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IET Quantum Communication

Fock States in Additive Gaussian Noise Channels: Analytical and Numerical Considerations

Emad Zinoghli, Jawad A. Salehi

Published Jan 1, 2025• 1 citation
Publisher

Abstract

ABSTRACT In this paper, we study the effects of additive Gaussian noise on Fock states. We put forth a simple analytical formula for the resulting output states. Additionally, we conduct numerical analysis into several key properties of noisy Fock states, including their purity, nonclassicality and non‐Gaussianness, with respect to the noise parameter. Finally, we examine the impact of noise on entangled N00N states, focusing on its entanglement‐breaking effects, which we quantify using the logarithmic negativity measure. Regarding purity, we observe that for a fixed noise level, the purity of a noisy Fock state decreases as the number of photons increases. In terms of non‐Gaussianity, we show that at any given noise level, higher Fock states exhibit higher non‐Gaussianity compared to lower ones. Although all noisy Fock states eventually lose their nonclassical characteristics under sufficient noise, higher Fock states exhibit more pronounced nonclassical features in low‐noise conditions, whereas lower Fock states show greater nonclassicality in high‐noise environments. We quantitatively show that the state is the most robust against additive Gaussian noise among the N00N states.

DOI
10.1049/qtc2.70011

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Journal of Optical Technology•Mar 1, 2025•2 citations
ABSTRACT In this paper, we study the effects of additive Gaussian noise on Fock states. We put forth a simple analytical formula for the resulting output states. Additionally, we conduct numerical analysis into several key properties of noisy Fock states, including their purity, nonclassicality and non‐Gaussianness, with respect to the noise parameter. Finally, we examine the impact of noise on entangled N00N states, focusing on its entanglement‐breaking effects, which we quantify using the logarithmic negativity measure. Regarding purity, we observe that for a fixed noise level, the purity of a noisy Fock state decreases as the number of photons increases. In terms of non‐Gaussianity, we show that at any given noise level, higher Fock states exhibit higher non‐Gaussianity compared to lower ones. Although all noisy Fock states eventually lose their nonclassical characteristics under sufficient noise, higher Fock states exhibit more pronounced nonclassical features in low‐noise conditions, whereas lower Fock states show greater nonclassicality in high‐noise environments. We quantitatively show that the state is the most robust against additive Gaussian noise among the N00N states.
Abstract Non‐Gaussian and nonclassical states and processes are already found to be important resources for performing various tasks related to quantum gravity and quantum information processing. Considering these facts, a quantitative analysis of the nonclassical and non‐Gaussian features is performed here for photon added displaced Fock state, as a test case, using a set of measures, namely entanglement potential, Wigner–Yanese skew information, Wigner logarithmic negativity, and relative entropy of non‐Gaussianity. It is observed that Fock parameter always increases the amount of nonclassicality and non‐Gaussianity, while photon addition is effective only for small values of the displacement parameter. Further, the nonclassical and non‐Gaussian effects decrease initially with an increase in the displacement parameter before increasing for the large displacement to saturate to the corresponding Fock state (equivalently displaced Fock state) value. Finally, dynamics of the Wigner function under the effect of photon loss channel is used to show that only highly efficient detectors are able to detect Wigner negativity.
Non-Gaussian and nonclassical states and processes are already found to be important resources for performing various tasks related to quantum gravity and quantum information processing. The effect of non-Gaussianity inducing operators on the nonclassicality of quantum states has also been studied rigorously. Considering these facts, a quantitative analysis of the nonclassical and non-Gaussian features is performed here for photon added displaced Fock state, as a test case, using a set of measures like entanglement potential, Wigner Yanese skew information, Wigner logarithmic negativity and relative entropy of non-Gaussianity. It is observed that photon addition (Fock parameter) significantly increases the amount of nonclassicalty and non-Gaussianity for small (large) values of the displacement parameter, which decreases both the quantum features monotonically. In this respect, the role of Fock parameter is found to be more prominent and stronger compared to photon addition. Finally, the dynamics of Wigner function under the effect of photon loss channel is used to show that only highly efficient detectors are able to detect Wigner negativity.
In this paper, a quantitative investigation of the non-classical and quantum non-Gaussian characters of the photon-subtracted displaced Fock state [Formula: see text], where k is the number of photons subtracted and n is Fock parameter, is performed by using a collection of measures like Wigner logarithmic negativity, linear entropy potential, skew information-based measure, and relative entropy of quantum non-Gaussianity. It is noticed that the number of photons subtracted ( k) changes the nonclassicality and quantum non-Gaussianity in a significant amount in the regime of small values of the displacement parameter, whereas the Fock parameter ( n) presents a notable change in the large regime of the displacement parameter. In this respect, the role of the Fock parameter is found to be stronger as compared to the photon subtraction number. Finally, the Wigner function dynamics considering the effects of photon loss channel is used to show that the Wigner negativity can only be detected by highly efficient detectors.
We present a framework for studying linear bosonic non-Gaussian channels. Our emphasis is on a class of channels that we call photon-added Gaussian channels and these are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian regime for numerous tasks in continuous-variable quantum information processing including universal quantum computation. These channels are obtained by extending Gaussian channels with photon addition applied to the ancilla ports giving rise to a one-parameter family of non-Gaussian channels indexed by photon number n≥1n \geq 1n≥1. We derive its operator-sum representation which is indispensable in the present context. We observe that these channels are Fock-preserving (or coherence non-generating in the Fock basis). Further, noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels. We then report examples of activation of nonclassicality, using this method of photon-addition, at outputs of channels that would otherwise output only classical states. We also derive many structure theorems and information theoretic properties of these channels.
Abstract Quantum decoherence due to imperfect manipulation of quantum devices is a key issue in the noisy intermediate-scale quantum (NISQ) era. Standard analyses in quantum information and quantum computation use error rates to parameterize quantum noise channels. However, there is no explicit relation between the decoherence effect induced by a noise channel and its error rate. In this work, we propose to characterize the decoherence effect of a noise channel by the physical implementability of its inverse, which is a universal parameter quantifying the difficulty to simulate the noise inverse with accessible quantum channels. We establish two concise inequalities connecting the decrease of the state purity and logarithmic negativity after a noise channel to the physical implementability of the noise inverse, which is required to be decomposed as mutually orthogonal unitaries or product channels respectively. Our results are numerically demonstrated on several commonly adopted two-qubit noise models. We believe that these relations contribute to the theoretical research on the entanglement properties of noise channels and provide guiding principles for quantum circuit design.
Subject of study. Schemes for generating non-Gaussian quantum states and the states required for quantum error correction protocols are investigated. Aim of study. The primary objectives were to generalize methods and approaches for describing the generation of non-Gaussian states in measurement schemes to determine the most effective model for describing the generation process and to assess a model for generating squeezed Fock states and a quantum error correction code based on such states. Method. A theoretical analysis of the wavefunction evolution of various non-Gaussian states in particle-number measurement schemes was performed; in this analysis, squeezed states were used as inputs. Main results. A scheme for generating squeezed Fock states was theoretically examined. An explicit analytical expression for the output wavefunction was constructed to completely analyze the output states depending on the parameters of the scheme under consideration. A set of conditions imposed on the parameters of a two-mode entangled Gaussian state, i.e., the “universal solution regime,” was outlined. This regime guaranteed the generation of squeezed Fock states with a high probability. Practical significance. The results demonstrated the ability of the universal solution regime to generate squeezed Fock states of arbitrary order for a given squeezing parameter. The feasibility of using squeezed Fock states in quantum error correction codes was analyzed. A comparative study of squeezed Fock states and squeezed Schrödinger cat states as codewords confirmed squeezed Fock states as robust solutions to ensure information protection in channels subjected to particle loss and dephasing.