Heisenberg's uncertainty principle

Busch, Paul; Heinonen, Teiko; Lahti, Pekka

doi:10.1016/j.physrep.2007.05.006

Cited by 408 publications

(441 citation statements)

References 98 publications

(119 reference statements)

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“…We then examine the importance of the commutation [4,13,76,270,271,272] of the measured observable with the Hamiltonian of the system (subsection 8.2). Finally we exhibit a process which might allow imperfect simultaneous measurements of non-commuting observables (subsection 8.3) [273,274,275,276,277,278].…”

Section: Imperfect Measurements Failures and Multiple Measurementsmentioning

confidence: 99%

“…Its recent developments are given in [273,274,275,276,277] (among other references) and reviewed in [278].…”

Section: երկու երնեկ մի տեղ չեն լինումmentioning

confidence: 99%

“…It is, however, physically sensible to imagine a setting with which we would try to perform such a measurement approximately [273,274,275,276,277,278,284]. It is interesting to analyze the corresponding dynamical process so as to understand how it differs from a standard measurement.…”

Section: Dutch and French Proverbsmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

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Section: Imperfect Measurements Failures and Multiple Measurementsmentioning

confidence: 99%

“…Its recent developments are given in [273,274,275,276,277] (among other references) and reviewed in [278].…”

Section: երկու երնեկ մի տեղ չեն լինումmentioning

confidence: 99%

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…Forcing two devices to make a simultaneous measurement is, in fact, to adjust them to start the process at, say, t 0 and finish it at t 0 + ∆t, so that both occur within [t 0 , t 0 + ∆t]. According to our model, however, the probing associated toσ 1 happens at a precise time t (1) p , while that ofσ 3 occurs at t (3) p . The assumption that the devices make measurements with the same duration ∆t is by no means essential and, again, aims to simplify the presentation.…”

Section: Two-level Systemsmentioning

confidence: 99%

Estimating the reduction time of quantum states

Parisio

2011

Phys. Rev. A

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An effective description of microscopic measurements is given, in which the precise moment of probing is not determined. Within this scenario we propose a scheme that relies on an "attempt" to make a forbidden simultaneous measurement of two incompatible observables. Although bound to failure in what concerns this goal, the process can lead to experimentally accessible information on a possibly non-vanishing time δt elapsed in the collapsing of the wave function, even if the duration ∆t of the individual measurements is much larger than δt.

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“…In the standard account, the measured system interacts with a probe system, resulting in an entangled state for the total system. We can assume a similar scheme for approximate joint measurement of both position and momentum since the existence of such schemes is warranted by the existence of POMs that represent joint observables for momentum and position (as reviewed in [35]). …”

Section: Elements Of Unsharp Quantum Reality and Their Evolutionmentioning

confidence: 99%

Unsharp Quantum Reality

Busch

Jaeger

2010

Found Phys

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ABSTRACT. The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it a concept of joint properties. A property manifests itself as an element of unsharp reality by its power, or tendency, of becoming actual or actualizing a specific measurement outcome, where this tendency of actualization is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way.

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Heisenberg's uncertainty principle

Cited by 408 publications

References 98 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

Estimating the reduction time of quantum states

Unsharp Quantum Reality

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