Manipulating light by adding and subtracting individual photons is a powerful approach with a principal drawback: the operations are fundamentally probabilistic and the probability is often small. This limits not only the fundamental scalability but also the number of operations that can be applied in realistic experimental settings. We propose and analyze a loop-based technique which can significantly increase the probability of success while preserving the quality of the photon subtraction. We show the improvement both in single mode preparation and manipulation of non-Gaussian states with negative Wigner functions and in two-mode entanglement distillation protocol with Gaussian states of light.
Manipulating light by adding and subtracting individual photons is a powerful approach with a principal drawback: the operations are fundamentally probabilistic and the probability is often small. This limits not only the fundamental scalability but also the number of operations that can be applied in realistic experimental settings. We propose and analyze a loop-based technique which can significantly increase the probability of success while preserving the quality of the photon subtraction. We show the improvement both in single mode preparation and manipulation of non-Gaussian states with negative Wigner functions and in two-mode entanglement distillation protocol with Gaussian states of light.
Photon subtraction (PS), due to its feasibility in physical implementation, has been widely utilized in Gaussian entanglement distillation. However, in this paper, we will show that photon addition (PA) can be employed to provide an additional enhancement in both the quality of distilled entanglement and the success probability if the input state is a weak two-mode squeezed vacuum state. Moreover, compared with biside PS, the distillation probability gains a $O(\frac{1}{{\ensuremath{\lambda}}^{2}})$ improvement, which increases rapidly when $\ensuremath{\lambda}\ensuremath{\ll}1$. Our PA-based scheme is obtained first by single-photon injection and later by vacuum state projection. The performance of PA in the presence of both an approximated single photon and amplitude-damping noise has been analyzed. Our result sheds more light on the indispensable non-Gaussian ingredients in Gaussian-state distillation and could be of great use in developing more efficient distillation schemes. Finally, the sensitivity of the PA scheme to inefficient photon detection has also been investigated.
The non-Gaussian operations effected by adding or subtracting a photon on entangled optical beams emerging from a parametric down-conversion process have been suggested to enhance entanglement. Heralded photon addition or subtraction is, as a matter of fact, at the heart of continuous-variable entanglement distillation. The use of such processes has recently been experimentally demonstrated in the context of the generation of optical coherent-state superpositions or the verification of canonical commutation relations. Here, we carry out a systematic study of the effect of local photon additions and subtractions on a two-mode squeezed vacuum state, showing that the entanglement generally increases with the number of such operations. This is analytically proven when additions or subtractions are restricted to one mode only, while we observe that the highest entanglement is achieved when these operations are equally shared between the two modes. We also note that adding photons typically provides a stronger entanglement enhancement than subtracting photons, while photon subtraction performs better in terms of energy efficiency. Furthermore, we analyze the interplay between entanglement and non-Gaussianity, showing that it is more subtle than previously expected.
Single-photon-level non-Gaussian operations—photon addition, photon subtraction, and their coherent superposition—are powerful tools with which to increase entanglement in continuous-variable optical states. Although such operations are typically not deterministic, there may be other advantages such as noiseless manipulation. Therefore, to fully account for the efficacy of a particular non-Gaussian operation in a practical scenario, we develop figures of merit which trade off the advantages of such protocols against their success probability. Specifically, we define 'entanglement enhancement rate' as the increase in entanglement per trial of a generic non-Gaussian operation on a two-mode squeezed vacuum (TMSV) state. We consider states generated by photon-subtraction, photon-addition and a coherent superposition of subtraction and addition. We compare each strategy when applied to one or both modes of a TMSV state, and also in the presence of channel losses prior to the operation. In many cases, additional properties are analytically calculable, including excess noise arising from the operation and the fidelity of the resulting states to particular Gaussian and non-Gaussian states. Finally, by incorporating loss, we derive optimal interaction parameters for each non-Gaussian operation which maximize the effectiveness of the particular protocol under investigation.
Photon subtraction (PS) can enhance entanglement, which, for pure states, induces a decrease in the purity of reduced states. In contrast, by analyzing the purities of Gaussian states before and after subtracting or adding a single photon, we prove that the purity of a Gaussian state can be increased by less than 20%. On the one hand, it reveals that PS and photon addition (PA) can reduce entanglement, and on the other hand, it shows that PS or PA can achieve a limited amount of Gaussian state purification. Through the analysis of several examples, we demonstrate the inherent mechanism and applicable scope of photon-subtraction-based purification. We further compare the performance between PS and PA for purifying single-mode Gaussian states, and analyze their capabilities in generating Wigner negativity within purification regimes. In a multimode system, we find that PS can simultaneously increase entanglement and purify some of the reduced states. These findings demonstrate the new application potential of PS and PA, specifically their capability to directly suppress Gaussian noise.
Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.
Abstract The quantum state probabilistic amplifier is a valuable tool for significantly amplifying quantum states without introducing additional noise. However, its inherently probabilistic nature often results in a low success rate, limiting scalability and practical deployment. In this paper, we propose a loop-based amplification scheme that integrates thermal noise addition with photon subtraction. This approach notably increases the success probability P and the fidelity of the amplified quantum state. Although a trade-off exists between P and the amplification gain, our scheme achieves favorable gain across all scenarios. Furthermore, the phase variance of the output state is minimized through optimization in each case. Analytical results demonstrate that configurations with higher maximum loop iterations preserve more Gaussian characteristics in the output state compared to direct photon subtraction. Finally, we examine the performance under non-ideal conditions and suggest potential avenues for further enhancement.