Correlation between Measurements in Quantum Theory

Margenau, Henry; Hill, Robert Nyden

doi:10.1143/ptp.26.722

Cited by 268 publications

(129 citation statements)

References 2 publications

Supporting

Mentioning

123

Contrasting

Unclassified

Order By: Relevance

“…For nonclassical states, P takes negative values or fails to be a proper function becoming more singular than a delta function. Nevertheless, this is not the unique definition and some other correspondences between states and phase-space distributions may be adopted [8,9], leading in general to different conclusions [10].…”

Section: Classical Upperbound On the Product Of Probabilities Of mentioning

confidence: 99%

Nonclassicality in the statistics of noncommuting observables: Nonclassical states are more compatible than classical states

Luis

2011

Phys. Rev. A

View full text Add to dashboard Cite

We study nonclassicality in the product of the probabilities of noncommuting observables. We show that within the quantum theory, nonclassical states can provide larger probability product than classical states, so that nonclassical states approach the nonfluctuating states of the classical theory more closely than classical states. This is particularized to relevant complementary observables such as conjugate quadratures, phase and number, quadrature and number, and orthogonal angular momentum components.

show abstract

Section: Classical Upperbound On the Product Of Probabilities Of mentioning

confidence: 99%

Nonclassicality in the statistics of noncommuting observables: Nonclassical states are more compatible than classical states

Luis

2011

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…It was independently rediscovered and generalized to arbitrary observables by Dirac [5] and Barut [6]. The real part of this distribution was examined in phase space by Terletsky [7] and for arbitrary pairs of * Electronic address: lars.m.johansen@hibu.no observables by Barut [6] and Margenau and Hill [8]. The question of a possible connection between the Kirkwood distribution and measurement disturbance was raised by Prugovečki [9].…”

Section: Introductionmentioning

confidence: 99%

Quantum theory of successive projective measurements

2007

View full text Add to dashboard Cite

We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in successive projective measurements. The complex modification term is a measure of measurement disturbance. A selective phase rotation is needed to obtain the imaginary part. This leads to a complex quasiprobability, the Kirkwood distribution. We show that the Kirkwood distribution contains full information about the state if the two observables are maximal and complementary. The Kirkwood distribution gives a new picture of state reduction. In a nonselective measurement, the modification term vanishes. A selective measurement leads to a quantum state as a nonnegative conditional probability. We demonstrate the special significance of the Schwinger basis.

show abstract

“…One may, instead of performing a weak measurement between pre-and postselection, try to guess the value ofĉ. The best possible guess between preand postselection is nothing else than the weak value.Furthermore, it can be shown [14] that the real part of the weak value can be expressed as a conditional moment of the Margenau-Hill distribution [15]. More generally, the weak value is a conditional moment of the standard ordered distribution [16], which is the complex conjugate of the Kirkwood distribution [17].…”

mentioning

confidence: 99%

Weak Measurements with Arbitrary Probe States

Johansen

2004

Phys. Rev. Lett.

View full text Add to dashboard Cite

The exact conditions on valid pointer states for weak measurements are derived. It is demonstrated that weak measurements can be performed with any pointer state with vanishing probability current density. This condition is found both for weak measurements of noncommuting observables and for c-number observables. In addition, the interaction between pointer and object must be sufficiently weak. There is no restriction on the purity of the pointer state. For example, a thermal pointer state is fully valid.PACS numbers: 03.65.Ta In "orthodox" quantum mechanics, the result of a "measurement" is always one of the eigenvalues of the observable. In the last pages of his textbook on quantum mechanics [1], von Neumann provided a model of a measurement where the object under study was interacting with a measurement pointer. By assuming that the initial uncertainty of the pointer was small, von Neumann demonstrated that the pointer would display one of the eigenvalues of the object observable.Aharonov, Albert and Vaidman (AAV) considered the same experimental arrangement [2]. However, they made the opposite assumption, namely that the initial uncertainty of the pointer was large. They demonstrated that despite this, the pointer would on average show the correct expectation value of an observableĉ, although it could not distinguish separate eigenvalues. Their most interesting discovery, though, was that if a projective measurement of a second observabled was made on the object after the interaction, the average meter reading conditioned on the result of the measurement on the object would be the real part of the quantityThe authors introduced the name "weak value" for this quantity. They observed that the values of c w might lie outside the range of eigenvalues of the observableĉ. It has been contested whether the experimental arrangement of AAV qualifies as a "measurement", and whether it has any meaning to ascribe to c w a significance as a "value" of the observableĉ [3][4][5]. Despite initial scepticism, weak values have found applications in a variety of systems. A classical optical analog [6] of the original experiment proposed by AAV has been realized experimentally [7]. The polarization state of a classical radiation field can be treated as analogous to a spin-1 2 system, and the weak value of polarization may exceed the eigenvalue range [8,9]. It has also been found that weak values have applications within classical optical communication [10,11]. These examples demonstrate * Electronic address: lars.m.johansen@hibu.no that weak values have applications beyond quantum mechanics. In fact, it is not unfamiliar that the quantum formalism can be applied even to classical systems where two observables cannot be jointly measured with arbitrary accuracy. This is known e.g. in signal processing, where the Wigner distribution for time and frequency has gained popularity [12].It was recently found that "weak values" have a deeper significance when considered from the viewpoint of standard Bayesian estimation theory [13]....

show abstract

Correlation between Measurements in Quantum Theory

Cited by 268 publications

References 2 publications

Nonclassicality in the statistics of noncommuting observables: Nonclassical states are more compatible than classical states

Nonclassicality in the statistics of noncommuting observables: Nonclassical states are more compatible than classical states

Quantum theory of successive projective measurements

Weak Measurements with Arbitrary Probe States

Contact Info

Product

Resources

About