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arXiv:2211.09012 · Optical Switching and Networking

Quantum capacity of a deformed bosonic dephasing channel

Shahram Dehdashti, Janis Nötzel, Peter van Loock

Published Jul 4, 2025• 4 citations
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Abstract

In this paper, using the notion of nonlinear coherent states, we define a deformed bosonic dephasing channel modelling the impact of a Kerr medium on a quantum state, as it occurs, for instance, in quantum communication based on optical fibers. We show that, in certain regimes, the Kerr nonlinearity is able to compensate the dephasing. In addition, our studies reveal that the quantum capacity of the deformed bosonic dephasing channel can be greater than that of the undeformed, standard bosonic dephasing channel for certain nonlinearity parameters.

DOI
10.1016/j.osn.2025.100814

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•Jan 1, 2009•2 citations
In this paper, using the notion of nonlinear coherent states, we define a deformed bosonic dephasing channel modelling the impact of a Kerr medium on a quantum state, as it occurs, for instance, in quantum communication based on optical fibers. We show that, in certain regimes, the Kerr nonlinearity is able to compensate the dephasing. In addition, our studies reveal that the quantum capacity of the deformed bosonic dephasing channel can be greater than that of the undeformed, standard bosonic dephasing channel for certain nonlinearity parameters.
Phase damping is the main decoherence in the evolution of quantum states. In most of the known quantum computing and quantum information processing, devices have amplitude damping times that are around 1-2 orders of magnitude larger than the corresponding dephasing times. For lossy optical fibre as a quantum channel, the quantum capacity is well known. The channel is degradable. We know that dephasing channel is also degradable, thus it can be anticipate that the channel capacity is available. We calculate the capacity with various methods in this paper.
We study the LOCC-assisted quantum capacity of a bosonic dephasing channel with energy constraint on the input states. We start our analysis by focusing on the energy-constrained squashed entanglement of the channel, which is an upper bound for the energy-constrained LOCC-assisted quantum capacity. As computing energy-constrained squashed entanglement of the channel is challenging due to a double optimization (over the set of density matrices and the isometric extensions of a squashing channel), we first derive an upper bound for it, and then, we discuss how tight that bound is for the energy-constrained LOCC-assisted quantum capacity of the bosonic dephasing channel. In doling so, we prove that the optimal input state is diagonal in the Fock basis. Then, we analyze two explicit examples of squashing channels through which we derive explicit upper and lower bounds for the energy-constrained LOCC-assisted quantum capacity of the bosonic dephasing channel in terms of its quantum capacity with different noise parameters. As the difference between upper and lower bounds becomes smaller by increasing the dephasing parameter, the bounds become tighter.
We present a systematic study of Schrödinger cat codes constructed from Kerr-type coherent states, including displaced Kerr coherent states and Barut--Girardello Kerr coherent states, each admitting two distinct families determined by the sign of the Kerr nonlinearity. By tuning the Kerr parameter and coherent-state amplitude, these states interpolate between su(2)\mathfrak{su}(2)su(2), su(1,1)\mathfrak{su}(1,1)su(1,1) coherent states, providing a unified and versatile foundation for this type of bosonic quantum error correction. Unlike standard two-component Schrödinger cat codes, where a single photon-loss event induces an uncorrectable bit-flip, the nonlinear phase-space structure of Kerr cat states enables simultaneous detection and correction of both photon-loss and dephasing errors within a unified recovery framework, with optimal recovery operations determined via convex optimization. We demonstrate that Kerr cat encodings significantly outperform conventional cat codes under combined loss and dephasing noise, and that judicious parameter optimization can suppress both error channels to a level that reduces the overhead of additional error correction layers. We further show that Kerr-deformed coherent-state manifolds under engineered two-photon driving emerge as effective steady states of driven-dissipative dynamics, with single-photon decoherence strongly suppressed and leakage outside the protected manifold appearing only as higher-order corrections in the deformation strength. Our extended formalism identifies generalized Kerr Schrödinger cat codes as promising candidates for fault-tolerant bosonic quantum computation in experimental platforms such as nonlinear photonics.
We develop a unified framework for studying superposed coherent states in coupled nonlinear bosonic systems using a q-deformed Kerr oscillator model. A quantitative measure, termed catability, is introduced to quantify robustness and structural coherence of Schrödinger-cat-like states under nonlinear and deformation effects within the framework. Within the q-deformed bosonic algebra, we analyze the dynamics of two coupled Kerr oscillators to demonstrate that the deformation parameter governs coherence redistribution and nonlinear coupling-induced state transformation. Establish local cat states emerge from the relation between Kerr nonlinearity and q-deformed interactions, coherence transfer between subsystems becomes sensitive to the deformation strength. In this case, construct a phase diagram of catability, revealing distinct regimes of quantum behavior, identifying coupling-driven quantum phase transitions in a deformed algebraic structure system. The generalized analysis extended the covariant formulation and graphene-inspired catability operators generalized curved space-time backgrounds, establishing a connection between nonlinear quantum optics, condensed matter analog systems, relativistic quantum structures framework. In this context, results explain complete description deformationcontrolled quantum coherence and establish new directions for engineered nonclassical states in complex quantum systems.
In this paper, two distinct classes of generalized deformed Kerr states are introduced by considering the standard and deformed Kerr mediums, when the initial field state that enters the Kerr medium has been prepared in the well-known nonlinear coherent state. Indeed, the conversion of the third-order susceptibility of the (standard) Kerr medium to its deformed counterpart via an intensity-dependent function K ( n ) is performed. Interestingly, the obtained generalized states are still of f -deformed type, with a special form of the nonlinearity function. Some physical realizations of the proposed approach are presented. Finally, the nonclassicality features, the quantum phase properties and the autocorrelation function of the introduced states are studied numerically.