New approach for normalization and photon-number distributions of photon-added (-subtracted) squeezed thermal states

Using the thermal field dynamics theory to convert the thermal state to a "pure" state in doubled Fock space, it is found that the average value of e^{fa^{{\dag}}a} under squeezed thermal state (STS) is just the generating function of Legendre polynomials, a remarkable result. Based on this point, the normalization and photon-number distributions of m-photon added (or subtracted) STS are conviently obtained as the Legendre polynomials. This new concise method can be expanded to the entangled case.Comment: 5 pages, no figur

Quantum steering for two-mode states with Continuous-variable in laser channel

The Einstein-Podolsky-Rosen steering is an important resource for one-sided device independent quantum information processing. This steering property will be destroyed during the interaction between quantum system and environment for some practical applications. In this paper, we use the representation of characteristic function for probability to examine the quantum steering of two-mode states with continuous-variable in laser channel, where both the gain factor and the loss effect are considered. Firstly, we analyse the steering time of two-mode squeezed vacuum state under one-mode and two-mode laser channel respectively. We find the gain process will introduce additional noise to the two-mode squeezed vacuum state such that the steerable time is reduced. Secondly, by quantising quantum Einstein-Podolsky-Rosen steering, it shows that two-side loss presents a smaller steerability than one-side loss although they share the same two-way steerable time. In addition, we find the more gained party can steer the others state, while the other party cannot steer the gained party in a certain threshold value. In this sense, it seems that the gain effect in one party is equivalent to the loss effect in the others party. Our results pave way for the distillation of Einstein-Podolsky-Rosen steering and the quantum information processing in practical quantum channels

Phase estimation via number-conserving operation inside the SU(1,1) interferometer

Utilizing nonlinear elements, SU(1,1) interferometers demonstrate superior phase sensitivity compared to passive interferometers. However, the precision is significantly impacted by photon losses, particularly internal losses. We propose a theoretical scheme to improve the precision of phase measurement using homodyne detection by implementing number-conserving operations (PA-then-PS and PS-then-PA) within the SU(1,1) interferometer, with the coherent state and the vacuum state as the input states. We analyze the effects of number-conserving operations on the phase sensitivity, the quantum Fisher information, and the quantum Cramer-Rao bound under both ideal and photon losses scenarios. Our findings reveal that the internal non-Gaussian operations can enhance the phase sensitivity and the quantum Fisher information, and effectively improve the robustness of the SU(1,1) interferometer against internal photon losses. Notably, the PS-then-PA scheme exhibits superior improvement in both ideal and photon losses cases in terms of phase sensitivity. Moreover, in the ideal case, PA-then-PS scheme slightly outperforms PS-then-PA scheme in terms of the quantum Fisher information and the Quantum Cramer-Rao. However, in the presence of photon losses, PS-then-PA scheme demonstrates a greater advantage.Comment: arXiv admin note: text overlap with arXiv:2311.1461

Quantum multiparameter estimation with multi-mode photon catalysis entangled squeezed state

We propose a method to generate the multi-mode entangled catalysis squeezed vacuum states (MECSVS) by embedding the cross-Kerr nonlinear medium into the Mach-Zehnder interferometer. This method realizes the exchange of quantum states between different modes based on Fredkin gate. In addition, we study the MECSVS as the probe state of multi-arm optical interferometer to realize multi-phase simultaneous estimation. The results show that the quantum Cramer-Rao bound (QCRB) of phase estimation can be improved by increasing the number of catalytic photons or decreasing the transmissivity of the optical beam splitter using for photon catalysis. In addition, we also show that even if there is photon loss, the QCRB of our photon catalysis scheme is lower than that of the ideal entangled squeezed vacuum states (ESVS), which shows that by performing the photon catalytic operation is more robust against photon loss than that without the catalytic operation. The results here can find important applications in quantum metrology for multiparatmeter estimation