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Proceedings of the YSU A Physical and Mathematical Sciences

DEFINITION OF CONTROL SIGNALS FOR PERFORMING CERTAIN GATES BY KERR CELLS IN A NONLINEAR RESONATOR

H.S. Karayan, A.G. Chibukhchyan

Published Jun 15, 2017• 0 citations
Publisher

Abstract

Considered the effects of external optical signals on the entangled states of the Fock of Kerr qubits in a nonlinear resonator. The necessary time dependence of the Hamiltonian for the realization of negation, Hadamard and controlled negation operators for the algebra of quantum logic have been found.
DOI
10.46991/pysu:a/2017.51.2.199

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In this paper, we investigated the dynamics of entanglement of pairs of qubits in a system of three identical qubits that interact non-resonantly with the selected mode of a microwave resonator without loss with the Kerr medium by means of single-photon transitions. We have found solutions to the quantum time Schrodinger equation for the total wave function of the system for the initial separable, biseparable and true entangled states of qubits and the Fock initial state of the resonator field. Based on these solutions, the criterion of entanglement of qubit pairs — negativity is calculated. The results of numerical simulation of the negativity of qubit pairs have shown that the presence of disorder and Kerr nonlinearity in the case of an initial non-entangled state of a pair of qubits can lead to a significant increase in the degree of their entanglement. In the case of an initial entangled state of a pair of qubits, the disorder and the Kerr medium can lead to a significant stabilization of the initial entanglement.
Decoherence effect on quantum entanglement of two optical qubits in a lossy cavity interacting with a nonlinear medium (Kerr nonlinearity) is analysed. The qubits are assumed to be initially in the maximally entangled states (Bell or Bell-like states) or the maximally entangled mixed states, on the example of Werner and Werner-like states. Two kinds of measures of the entanglement are considered: the concurrence to describe a decay of the entanglement of formation of the qubits, and the negativity to determine a decay of the entanglement cost under positive-partial-transpose-preserving operations. It is observed that the Kerr nonlinearity, in the discussed decoherence model, does not affect the entanglement of the qubits initially in the Bell or Werner states, although the evolution of the qubits can depend on this nonlinearity explicitly. However, it is shown that for the initial Bell-like state and the corresponding Werner-like state, the loss of the entanglement can be periodically reduced by inserting the Kerr nonlinearity in the lossy cavity. Moreover, the relativity of the entanglement measures is demonstrated, to our knowledge for the first time, as a result of a physical process.
Decoherence effect on quantum entanglement of two optical qubits in a lossy cavity interacting with a nonlinear medium (Kerr nonlinearity) is analyzed. The qubits are assumed to be initially in the maximally entangled states (Bell or Bell-like states) or the maximally entangled mixed states, on the example of Werner and Werner-like states. Two kinds of measures of the entanglement are considered: the concurrence to describe a decay of the entanglement of formation of the qubits, and the negativity to determine a decay of an upper bound of the entanglement of distillation. It is observed that the Kerr nonlinearity does not affect the entanglement of the qubits initially in the Bell or Werner states, although the evolution of the qubits can depend on this nonlinearity explicitly. However, it is shown that for the initial Bell-like state and the corresponding Werner-like state, the loss of entanglement can be periodically reduced by inserting the Kerr nonlinearity in the lossy cavity.
Background. The need to implement controlled coupling between qubits, which are the logical elements of quantum devices such as quantum computers and quantum networks, requires, along with the use of traditional methods, the development of new, more effective ways to organize the interaction of qubits with the microwave fields of resonators used to generate and control the entanglement of qubits. As one of these methods, a method based on the influence of frequency-regulated radio frequency signals on a superconducting Josephson qubit connected by a large Josephson junction to a free qubit has been proposed. Aim. The influence of the Kerr medium of the resonator, in which one of the two qubits is placed, on their entanglement induced by the coherent or thermal frequency-regulated radio frequency field of the resonator is considered. Methods. To analyze the dynamics of the system under consideration, the solution of the quantum Liouville equation for the full density matrix is studied. An exact solution o this equation is found in the case of initial separable and entangled states of qubits. The exact solution of the evolution equation is used to calculate the criterion of qubit-qubit entanglement – cconcurrence. Numerical modeling of the concurrence was carried out for various states of qubits, coherent and thermal fields of the resonator, as well as various values of the intensity of the resonator field and the Kerr nonlinearity parameter. Results. It is shown that for separable initial states of qubits, the inclusion of Kerr nonlinearity reduces the maximum degree of entanglement of qubits. For an entangled initial state of qubits, the possibility of creating long-lived entangled states in the presence of Kerr nonlinearity is shown. Conclusion. The type of initial states of qubits and the range of values of the intensities of the resonator fields and the Kerr nonlinearity parameters have been established, for which the most effective control and operation of the evolution of qubits, as well as the degree of their entanglement, in the physical system under consideration, is possible.