Is the Quantum State Real in the Hilbert Space Formulation?

Mani L. Bhaumik


The persistent debate about the reality of a quantum state has recently come under limelight because of its importance to quantum information and the quantum computing community. Almost all of the deliberations are taking place using the elegant and powerful but abstract Hilbert space formalism of quantum mechanics developed with seminal contributions from John von Neumann. Since it is rather difficult to get a direct perception of the events in an abstract vector space, it is hard to trace the progress of a phenomenon. Among the multitude of recent attempts to show the reality of the quantum state in Hilbert space, the Pusey–Barrett–Rudolph theory gets most recognition for their proof. But some of its assumptions have been criticized, which are still not considered to be entirely loophole free. A straightforward proof of the reality of the wave packet function of a single particle has been presented earlier based on the currently recognized fundamental reality of the universal quantum fields. Quantum states like the atomic energy levels comprising the wave packets have been shown to be just as real. Here we show that an unambiguous proof of reality of the quantum states gleaned from the reality of quantum fields can also provide an explicit substantiation of the reality of quantum states in Hilbert space.

Quanta 2020; 9: 37–46.

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ISSN: 1314-7374