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Optical Fiber Technology

The calculation of soliton pulses entanglement in optical fiber using field discretization and Schmidt decomposition

Yulia A. Mazhirina, Mikhail Vladimirovich Fedorov, L. A. Kochkurov, Leonid A. Melnikov

Published May 4, 2025• 1 citation
Publisher
DOI
10.1016/j.yofte.2025.104237

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The quantum theory of pulse propagation in a nonlinear optical fiber is presented using the time-dependent Hartree approximation. This formulation clarifies the connections between the quantum theory of soliton propagation and single-mode theories that have been used to describe the effects of self-phase modulation. An approximate solution is obtained for coherent-state soliton pulses that gives excellent agreement with numerical calculations for the quadrature phase amplitudes of the field. These amplitudes are found to undergo a series of collapses and revivals with propagation; the first collapse is related to the appearance of interference fringes in the field Q function.
Quantum entangled state and some common methods to measure entanglement are introduced, and Schmidt decomposition of 2-qubit quantum state and the method to identify the entangled state are induced. A method to calculate the degree of entanglement is also given, which is obtained very easily by using the Schmidt decomposition. An example about NMR quantum computation is discussed to illustrate the application of the Schmidt decomposition. The evolution of the state of sub-system is described by using the Bloch vector, which demonstrates the geometric prospect of quantum system.
The bipartite entanglement of a pure quantum state is known to be characterized by its Schmidt decomposition. In particular the state is maximally entangled when all the Schmidt coefficients are equal. We point out a convenient method which always yields a single analytical condition for the state to be maximally entangled, in terms of its expansion coefficients in any basis. The method works even when the Schmidt coefficients cannot be calculated analytically, and does not require their calculation. As an example this technique is used to derive the Bell basis for a system of two qubits. In a second example the technique shows a particular state to \textit{never} be maximally entangled, a general conclusion that cannot be reached using the Schmidt decomposition.