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Physics Letters A

Quantum state nonclassicality in weak measurements in view of Bochner's criteria

E. Rafiepoor, Saeed Batebi, M. R. Bazrafkan

Published Jul 9, 2018• 3 citations
Publisher
DOI
10.1016/j.physleta.2018.07.009

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In this work we generalize the Bochner criterion addressing the characteristic function, i.e., the Fourier transform, of the Glauber-Sudarshan phase-space function. For this purpose we extend the Bochner theorem by including derivatives of the characteristic function. The resulting necessary and sufficient nonclassicality criteria unify previously known moment-based criteria with those based on the characteristic function. For applications of the generalized nonclassicality probes, we provide direct sampling formulas for balanced homodyne detection. A squeezed vacuum state is experimentally realized and characterized with our method. This complete framework---theoretical unification, sampling approach, and experimental implementation---presents an efficient toolbox to characterize quantum states of light for applications in quantum technology.
Using Bochner's theorem, we derive a necessary and sufficient hierarchy of measurable conditions in terms of the characteristic function of quasi-moments of a weakly measured observable. A quantum system that violates any of these conditions is nonclassical in weak measurements. Then, we formulate nonclassicality conditions obtained in terms of modular values that can be easily measured by performing a tomography of the final state of a qubit device. This method provides us direct access to the characteristic function as the generating function of quasi moments of weakly measured observable. In this way, We solve the problem of experimental restrictions on measuring the infinite number of weak quasi-moments.
We investigate the effects of weak value amplification on the nonclassical properties of the two-mode squeezed vacuum state. We calculate the quadrature squeezing and second-order cross-correlation functions to demonstrate the advantages of postselective weak measurement (WM). We also examine the entanglement between the two modes by evaluating various entanglement criteria, including the Cauchy-Schwartz inequality, Hillery-Zubairy correlation, and Einstein-Podolsky-Rosen correlations. Our results show that postselected von Neumann measurements significantly optimize the two-mode squeezed vacuum state. Notably, the amplification effect of weak values plays a critical role in this process. We demonstrated that in the WM regime, as the weak values increase, the nonclassical properties of the two-mode squeezed vacuum state such as entanglement and correlations between the two modes become more pronounced compared to the original state. We also propose possible implementation methods for our approach using trapped ion systems and optical platforms. Our enhanced two-mode squeezed vacuum state may have potential applications in quantum information processing scenarios, such as single-photon generation, advanced imaging techniques, quantum computation, and long-distance quantum communication.