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Laser Physics Letters

Comparison of nonclassical properties resulting from non-Gaussian operations

Fang Jia, Wei Ye, Qi Wang, Liyun Hu, Hong-Yi Fan

Published Nov 23, 2018• 10 citations
Publisher

Abstract

Abstract Based on an asymmetrical beam splitter (ABS) and conditional measurement, we have investigated the nonclassical properties of non-Gaussian states in a unified form, including photon subtraction, photon addition and quantum catalysis, by deriving analytical expressions for photon number, squeezing effect, Mandel Q parameter and Wigner function. It is found that these properties not only depend on squeezing parameter and measurement, but also on the transmissivity of the ABS. Photon addition and quantum catalysis present a higher probability in the regions of low and high transmissivity, respectively. Although both single-photon subtraction and addition share a clear negative volume, the latter is considered to be a better choice for producing nonclassical states than the two others, if both success probability and negative volume in the small squeezing region are taken into consideration. Quantum catalysis is better in the large squeezing region and with low transmissivity. These results provide some reference for generating such non-Gaussian states.

DOI
10.1088/1612-202x/aaeda5

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Photon addition and subtraction are well-known to render Gaussian states non Gaussian. We evaluate how their optical nonclassicality is affected by the photon addition/subtraction process. It is known that photon addition always transforms a Gaussian state into a nonclassical state. We show that photon subtraction transforms classical states into classical ones and nonclassical ones into nonclassical ones. For a quantitative analysis of the resulting nonclassicality, we use a recently introduced nonclassicality witness, the quadrature coherence scale, and compute the relative nonclassicality gain of the single-photon added/subtracted Gaussian states with respect to the original Gaussian states. For arbitrary single-mode Gaussian states, we show that this relative gain can be substantial in both cases. Whereas the gain is always higher for photon-added states, it is only slightly so for a large parameter range and in particular in the limit of high squeezing, where both gains are identical. We also analyze the Wigner negative volume of the photon-added/subtracted states. Whereas photon-added Gaussian states are never Wigner positive, we show that single-mode photon-subtracted states are Wigner positive if and only if they are weakly nonclassical or classical. Our analysis relies on explicit and general expressions for the characteristic and Wigner functions of photon added/subtracted multi-mode Gaussian states that we obtain simply.
We theoretically introduce a new kind of non-Gaussian state, namely, the mixture of multiphoton added thermal states, achieved through multiphoton measurements at one output port of the beam splitter (termed multiphoton catalysis) for thermal state input. We discuss the success probabilities of detection (the normalization factors). Furthermore, we investigate their nonclassical properties based on the nonclassical depth, photon number distribution, and photocount distribution. It is shown that the multiphoton catalysis presents a better nonclassical performance by controlling the thermal parameter, catalyzed photon number and the transmissivity of the beam splitter. In addition, the nonclassicality is further examined through the partial negativity of the Wigner function, which reveals that multiphoton catalysis operation can prepare highly nonclassical quantum states. These results indicate that the preparation of a non-Gaussian states may have potential applications in the realms of quantum information processing and quantum metrology.
We theoretically analyze phase sensitivity using a parity-detection-based Mach-Zehnder interferometer (MZI) with the input states generated by performing non-Gaussian operations, viz., photon subtraction, photon addition, and photon catalysis, on a two-mode squeezed vacuum (TMSV) state. Since these non-Gaussian operations are probabilistic, it is of utmost importance to take the success probability into account. To this end, we consider a realistic model of photon subtraction, addition, and catalysis and derive a single expression of the Wigner function for photon subtracted, added, and catalyzed TMSV states. The Wigner function is used to evaluate the lower bound on the phase sensitivity via quantum Cram\'er-Rao bound and parity-detection-based phase sensitivity in the MZI. We identify the ranges of squeezing and transmissivity parameters where the non-Gaussian states provide better phase sensitivity than the TMSV state. Taking the success probability into account, it turns out that the photon addition is the most advantageous among all three non-Gaussian operations. We hope that the generalized Wigner function derived in this paper will be useful in various quantum information protocols and state characterization.
Nonclassicality of optical fields are the key resources in quantum information processing.Recently, Agarwal [New J. Phys., 13, 073008(2011)] proposed a method for engineering of a two-mode vortex state, a non-Gaussian state, by subtracting a photon from a two-mode squeezed state produced by down-converter from idler mode via a beam splitter with low reflectivity and detection of one photon by the avalanche photo diode (APD), or even better by a single-photon detector.We study the nonclassicalities of this state in terms of squeezing, antibunching, photon number correlation and distribution of photon number.In addition, we study higher-order nonclassical properties, viz., sum squeezing.We find that the non-Gaussian state shows strong nonclassical effects.
Abstract We consider distillation of squeezing in single mode squeezed vacuum state using three different probabilistic non-Gaussian operations: photon subtraction (PS), photon addition (PA) and photon catalysis (PC). To achieve this, we consider a practical model to implement these non-Gaussian operations and derive the Wigner characteristic function of the resulting non-Gaussian states. Our result shows that while PS and PC operations can distill squeezing, PA operation cannot. Furthermore, we delve into the success probabilities associated with these non-Gaussian operations and identify optimal parameters for the distillation of squeezing. Our current analysis holds significant relevance for experimental endeavors concerned with squeezing distillation.