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Optics Continuum

Quantifying quantum coherence of optical cat states in a noisy channel

Fengyi Xu, Miao Zhang, Meihong Wang, Xiaolong Su

Published May 28, 2025• 2 citations
Publisher

Abstract

Quantum coherence is one of the most fundamental features of quantum mechanics that underlines the unique characteristics of quantum technology. Optical cat state is a superposition of two coherent states and has broad applications in quantum information and quantum metrology. In the application of optical cat state, it is essential to investigate the quantum coherence of it when it interacts with the environment. In this manuscript, we present the quantum coherence of an optical cat state in a noisy channel by calculating the relative entropy in Fock basis. We show that the quantum coherence of an optical cat state is robust against loss and noise in a noisy channel. Different from quantum coherence, the negativity of the Wigner function and the fidelity of the cat state are not robust against loss and noise. Our result provides a reference for applying optical cat states in a noisy environment.

DOI
10.1364/optcon.561255

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Quantum coherence is one of the most fundamental features of quantum mechanics that underlines the unique characteristics of quantum technology. Optical cat state is a superposition of two coherent states and has broad applications in quantum information and quantum metrology. In the application of optical cat state, it is essential to investigate the quantum coherence of it when it interacts with the environment. In this manuscript, we present the quantum coherence of an optical cat state in a noisy channel by calculating the relative entropy in Fock basis. We show that the quantum coherence of an optical cat state is robust against loss and noise in a noisy channel. Different from quantum coherence, the negativity of the Wigner function and the fidelity of the cat state are not robust against loss and noise. Our result provides a reference for applying optical cat states in a noisy environment.
The optical cat state plays an essential role in quantum computation and quantum metrology. Here, we experimentally quantify quantum coherence of an optical cat state by means of relative entropy and the l 1 norm of coherence in a Fock basis based on the prepared optical cat state at the rubidium D1 line. By transmitting the optical cat state through a lossy channel, we also demonstrate the robustness of quantum coherence of the optical cat state in the presence of loss, which is different from the decoherence properties of fidelity and Wigner function negativity of the optical cat state. Our results confirm that quantum coherence of optical cat states is robust against loss and pave the way for the application of optical cat states.
Besides quantum entanglement and steering, quantum coherence has also been identified as a useful quantum resource in quantum information. It is important to investigate the evolution of quantum coherence in practical quantum channels. In this paper, we experimentally quantify the quantum coherence of a squeezed state and a Gaussian Einstein–Podolsky–Rosen (EPR) entangled state transmitted in Gaussian thermal noise channel. By reconstructing the covariance matrix of the transmitted states, quantum coherence of these Gaussian states is quantified by calculating the relative entropy. We show that quantum coherence of the squeezed state and the Gaussian EPR entangled state is robust against loss and noise in a quantum channel, which is different from the properties of squeezing and Gaussian entanglement. Our experimental results pave the way for application of Gaussian quantum coherence in lossy and noisy environments.
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The coherent superposition of quantum states is one of the characteristic features of quantum mechanics, and it is also physical resource of quantum information processing. The coherence of quantum system can not last a long time as the effect of the noise. How well has the noisy channel preserved the quantum coherence of the quantum system? Based on the relative entropy of coherence, in this paper, we discuss the coherence, entanglement and quantum correlations in the bipartite quantum system. To discuss the effect of the noise, we then give a definition of the decayed amount of the maximal quantum coherence, i.e., the decay of coherence. Then we obtain that the uncertainty relations between entanglement and the coherence with respect to the noisy models. Finally, we used the measure of the decay of coherence to discuss how well several noisy channels preserves the coherence.
As one of the most remarkable features of quantum mechanics, quantum coherence is regarded as an invaluable quantum resource in quantum information. Using the optical fiber as one of the effective quantum channels, the remote distribution of quantum coherence through fiber is essential for potential practical applications. Here we propose the remote distribution scheme of the quantum coherence resource through an optical fiber. The two-mode squeezed state (TMSS) generated by the nondegenerate optical parametric amplifier is distributed through optical fibers, and the quantum coherence of the TMSS is analyzed by the relative entropy of the covariance matrix. We show that quantum coherence is robust against the distribution distance even if the entanglement disappears at short distribution distance due to the loss and excess noise in fiber channels. Our results provide a direct reference for the potential practical applications of quantum coherence.
Abstract In the domain of quantum metrology, cat states have demonstrated their utility despite their inherent fragility with respect to losses. Here, we introduce noise robust optical cat states which exhibit a metrological robustness for phase estimation in the regime of high photon numbers. These cat states are obtained from the intense laser driven process of high harmonic generation (HHG), and show a resilience against photon losses. Focusing on a realistic scenario including experimental imperfections we opt for the case in which we can maximize the lower bound of the quantum Fisher information (QFI) instead of analyzing the best case scenario. We show that the decrease of the QFI in the lossy case is suppressed for the HHG-cat state compared to the even and odd counterparts. In the regime of small losses of just a single photon, the HHG-cat state remains almost pure while the even/odd cat state counterparts rapidly decohere to the maximally mixed state. More importantly, this translates to a significantly enhanced robustness for the HHG-cat against photon loss, demonstrating that high photon number optical cat states can indeed be used for metrological applications even in the presence of losses.