Determination of weak values of quantum operators using only strong measurements

Abstract

Weak values have been shown to be helpful especially when considering them as the outcomes of weak measurements. In this paper we show that in principle, the real and imaginary parts of the weak value of any operator may be elucidated from expectation values of suitably defined density, flux and hermitian commutator operators. Expectation values are the outcomes of strong (projective) measurements implying that weak values are general properties of operators in association with pre-and post-selection and they need not be preferentially associated with weak measurements. They should be considered as an important measurable property which provides added information as compared with the "standard" diagonal expectation value of an operator. As a first specific example we consider the determination of the real and imaginary parts of the weak value of the momentum operator employing projective time of flight experiments. Then the results are analyzed from the point of view of Bohmian mechanics. Finally we consider recent neutron interferometry experiments used to determine the weak values of the neutron spin.

Strengthening weak measurements of qubit out-of-time-order correlators

“…Typically, determining complex quantities like operator correlators requires the use of weak measurements (φ ≈ 0) to prevent state disturbance [36,37]. In special cases, however, relevant information may still be contained in the collected measurement statistics in spite of any state disturbance [39,40,65]. In the Appendix, we show that this is the case for qubits, where the following remarkable identities hold for any coupling-strength angle φ and thus enable the improved correlator measurement protocols that are detailed in the following sections: (a) the anticommutator identities…”

Operational formulation of weak values without probe systems

“…While our measurement method is an alternative to weak measurement to obtain weak values, some other weak-value measurement methods have been proposed so far [41][42][43][44][45][46][47][48]. Here, we mention these weak-value measurement methods other than weak measurement and compare the advantages of each method and our measurement method.…”

“…Some of the methods previously reported [41][42][43][44][45][46] employ indirect (von Neumann) measurement via strong system-probe interactions. The others [47,48] are di-rect measurement methods, in which weak values are obtained from a combination of several projective (strong) measurements of pre-selected systems. These methods have an advantage over weak measurement in terms of efficiency because of the strong interactions or measurements, while the pre-and post-selected systems are strongly disturbed.…”

A framework for measuring weak values without weak interactions and its diagrammatic representation

“…In these previous studies, weak values have been obtained by weak measurements, which involve weak system-probe interactions. However, this is not the only possible method for their determination, and several alternative weak value measurement techniques that do not involve weak system-probe interactions have been recently developed, including those using strong system-probe interactions [26][27][28][29], modular values [30], quantum control interactions [31,32], an enlarged Hilbert space [33], coupling-deformed pointer observables [34], and a combination of several strong measurements of the system [35]. It should be noted here that most of them [26][27][28][29][30][31][32][33] and some weak measurement experiments [2][3][4][5][6][7][8][9][10][16][17][18][19][20][21][22][23][24] use qubit systems as the probes.…”