arXiv subjects

A. D. Parks

Publications and source records attributed to A. D. Parks.

7 recordsLinked to original sources

arXiv2021

PT and Anti-PT Symmetry Arising in Time Dependent Weak Value Measurements

Parks introduced a formulation of time dependent weak values in 2008, which is the formalism we use in this paper. In this paper we extend notions from time dependent weak values to show that Hamiltonians associated with weak value measurements can be shown to exhibit even or odd symmetric properties. They exhibit PT or anti-PT symmetry, respectively. These symmetries are manifested during the measurement process as pointer translations, which have vanishing imaginary or vanishing real parts. The consequence of this that one can characterize some of the aspects of these symmetries of the time dependent Hamiltonians that arise from time dependent weak values. This allows one to generalize some work on non-Hermitian variables in quantum mechanics (QM) due to Bender related to weak values and weak measurement. We also speculate how these symmetries might apply to distinguishing between the various two-time interpretations of QM in the Conclusions of this paper.

quant-ph↗

arXiv2018

A note concerning the modular valued von Neumann interaction operator

The modular valued operator $\widehat{V}_m$ of the von Neumann interaction operator for a projector is defined. The properties of $\widehat{V}_m$ are discussed and contrasted with those of the standard modular value of a projector. The associated notion of a faux qubit is introduced and its possible utility in quantum computation is noted. An experimental implementation of $\widehat{V}_m$ is also highlighted.

quant-ph↗

arXiv2012

A Note Concerning von Neumann Projector Measurement Pointer States, Weak Values, and Interference

It is well known that the pointer state |Φ> resulting from the von Neumann measurement of a projection operator A performed upon an ensemble of quantum systems in the preselected state |ψ> depends upon A|ψ>. Here it is shown that the pointer state |Ψ> obtained from such a measurement performed upon an ensemble that is also postselected depends upon the weak value of A - regardless of the measurement interaction strength. It is also found that, while the spatial distribution of |Ψ> exhibits interference, the idempotency of A prohibits interference in that of |Φ>. This is explained in terms of welcher Weg information.

quant-ph↗

arXiv2011

Variance Control in Weak Value Measurement Pointers

The variance of an arbitrary pointer observable is considered for the general case that a complex weak value is measured using a complex valued pointer state. For the typical cases where the pointer observable is either its position or momentum, the associated expressions for the pointer's variance after the measurement contain a term proportional to the product of the weak value's imaginary part with the rate of change of the third central moment of position relative to the initial pointer state just prior to the time of the measurement interaction when position is the observable - or with the initial pointer state's third central moment of momentum when momentum is the observable. These terms provide a means for controlling pointer position and momentum variance and identify control conditions which - when satisfied - can yield variances that are smaller after the measurement than they were before the measurement. Measurement sensitivities which are useful for estimating weak value measurement accuracies are also briefly discussed.

quant-ph↗

arXiv2010

Experimental Evidence for a Dynamical Non-Locality Induced Effect in Quantum Interference Using Weak Values

The quantum theoretical concepts of modular momentum and dynamical non-locality, which were introduced four decades ago, have recently been used to explain single particle quantum interference phenomena. Although the non-local exchange of modular momentum associated with such phenomena cannot be directly observed, it has been suggested that effects induced by this exchange can be measured experimentally using weak measurements of pre- and post-selected ensembles of particles. This paper reports on such an optical experiment that yielded measured weak values that were consistent with the theoretical prediction of an effect induced by a non-local exchange of modular momentum.

quant-ph↗

arXiv2010

Exact Pointer Properties for Quantum System Projector Measurements with Application to Weak Measurements and Their Accuracy

Exact pointer states are obtained for projection operator measurements performed upon pre-selected (PS) and upon pre- and post-selected (PPS) quantum systems. These states are used to provide simple exact expressions for both the pointer spatial probability distribution profiles and the mean values of arbitrary pointer observables associated with PS and PPS projection operator measurements that are valid for any strength of the interaction which couples a measurement pointer to the quantum system. These profiles and mean values are compared in order to identify the effects of post-selection upon projector measurement pointers. As a special case, these mean value results are applied to the weak measurement regime - yielding PS and PPS mean value expressions which are valid for any operator (projector or non-projector). Measurement sensitivities which are useful for estimating weak measurement accuracies for PS and PPS systems are also obtained and discussed.

quant-ph↗

arXiv2006

Tripartite loss model for Mach-Zehnder interferometers with application to phase sensitivity : Complete expressions for measurement operator mean values, variances, and cross correlations

A generalized analytical tripartite loss model is posited for Mach-Zehnder interferometer (MZI) phase sensitivity which is valid for both arbitrary photon input states and arbitrary system environmental states. This model is shown to subsume the phase sensitivity models for the lossless MZI and the ground state MZI. It can be employed to develop specialized models useful for estimating phase sensitivities, as well as for performing associated design trade-off analyses, for MZIs which operate in environmental regimes that are not contained within the ground state MZI's envelope of validity. As a simple illustration of its utility, the model is used to develop phase sensitivity expessions for an MZI with "excited" internal arms and an MZI with "excited" output channels. These expressions yield a conditional relationship between the expected number of photons entering an MZI and its efficiency parameters which-when satisfied-predicts an enhanced phase sensitivity for the MZI with "excited" output channels relative to that for the MZI with "excited" internal arms.

physics.ins-det↗