Reconstruction of spin states and its conceptual implications

TL;DR

This paper reviews methods for reconstructing quantum spin states using Stern-Gerlach measurements, highlighting how this enables expectation value determination and offers a new perspective on Schrödinger's equation.

Contribution

It introduces non-tomographic spin state reconstruction techniques and explores their implications for quantum measurement and the formulation of quantum mechanics.

Findings

Reconstruction allows experimental expectation value measurement of arbitrary operators.

It suggests reformulating Schrödinger's equation using only expectation values.

Non-tomographic methods provide alternative approaches to quantum state determination.

Abstract

State reconstruction for quantum spins is reviewed. Emphasis is on non-tomographic approaches which are based on measurements performed with a Stern-Gerlach apparatus. Two consequences of successfully implemented state reconstruction are pointed out. First, it allows one to determine experimentally the expectation value of an arbitrary operator without a device measuring it. Second, state reconstruction suggests a reformulation of Schroedinger's equation in terms of expectation values only, without explicit reference to a wave function or a density operator.