The Wavefunction and the Quantum State

C. S. Unnikrishnan

The physical states of matter and fields are represented in the quantum theory with complex valued wavefunctions, or more generally by quantum states in an abstract linear vector space. Determining the physical nature of wavefunctions remains an open problem that is at the very core of quantum mechanics, About a decade ago, Pusey, Barret and Rudolf (PBR) claimed to prove an ontologically real status of wavefunctions by ruling out ψ -epistemic models. The result was obtained by associating wavefunctions to hypothetical distributions of notional physical states, and by examining whether some physical states were associated with more than one wavefunction, a criterion they chose for defining a wavefunction as ‘epistemic’. I show that the starting assumption in the PBR argument, of associating a wavefunction with a distribution of physical states, is flawed and contradictory to the linear structure of quantum mechanics coupled with its quadratic Born’s rule. Since none of the axioms or calculations of observable statistical results in the standard quantum theory depends on specifying the physical nature of a ψ -function, the considerations in the PBR paper, involving a standard process of the preparation and projective measurements of quantum states, cannot address the ontological status of the wavefunctions in space and time.

E. Munguía-González, S. Rego, J. K. Freericks

With the successes of the laser interferometer gravitational-wave observatory, we anticipate increased interest in working with squeezed states in the undergraduate and graduate quantum-mechanics classroom. Because squeezed-coherent states are minimum uncertainty states, their wavefunctions in position and momentum space must be Gaussians. But this result is rarely discussed in treatments of squeezed states in quantum textbooks or quantum optics textbooks. In this work, we show three different ways to construct the wavefunction for squeezed-coherent states: (i) a differential equation-based approach; (ii) an approach that uses an expansion in terms of the simple-harmonic oscillator wavefunctions; and (iii) a fully operator-based approach. We do this to illustrate that the concept of the wavefunction can be introduced no matter what methodology an instructor wishes to use. We hope that working with the wavefunction will help demystify the concept of a squeezed-coherent state.

Luca Salasnich

Jincheng Zhang

Quantum wavefunctions represent the fundamental building blocks of quantum systems, and their collapse into definite states is a crucial aspect of quantum computation. This paper explores a novel computational model centered around the concept of 'wavefunction collapse' as a dynamic resource allocation scheme. Traditional approaches often focus on the abrupt collapse of a single wavefunction, whereas we propose a system where wavefunction states are treated as 'resource units' that can be allocated and repurposed based on task-specific requirements. This shift aims to overcome the limitations of standard collapse models and potentially unlock new avenues for quantum computing. The core mechanism involves introducing a 'wavefunction state vector' representation, allowing for a more granular control over quantum state evolution through a probabilistic allocation algorithm. This research investigates the potential of this approach to enhance computational efficiency and explore novel applications within the quantum realm.

Martin Ringbauer