Measurement of a degenerate (or non-degenerate) discrete observable is investigated in the framework of quantum measurement theory short of collapse, i.e. premeasurement theory, based on a unitary evolution operator that includes the measurement interaction between object and measuring instrument. A pointer observable with eigen-projectors of, in general, many (or even infinitely) dimensional ranges is introduced as a new approach. It leads to redundant entanglement in the final state. As the first main result, the basic dynamical relation of the approach is derived. It is shown to be equivalent to the calibration condition, which is known to define general exact measurement. The latter is given a practical form. Complete measurement (premeasurement with objectification or collapse), which is in some sense implied by the premeasurement theory, performed on a subsystem of a bipartite object in a pure state is studied with particular attention to its effect on the opposite, interactionally unaffected subsystem. The change of state of the latter is derived for exact complete subsystem measurement, and it is shown that the change is the same as for the simplest, i.e. ideal measurement (this is the second main result). It is applied to the case of twin observables and thus distant measurement obtains a new, more satisfactory, foundation (the third main result). Distant measurement is a basic concept in the EPR phenomenon. The well-known importance of the latter implies importance of the former.
Measurement of a degenerate (or non-degenerate) discrete observable is investigated in the framework of quantum measurement theory short of collapse, i.e. premeasurement theory, based on a unitary evolution operator that includes the measurement interaction between object and measuring instrument. A pointer observable with eigen-projectors of, in general, many (or even infinitely) dimensional ranges is introduced as a new approach. It leads to redundant entanglement in the final state. As the first main result, the basic dynamical relation of the approach is derived. It is shown to be equivalent to the calibration condition, which is known to define general exact measurement. The latter is given a practical form. Complete measurement (premeasurement with objectification or collapse), which is in some sense implied by the premeasurement theory, performed on a subsystem of a bipartite object in a pure state is studied with particular attention to its effect on the opposite, interactionally unaffected subsystem. The change of state of the latter is derived for exact complete subsystem measurement, and it is shown that the change is the same as for the simplest, i.e. ideal measurement (this is the second main result). It is applied to the case of twin observables and thus distant measurement obtains a new, more satisfactory, foundation (the third main result). Distant measurement is a basic concept in the EPR phenomenon. The well-known importance of the latter implies importance of the former.
A detailed theory of quantum premeasurement dynamics is presented in which a unitary composite-system operator that contains the relevant object-measuring-instrument interaction brings about the final premeasurement state. It does not include collapse, and it does not consider the environment. It is assumed that a discrete degenerate or non-degenerate observable is measured. Premeasurement is defined by the calibration condition, which requires that every initially statistically sharp value of the measured observable has to be detected with statistical certainty by the measuring instrument. The entire theory is derived as a logical consequence of this definition using the standard quantum formalism. The study has a comprehensive coverage, hence the article is actually a topical review. Connection is made with results of other authors, particularly with basic works on premeasurement. The article is a conceptual review, not a historical one. General exact premeasurement is defined in 7 equivalent ways. Nondemolition premeasurement, defined by requiring preservation of any sharp value of the measured observable, is characterized in 10 equivalent ways. Overmeasurement, i. e., a process in which the observable is measured on account of being a function of a finer observable that is actually measured, is discussed. Disentangled premeasurement, in which, by definition, to each result corresponds only one pointer-observable state in the final composite-system state, is investigated. Ideal premeasurement, a special case of both nondemolition premeasurement and disentangled premeasurement, is defined, and its most important properties are discussed. Finally, disentangled and entangled premeasurements, in conjunction with nondemolition or demolition premeasurements, are used for classification of all premeasurements.
It is assumed that an arbitrary composite bipartite pure state in which the two subsystems are entangled is given, and it is investigated how the entanglement transmits the influence of measurement on only one of the subsystems to the state of the opposite subsystem. It is shown that any exact subsystem measurement has the same influence as ideal measurement on the opposite subsystem. In particular, the distant effect of subsystem measurement of a twin observable, i. e., so-called 'distant measurement', is always ideal measurement on the distant subsystem no matter how intricate the direct exact measurement on the opposite subsystem is.
A unitary operator is defined, connecting the states of the measured system and the measuring-instrument system before and after interaction, by means of which the post-interaction values of S in the instrument can be used to calculate the pre-interaction 〈R〉av and ${\ensuremath{\Delta}}^{2}R$ in the measured system, where R and S are Hermitian operators. The premeasurement state of the instrument need not be known, and the same measurement operator is applicable whether the system to be measured is originally described by a pure case or a mixture. Finally, this theory is contrasted briefly with the measurement theory of von Neumann.
Quantum-mechanical interpretation-related implications of the theory of unitary premeasurement [1] on complete measurement (objectification or collapse included) are investigated in the present article with a view to give an affirmative answer to the question in the title. It is argued that both Bohr's and von Neumann's ideas lead to those of Everett. Hence, the latter can be, in some sense, considered to be a continuation and elaboration of both former approaches. The importance of the idea of relativeness in Everett's theory is emphasized. To free the relative-state theory from its roots both of classicalness and of subjective observation in the argument of this study, the general or unfolded version of Everett's theory is sketched.
A measurement model is a framework that describes a quantum measurement process. In this article we restrict attention to MMs on finite-dimensional Hilbert spaces. Suppose we want to measure an observable A whose outcomes Ax are represented by positive operators (effects) on a Hilbert Space H. We call H the base or object system. We interact H with a probe system on another Hilbert space K by means of a quantum channel. The probe system contains a probe (or meter or pointer) observable F whose outcomes Fx are measured by an apparatus that is frequently (but need not be) classical in practice. The MM protocol gives a method for determining the probability of an outcome Ax for any state of H in terms of the outcome Fx. The interaction channel usually entangles this state with an initial probe state of K that can be quite complicated. However, if the channel is nondisturbing in a sense that we describe, then the entanglement is considerably simplified. In this article, we give formulas for observables and instruments measured by nondisturbing MMs. We begin with a general discussion of nondisturbing operators relative to a quantum context. We present two examples that illustrate this theory in terms of unitary nondisturbing channels.
A local measurement on one member of an entangled composite system is said to change the distant member's state instantaneously. Taken without qualification, this is misleading. A selective measurement changes the conditional state assigned to the remote subsystem once a local outcome is specified; a non-selective measurement, where that outcome is ignored, leaves the remote reduced density operator unchanged. This distinction reconciles quantum state update with operational no-signalling and provides the setting for Einstein–Podolsky–Rosen steering. This review develops measurement using density operators, completely positive instruments, Kraus representations, partial traces, conditional states, and steering assemblages. It derives the invariance of remote marginal statistics under local trace-preserving operations and contrasts this with Bell-local factorization. It examines the hierarchy among entanglement, steering, and Bell nonlocality, joint measurability, remote state preparation, and one-sided device-independent protocols. The article considers spacelike-separated measurements, microcausality in relativistic quantum theory, and ontological readings of selective state update offered by Everettian, Bohmian, collapse, and relational approaches. Decoherence is treated as the process through which local outcomes become records, while quantum Darwinism accounts for their redundant local accessibility. It highlights gaps in literature, and concludes that entanglement permits nonclassical conditional correlations, but local measurement supplies no controllable superluminal signal.