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arXiv:2110.13724

Quantum state engineering using weak measurement

Qiang Hu, Taximaiti Yusufu, Yusuf Turek

Published Oct 26, 2021• 0 citations
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Abstract

State preparation via postselected weak measurement in three wave mixing process is studied. Assuming the signal input mode prepared in a vacuum state, coherent state or squeezed vacuum state, separately, while the idler input prepared in weak coherent state and passing the medium characterized by the second-order nonlinear susceptibility. It is shown that when the single photon is detected at one of the output channels of idler beam's path, the signal output channel is prepared in single-photon Fock state, single-photon-added coherent state or single-photon-added squeezed vacuum state with very high fidelity, depending upon the input signal states and related controllable parameters. The properties including squeezing, signal amplification, second order correlation and Wigner functions of the weak measurement based output states are also investigated. Our scheme promising to provide alternate new effective method for producing useful nonclassical states in quantum information processing.

DOI
10.48550/arxiv.2110.13724

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State preparation via postselected weak measurement in three wave mixing process is studied. Assuming the signal input mode prepared in a vacuum state, coherent state or squeezed vacuum state, separately, while the idler input prepared in weak coherent state and passing the medium characterized by the second-order nonlinear susceptibility. It is shown that when the single photon is detected at one of the output channels of idler beam's path, the signal output channel is prepared in single-photon Fock state, single-photon-added coherent state or single-photon-added squeezed vacuum state with very high fidelity, depending upon the input signal states and related controllable parameters. The properties including squeezing, signal amplification, second order correlation and Wigner functions of the weak measurement based output states are also investigated. Our scheme promising to provide alternate new effective method for producing useful nonclassical states in quantum information processing.
State preparation via postselected weak measurements in a three-wave mixing process is studied. We assume the signal input mode is prepared in a vacuum state, coherent state, or squeezed vacuum state, while the idler input is prepared in a weak coherent state and passes the medium characterized by the second-order nonlinear susceptibility. It is shown that when the single photon is detected at one of the output channels of the idler beam's path, the signal output channel is prepared in a single-photon Fock state, single-photon-added coherent state, or single-photon-added squeezed vacuum state with very high fidelity, depending upon the input signal states and related controllable parameters. The properties of squeezing, signal amplification, second-order correlation, and the Wigner functions of the weak-measurement-based output states are also investigated. Our scheme promises to provide an alternate effective method for producing useful nonclassical states in quantum information processing.
Abstract We introduce a protocol for generating a broad class of non-Gaussian (nG) quantum states via postselected weak measurement techniques. The scheme involves injecting an arbitrary quantum state and a single photon into the signal and idler ports, respectively, of an interference setup that incorporates a third-order nonlinear medium. A nG state is conditionally produced at the signal output, heralded by the detection of a single photon in one of the idler output channels. The protocol exploits a weak cross-Kerr interaction and effective single-photon nonlinearity enhanced by the weak-value amplification. We show that by tuning the weak value of the photon number operator in the idler mode within experimentally feasible parameters, a wide variety of nG states can be generated with high fidelity. As specific examples, we demonstrate the generation of photon-added states, displaced and squeezed number states, and a continuum of intermediate nG states using coherent and squeezed vacuum inputs, respectively. Furthermore, we show that the protocol enables the enhancement of non-Gaussianity and the enlargement of Schrödinger cat (SC) states when ideal SC states are used as the input. Our results provide an alternative route for the conditional generation of tunable nG states, with potential applications in quantum information processing. This approach may also open new avenues for quantum state engineering using postselected weak measurements.
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.
In this paper, ordinary and amplitude-squared squeezing as well as Wigner functions of single-photon-added coherent state after postselected von Neumann measurements are investigated. The analytical results show that the weak measurement procedure, which is characterized by postselection and weak value, can significantly change the principal squeezing feature of the single-photon-added coherent state. From the analysis of the Winger function we notice that in the strong measurement regime significant interference structures manifest and the negative regions become larger than the initial pointer state. Our results indicate that after postselected von Neumann measurement the degree of nonclassicality of single-photon-added coherent state is increased. It is anticipated that this work may provide alternate and effective methods for solving the state optimization problems based on the single-photon-added coherent state pointer via a postselected von Neumann measurement technique.
We show that a continuous range of nonclassical states of light can be generated using conditional measurements on the idler mode of an optical parametric amplifier. The output state is prepared by introducing a coherent state in the signal mode of the amplifier with a single photon in the idler mode, followed by a conditional measurement of a single photon in the output idler mode. By varying the gain of the amplifier, this approach can produce a coherent state, a photon-added state, a displaced number state, or a continuous range of other nonclassical states with intermediate properties. We note that this approach can generate a photon-added state even though the postselected amplifier does not add any photons to the signal or idler modes. The ability to generate a continuous range of nonclassical states may have practical applications in quantum information processing.
Postselected von Neumann measurement characterized by postselection and weak value has been found to possess potential applications in quantum metrology and solved plenty of fundamental problems in quantum theory. As an application of this new measurement technique in quantum optics and quantum information processing, its effects on the features of single-mode radiation fields such as coherent state, squeezed vacuum state and Schrödinger cat sate are investigated by considering full-order effects of unitary evolution. The results show that the conditional probabilities of finding photons, second-order correlation functions, Qm -factors and squeezing effects of those states after the postselected measurement is significantly changed are comparable with the corresponding initial pointer states.