum information theories require relativity'

Markus Johansson

In [N. Friis, New J. Phys. 18, 033014 (2016)] the non-relativistic description of fermions is considered and in particular the role of the parity superselection rule in relation to the characterization of entanglement. An argument based on the spin-statistics connection is presented as a physical motivation for the parity superselection rule. Since the spin statistics connection was derived in the context of relativistic quantum mechanics it is argued that the inclusion of the parity superselection rule is motivated by Lorentz invariance. Based on this it is further argued that fermionic Quantum Information theory and the theory of special relativity are conceptually inseparable. In this comment a different, and well known, motivation for the parity superselection rule is given that does not rely on arguments from relativistic quantum mechanics, but instead uses the assumptions that the laws of physics are the same for different observers and the no-signalling principle.

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Quantum mechanics and quantum field theory of a fermion system

Wolfgang Bulla, K. Unterkofler

•Jan 1, 1986•0 citations
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.
In [N. Friis, New J. Phys. 18, 033014 (2016)] the non-relativistic description of fermions is considered and in particular the role of the parity superselection rule in relation to the characterization of entanglement. An argument based on the spin-statistics connection is presented as a physical motivation for the parity superselection rule. Since the spin statistics connection was derived in the context of relativistic quantum mechanics it is argued that the inclusion of the parity superselection rule is motivated by Lorentz invariance. Based on this it is further argued that fermionic Quantum Information theory and the theory of special relativity are conceptually inseparable. In this comment a different, and well known, motivation for the parity superselection rule is given that does not rely on arguments from relativistic quantum mechanics, but instead uses the assumptions that the laws of physics are the same for different observers and the no-signalling principle.