Abstract A study of non-Gaussian operations in a single/two-mode quantum state is of great importance because of the enhancement of non-classicality. Experimental evidence of the generation of a Pair Coherent State (PCS) and the feasibility of non-Gaussian operations using beam splitters and nonlinear crystals motivated us to study non-Gaussian PCS. Recently, we studied various nonclassicality criteria in a particular case of non-Gaussian PCS. Here, we explore different combinations of photon addition/subtraction in either mode of PCS. For example, we studied photon addition and subtraction (PAS), photon subtraction and addition (PSA), photon addition and addition (PAA), and photon subtraction and subtraction (PSS) in two modes of PCS. We present a quantitative measure of nonclassicality in the form of inequality known as Klyshko’s criterion for the different combinations of PCS to show the nonclassical behavior of the states quantitatively. Here, we also present the corresponding coefficients (C n ) for each different case of PCS and analyze the effect of photon addition and subtraction on the photon-number distribution, linear entropy, single-photon source efficiency (SPS), Q-function, and fidelity for quantum teleportation. We illustrate our results through numerical simulations and compare them with standard PCS. We observe the changes induced by different combinations in PCS, leading to enhanced nonclassicality. Our results show that the PSA and PSS configurations demonstrate the strongest Klyshko nonclassicality, while the PAA state exhibits maximal entanglement via linear entropy and strong efficiency. In particular, the PAS state achieves the highest teleportation fidelity (F > 0.88). These findings establish photon-added/subtracted PCS as practical and tunable resources for quantum communication and metrology tasks.
Abstract A study of non-Gaussian operations in a single/two-mode quantum state is of great importance because of the enhancement of non-classicality. Experimental evidence of the generation of a Pair Coherent State (PCS) and the feasibility of non-Gaussian operations using beam splitters and nonlinear crystals motivated us to study non-Gaussian PCS. Recently, we studied various nonclassicality criteria in a particular case of non-Gaussian PCS. Here, we explore different combinations of photon addition/subtraction in either mode of PCS. For example, we studied photon addition and subtraction (PAS), photon subtraction and addition (PSA), photon addition and addition (PAA), and photon subtraction and subtraction (PSS) in two modes of PCS. We present a quantitative measure of nonclassicality in the form of inequality known as Klyshko’s criterion for the different combinations of PCS to show the nonclassical behavior of the states quantitatively. Here, we also present the corresponding coefficients (C n ) for each different case of PCS and analyze the effect of photon addition and subtraction on the photon-number distribution, linear entropy, single-photon source efficiency (SPS), Q-function, and fidelity for quantum teleportation. We illustrate our results through numerical simulations and compare them with standard PCS. We observe the changes induced by different combinations in PCS, leading to enhanced nonclassicality. Our results show that the PSA and PSS configurations demonstrate the strongest Klyshko nonclassicality, while the PAA state exhibits maximal entanglement via linear entropy and strong efficiency. In particular, the PAS state achieves the highest teleportation fidelity (F > 0.88). These findings establish photon-added/subtracted PCS as practical and tunable resources for quantum communication and metrology tasks.
Abstract Recently, experimental demonstrations of the pair coherent state of microwave photons in superconducting cavities (PRX QUANTUM 4, 020319, 2023) and experimental results of photon addition and subtraction in multimode entangled optical fields (Physical Review Research 6, 013065, 2024) were reported. Motivated by these results, we study the nonclassical properties of non-Gaussian photon-added and subtracted pair coherent states. More specifically, we explore quantum polarization, quadrature squeezing, sum and difference squeezing, Shchukin-Vogel Entanglement, EPR entanglement correlation, two-mode higher-order antibunching, and quasiprobability distribution function (Q function). The effect of photon addition and subtraction is visible in this study with different parameters, as we compared our results with the original pair coherent state (PCS). This study provides a deeper understanding of the quantum behavior of modified pair coherent states, with potential implications for advancements in quantum optics and information processing.
Abstract We introduce a new state called photon-added-and-subtracted two modes pair coherent state (PAASTMPCS) by simultaneously adding and subtracting photons to the different modes of a pair coherent state. Its nonclassical and non-Gaussian properties are strengthened via the negative values of its Wigner function as the numbers of adding and subtracting photons are increased. It indicates that the PAASTMPCS is an entangled state. When increasing the numbers of photon-added and photon-subtracted to a pair coherent state, the degree of entanglement in the PAASTMPCS is enhanced compared with the original pair coherent state. By using a PAASTMPCS as a non-Gaussian entangled resource, the quantum teleportation processes are studied in detail. It is shown that the number sum and phase difference measurements protocol is more appropriate than the orthogonal quadrature components measurements protocol in the quantum teleportation process of a coherent state.
Abstract Pair coherent states (PCSs) as a kind of two-mode non-Gaussian and nonclassical states were introduced and studied. Some nonclassical characteristics of them such as two-mode sum-squeezing, two-mode antibunching, and entanglement have been well investigated. In this paper, we focus on studying the superposition of photon addition and subtraction to the PCSs called superposition of photon-added and photon-subtracted pair coherent states (SPAPSPCSs). Our main purpose is to show that the non-Gaussian feature and all the above-mentioned nonclassical properties of the SPAPSPCSs can be enhanced compared with the photon-added-and-subtracted two modes pair coherent states (PAASTMPCSs) and the original PCSs. In general, we demonstrate that the SPAPSPCSs have more enhanced non-Gaussian character and nonclassical properties than the PCSs and the PAASTMPCSs by examining the negativity of the Wigner function. Specifically, we indicate that both the SPAPSPCSs and the PAASTMPCSs can exist in two-mode sum-squeezing while the original PCSs (without photon-addition and photon-subtraction) cannot, and the degree of squeezing is stronger in the SPAPSPCSs than in the PAASTMPCSs. The obtained results also indicate that the superposition of photon addition and subtraction of the SPAPSPCSs plays a vital role in enhancing the two-mode antibunching property and the entanglement degree compared with the PCSs and the PAASTMPCSs.
Abstract Recently, it was reported that Quantum optical catalysis is a method capable of transforming Gaussian/non-Gaussian input states into non-Gaussian states without changing the photon number of the original state in Int. J. Theor. Phys. 62, 41 (2023). They have shown enhancement in non-Gaussianity after applying photon catalysis over a pair coherent state. Here in this work, we investigate the multi photon-catalysis phenomenon in a photon-added (in one mode) and photon-subtracted (in another mode) pair coherent state. The entanglement and non-Gaussian properties of the generated state multiphoton catalytic photon-added-and-subtracted pair coherent state (MC-PASPCS) are analyzed using linear entropy, logarithmic negativity, and a quantitative measure of non-Gaussianity. Furthermore, the usefulness of the proposed state as a quantum resource is examined through continuous-variable quantum teleportation fidelity. Our results show that the combined effect of photon addition/subtraction and multiphoton catalysis significantly enhances entanglement, non-Gaussianity, and teleportation performance in suitable parameter regimes compared with the original pair coherent state. The findings demonstrate that said states provides a controllable platform for generating highly non-Gaussian entangled states with potential applications in quantum information processing.
Abstract Recently, non-Gaussian operations on pair coherent states have been shown to significantly enhance various nonclassical properties, including linear entropy, Q -function, and fidelity. In the present work, we perform a systematic investigation of higher-order correlation functions (CFs) for different classes of non-Gaussian pair coherent states (NGPCSs). Such higher-order correlations are experimentally accessible and provide direct signatures of fundamental quantum phenomena, including photon antibunching, photon blockade (PB), the possibility of single photon source, and multiphoton suppression, which are crucial for quantum information and communication applications. By evaluating the normalized second-, third-, and fourth-order CFs, we analyze the emergence of higher-order antibunching and the possibility of the PB phenomenon as functions of the state parameter | ξ | and photon-operation parameters. All considered states satisfy the hierarchy g ( 4 ) ( 0 ) < g ( 3 ) ( 0 ) < g ( 2 ) ( 0 ) < 1 , and, for suitable parameter regimes, g ( n ) ( 0 ) → 0 , indicating strong suppression of multiphoton excitations and PB. A systematic analysis is provided for different classes of NGPCSs, e.g. photon-added-subtracted, photon-subtracted-added, photon-added-added, and photon-subtracted in two modes of pair coherent states. These observations are further supported by some statistical ratios of CFs, e.g. quality factors, multiphoton suppression ratios, and score. Our results establish non-Gaussian photon engineering as a powerful approach for tailoring multiphoton statistics and realizing controllable few-photon light sources. The engineered pair coherent states studied here thus provide promising platforms for applications in quantum communication, quantum information processing, and photonic quantum technologies.
Abstract The family of two-mode non-Gaussian entangled states, including the pair coherent states (PCSs) and their genealogies, has been extensively investigated regarding their quantum properties and their practical applications in quantum information. Specifically, certain states, such as the multiphoton catalytic pair coherent states (MCPCSs), have been newly introduced under specific experimental conditions. For a more feasible approach, in this paper, we introduce novel nonclassical states obtained by subtracting photons through conditional measurements using beam splitters applied to the two modes of the PCSs. These states are called pair coherent states with conditional measurements (PCSCMs). Our purpose is to demonstrate that the quantum features, such as entanglement, Einstein–Podolsky–Rosen (EPR) correlation, EPR steering, and the average fidelity in teleportation can be enhanced in comparison with both the original PCSs and the MCPCSs. In specific cases, several characteristics are observed in PCSCMs but not inspected in both PCSs and MCPCSs. In our findings, we prove that the quantum characteristics within the PCSCMs are influenced not just by the number of detected photons, denoted by variables k and l, but also by the discrepancy in photon numbers, especially by the difference of k − l.