Observation and Measurement

Shan Gao

Protective measurement is a new measuring method introduced by Aharonov, Anandan and Vaidman (1993). By a protective measurement, one can measure the expectation value of an observable on a single quantum system, even if the system is initially not in an eigenstate of the measured observable. This remarkable feature of protective measurements was challenged by Uffink (1999, 2012). He argued that only observables that commute with the system's Hamiltonian can be protectively measured, and a protective measurement of an observable that does not commute with the system's Hamiltonian does not actually measure the observable, but measure another related observable that commutes with the system's Hamiltonian. In this paper, we show that there are several errors in Uffink's arguments, and his alternative interpretation of protective measurements is untenable.

Atsushi Okamoto

The conceptual status of the quantum state prior to measurement remains one of the most fundamental unresolved issues in the interpretation of quantum mechanics. While the Copenhagen interpretation successfully explains how measurement produces definite outcomes, it provides no explicit conceptual category describing what should be regarded as existing before measurement. Our previous study focused on the conceptual status of measurement values and proposed that measurement grants accessibility to a potential observational candidate, thereby allowing an observed value to become operationally realized. The present work extends this perspective to a more fundamental question: the conceptual status of existence prior to measurement. Within the Intrinsic Observability Framework (IOF), we introduce potential observability as a conceptual category characterizing the pre-measurement domain. Here, observability does not refer to the standard quantum-mechanical notion of an observable represented by a Hermitian operator. Instead, it denotes the capacity of a pre-measurement structure to become an observed outcome through accessibility. In this framework, measurement is interpreted as the act that grants accessibility to one potential observational candidate, thereby establishing observability. From this viewpoint, the quantum state prior to measurement is understood neither as a collection of already existing observable values nor as an undefined probabilistic entity. Rather, it represents a structured domain of potential observability that provides the conceptual basis from which observed reality subsequently emerges. The present work therefore does not reject the Copenhagen interpretation. Instead, it proposes a conceptual extension that explicitly characterizes the previously unspecified pre-measurement domain. By distinguishing measurement values from existence and clarifying the role of potential observability, this study provides a more coherent conceptual foundation for understanding quantum states, measurement, and observed reality.

Miklós Rédei, A. Zartl, Erwin Schrödinger +9 more

Stanley Gudder

Christopher J. Fewster, Ian Jubb, Maximilian H. Ruep

Abstract In quantum measurement theory, a measurement scheme describes how an observable of a given system can be measured indirectly using a probe. The measurement scheme involves the specification of a probe theory, an initial probe state, a probe observable and a coupling between the system and the probe, so that a measurement of the probe observable after the coupling has ceased reproduces (in expectation) the result of measuring the system observable in the system state. Recent work has shown how local and causal measurement schemes may be described in the context of model-independent quantum field theory (QFT), but has not addressed the question of whether such measurement schemes exist for all system observables. Here, we present two treatments of this question. The first is a proof of principle which provides a measurement scheme for every local observable of the quantized real linear scalar field if one relaxes one of the conditions on a QFT measurement scheme by allowing a non-compact coupling region. Secondly, restricting to compact coupling regions, we explicitly construct asymptotic measurement schemes for every local observable of the quantized theory. More precisely, we show that for every local system observable A there is an associated collection of measurement schemes for system observables that converge to A . All the measurement schemes in this collection have the same fixed compact coupling zone and the same processing region. The convergence of the system observables holds, in particular, in GNS representations of suitable states on the field algebra or the Weyl algebra. In this way, we show that every observable can be asymptotically measured using locally coupled probe theories.