From the photon-added one-photon nonlinear coherent states $a^{\dagger m}|α,f>$, we introduce a new type of nonlinear coherent states with negative values of $m.$ The nonlinear coherent states corresponding to the positive and negative values of $m$ are shown to be the result of nonunitarily deforming the number states $|m>$ and $|0>$, respectively. As an example, we study the sub-Poissonian statistics and squeezing effects of the photon-added geometric states with negative values of $m$ in detail. Finally we investigate the photon-added two-photon nonlinear coherent states and find that they are still the two-photon nonlinear coherent states with certain nonlinear functions.
In this paper we investigate the security of continuous variable BB84 quantum key distribution protocol using single photon added then subtracted squeezed coherent state SPASSCS. It's found that the SPASSCS is a non-Gaussian and nonclassical state. Its non-Gaussianity and non-classicality are exhibited via the Wigner function. It's shown that the proposed state is generally robust against the eavesdropping strategies, such as intercept-resend attack and superior channel attack. Further, a comparative study has proved the strong efficiency of the proposed state over coherent state, squeezed coh…
In this paper, we construct the $m$-photon-added and $m$-photon-subtracted coherent states on a sphere. These states are shown to satisfy the usual conditions of continuity in the label, normalizability and the resolution of identity. The preparation of the constructed states, as the states of radiation field is considered. We examine and analyze the nonclassical properties of these states, including the photon mean number, Mandel parameter and quadrature squeezing. We find that these states are sub-Poissonian in nature, whereas the degree of squeezing is reduced (enhanced) by increasing $m$ f…
In this paper, We investigate three-mode photon-added Greenberger-Horne-Zeilinger (GHZ) entangled coherent states by repeatedly operating the photon-added operator on the GHZ entangled coherent states. The product of two Laguerre polynomials is demonstrated to be connected to the normalizing constant. The influence of the operation on the non-classical and non-Gaussian behavior of the GHZ entangled coherent states is investigated. Sub-Poissonian statistics, such as Mandel's parameter and the negativity of the Wigner function, show that non-classical properties can enhance GHZ entangled coheren…
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 von Neumann type measurement which is characterized by post-selection and weak value can significantly change the squeezing feature of single-photon-added coherent state. It is also found that the postselected measurement can increase the nonclassicality of the original state in strong measurement regimes. It is anticipated that this work could may provide an alternate and eff…
We theoretically investigate the phase sensitivity with parity detection on a Mach-Zehnder interferometer with a coherent state combined with a photon-added squeezed vacuum state. When the phase shift approaches zero, the squeezed vacuum state is indeed the optimal state within a constraint on the average number of photons. However, when the phase shift to be estimated slightly deviates from zero, the optimal state is neither the squeezed vacuum state nor the photon-subtracted squeezed vacuum state, but the photon-added squeezed vacuum state when they carry many photons. Finally, we show that …
In this work, the measurement transition as well as precision measurement advantages of single-photon-added coherent state after postselected von Neumann measurement are investigated. We noticed that the weak-to-strong measurement transition characterized by the shifts of pointer's position and momentum variables occurred in continuously by controlling a dimensionless parameter associated with system-pointer coupling. We calculate the ratio between the signal-to-noise ratio of nonpostselected and postselected measurements, and the latter is used to find the quantum Fisher information. We found…
The effects of von Neumann postselected measurement on nonclassicality of single-photon-added coherent state (SPACS) are studied. Explicit expressions and analytical results for various field properties of SPACS such as the photon number distribution, the Mandel Q_{m} factor and the squeezing parameter of field quadrature after postselected von Neumann measurement are investigated. The results showed that the nonclassicality of SPACS after measurement changed dramatically than initial state. The measurement let SPACS possess more strong sub-Poissonian photon statistics in some definite couplin…
The addition of a photon into the same mode as a coherent state produces a nonclassical state that has interesting features, including quadrature squeezing and a sub-Poissonian photon-number distribution. The squeezed nature of photon-added coherent (PAC) states potentially offers an advantage in quantum sensing applications. Previous theoretical works have employed a single-mode treatment of PAC states. Here, we use a continuous-mode approach that allows us to model PAC state pulses. We study the properties of a single-photon and coherent state wavepacket superimposed with variable temporal a…
The subtraction or addition of a prescribed number of photons to a field mode does not, in general, simply shift the probability distribution by the number of subtracted or added photons. Subtraction of a photon from an initial coherent state, for example, leaves the photon statistics unchanged and the same process applied to an initial thermal state increases the mean photon number. We present a detailed analysis of the effects of the initial photon statistics on those of the state from which the photons have been subtracted or to which they have been added. Our approach is based on two close…
We study a quantum system of coupled oscillators subject to a periodic excitation of its parameters. Using Floquet-Lyapunov theory we derive the linear integrals of motion of the system and relate their covariance matrix to that for the canonical observables. The operator integrals allows us to construct the intelligent (minimum uncertainty) states of the system and the corresponding photon-added states. We found explicit expressions for the wavefunction, Wigner function and covariance matrix of these states.
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 …
Boson sampling with displaced single-photon Fock states versus single-photon-added coherent states---The quantum-classical divide and computational-complexity transitions in linear optics
Nonclassical properties of photon added and subtracted displaced Fock states have been studied using various witnesses of lower- and higher-order nonclassicality. Compact analytic expressions are obtained for the nonclassicality witnesses. Using those expressions, it is established that these states and the states that can be obtained as their limiting cases (except coherent states) are highly nonclassical as they show the existence of lower- and higher-order antibunching and sub-Poissonian photon statistics, in addition to the nonclassical features revealed through the Mandel $Q_M$ parameter,…
The concept of photon added two-mode Schrödinger cat states in which both modes are independent is introduced, their non-classical properties and entanglement are studied. The introduced states emerge as the eigenstates of $f_1f_2a_1a_2$, where $f_1, f_2$ are nonlinear functions of the number operator and $a_1, a_2$ are annihilation operators. We study the evolution of these states under the canonical transformation using the parity operator for the case of standard coherent states of the harmonic oscillator. The non-classical properties of these states are evaluated especially by considering …
In this paper, a continuous variable B92 quantum key distribution (QKD) protocol is proposed using single photon added and subtracted coherent states, which are prepared by adding and subsequently subtracting a single photon on a coherent state. It is established that in contrast to the traditional discrete variable B92 protocol, this protocol for QKD is intrinsically robust against the unambiguous state discrimination attack, which circumvents the requirement for any uninformative states or entanglement used in corresponding discrete variable case as a remedy for this attack. Further, it is s…
Enhanced Phase Estimation via Photon-Added Two-Mode Squeezed States and Kerr Nonlinearity
Jiangxi Normal University（江西师范大学）；Jiangxi Normal University Science and Technology College（江西师范大学科学技术学院）；Institute for Military-Civilian Integration of Jiangxi Province（江西省军民融合研究院）
Higher-order nonclassical properties of r photon added and t photon subtracted qudit states (referred to as rPAQS and tPSQS, respectively) are investigated here to answer: How addition and subtraction of photon can be used engineer higher-order nonclassical properties of qudit states? To obtain the answer higher-order moment of relevant bosonic field operators are first obtained for rPAQS and tPSQS, and subsequently the same is used to study the higher-order nonclassical properties of the corresponding states. A few witnesses of higher-order nonclassicality (e.g. Higher-Order Antibunching, Hig…
