Manifestation of pointer-state correlations in complex weak values of quantum observables

Abstract

In the weak measurement (WM) scenario involving weak interaction and postselection by projective measurement, the empirical significance of weak values is manifested in terms of shifts in the measurement pointer's mean position and mean momentum. In this context, a general quantitative treatment is presented in this paper by taking into account the hitherto unexplored effect of correlations among the pointer degrees of freedom which pertain to an arbitrary multidimensional preselected pointer state. This leads to an extension of the earlier results, showing that, for complex weak values, the correlations among different pointer degrees of freedom can crucially affect the way the imaginary parts of the weak values are related to the observed shifts of the mean pointer position and momentum. The particular relevance of this analysis is discussed in the case of sequential weak interactions followed by a projective measurement enabling postselection (called sequential WM) which, in the special case, reduces to the usual WM scheme (involving a single weak interaction and postseletion) modified by the effect of pointer state correlations.

Quantification of concurrence via weak measurement

“…To extract the real and imaginary parts of the weak value two complementary pointer observables are usually used [19,[42][43][44], that is, two separate measurements have to be set up. Remarkably however, it is also possible to quantify both of these components simultaneously by using so-called Laguerre-Gaussian (LG) modes [29,45,46] as the initial pointer state due to the initial correlations [47] related to these states.…”

Joint weak value for all order coupling using continuous variable and qubit probe

“…Contrary to the strong measurement, in WM scenario, the average value of an observable (coined as weak value) can yield results beyond the eigenvalue spectrum of the measured observable. In last decade, a flurry of works have been reported, in which the WM and its implications have been extensively studied, both theoretically [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and experimentally [21][22][23][24][25][26][27][28][29][30][31][32][33]. In one hand, WM provides new insights into conceptual quantum paradoxes [3-5, 8, 20, 31] and on the other hand, it provides several practical applications, such as, identifying tiny spin Hall effect [24], detecting very small transverse beam deflections [26], measuring average quantum trajectories for photons [28], improving signal-to-noise ratio for determination of small phase through interferometry [27] and protecting a quantum state [32].…”

Quantum information transfer using weak measurements and any non-product resource state

“…This, in itself, is a challenge because the number of measurements for specific sets of observables to determine the respective probabilities and phases scales exponentially with the dimensionality of the state at hand. Weak values proposed in Aharonov, Albert and Vaid-man's seminal paper [20] are complex entities which appear as a shift in the expectation value of a pointer observable when a weak von Neumann interaction between the system and pointer states is followed by post selection on the system state [21,22]. Although weak measurements were initially introduced in the context of continuous variable Gaussian pointer states, the paradigm has since been theoretically and experimentally established for qubit pointer states [23][24][25], entangled pointer states [26,27] and most generally to arbitrary pointer states [28,29].…”