Collapse-in and collapse-out in partial measurement in quantum mechanics and its wise interpretation

Abstract

One central issue in quantum mechanics is the relation between the wavefunction and the quantum system it describes. As quantum mechanics is understood in different ways, the wavefunction is given various explanations. Some regard the wavefunction as ”epistemic”, that is, something reflected in the human mind, and some regard it as ”ontological”, i.e., something realistic. The orthodox interpretation of quantum mechanics of Copenhagen [1, 2] is epistemic and treats the wavefunction merely as a mathematical quantity. Recent examples of the ontological interpretation include the random discontinuous motion [3], ”Wavefunction Is the System Entity”(WISE) interpretation [4], and information complete interpretation [5]. WISE treats the wavefunction equivalently as the quantum system itself, that is, the quantum system is just the wavefunction, and the wavefunction is just the quantum system. These two are exactly the same. The quantum system, which is also the wavefunction, can exist in disjoint regions of space, travel at a finite speed, and collapse upon measurements. An encounter-delayedchoice experiment has been proposed and experimentally demonstrated recently [6]. In this short communication, we will concentrate on the partial measurement issue and give an explanation concerning the WISE interpretation. The essential idea of WISE is given in Ref. [4], together with the linear combination of unitaries (LCU) formalism of quantum computing. LCU has now become one of the major techniques in quantum algorithm design. The quantum circuit implementation of LCU is given in Refs. [7, 8], and a review of the subject is given in Ref.[9]. Partial measurement postulate. We recall first the measurement postulate in standard quantum mechanics. If a particle is in state |Ψ〉, a measurement of the variable (corresponding to) Ω will yield one of the eigenvalues ω with probability P (ω) ∝ |〈ω|Ψ〉|. The state of the system will change from |Ψ〉 to |ω〉 as a result of the measurement [10]. What will happen if the measurement is on part of the wave function (partial measurement) rather than on a full wave function (full measurement)? For instance, in a three-slits system, if one places a detector immediately after the first slit and places no detectors in the remaining