Measuring average of non-Hermitian operator with weak value in a Mach-Zehnder interferometer

Abstract

Quantum theory allows direct measurement of the average of a non-Hermitian operator using the weak value of the positive semidefinite part of the non-Hermitian operator. Here, we experimentally demonstrate the measurement of weak value and average of non-Hermitian operators by a novel interferometric technique. Our scheme is unique as we can directly obtain the weak value from the interference visibility and the phase shift in a Mach Zehnder interferometer without using any weak measurement or post selection. Both the experiments discussed here were performed with laser sources, but the results would be the same with average statistics of single photon experiments. Thus, the present experiment opens up the novel possibility of measuring weak value and the average value of non-Hermitian operator without weak interaction and post-selection, which can have several technological applications.

Local PT-symmetric evolutions on separable states and violation of no-signaling

“…Although the interpretation of P T -symmetric quantum mechanics remain contentious, it has been used in several areas [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Experiments related to such evolutions have been reported in .…”

Isolating noise and amplifying signal with quantum Cheshire cat

“…Weak values can be used in the direct measurement of a photon wavefunction [14,16], to measure the spin Hall effect [13], in quantum state tomography [17,18], in the geometric description of quantum states [19] and state visualization [20]. It also finds application in quantum thermometry [21], and measuring the expectation value of non-Hermitian operators [22,23]. Weak values have been shown to be acquire complex values [24], and weak values play important roles in the two-state vector formalism [25], a physical understanding of superoscillations [26], and in separating a quantum property from its system [27].…”

Can two quantum Cheshire cats exchange grins?

“…[19]. Among the myriad applications of weak measurements are observation of the spin Hall effect [25], resolving quantum paradoxes [26,28], quantum state visualization [27], quantum state tomography [28,29], direct measurement of wavefunction [30,31], probing contextuality [32] , measuring the expectation value of non-Hermitian operators [33,34] and quantum precision thermometry [35].…”