Effect of Noise on Practical Quantum Communication Systems

Abstract

Entanglement is an important resource for various applications of quantum computation. Another important endeavor is to establish the role of entanglement in practical implementation where system of interest is affected by various kinds of noisy channels. Here, a single classical bit is used to send information under the influence of a noisy quantum channel. The entanglement content of quantum states is computed under noisy channels such as amplitude damping, phase damping, squeesed generalised amplitude damping, Pauli channels and various collective noise models on the protocols of quantum key distribution.Keywords: Entanglement, quantum noise, markov process, optical-fiber, optical communication The operators which fulfill the criteria from Eqn.(1) to (3) is essentially considered under noisy channel condition. Similarly, for two transmissions through the channel the Kraus operator representation is as follows . This encoding is performed on the transmitted bit sent to Bob. After this, Alice sends these states via channel. Bob uses the action of the channel given in Eqn. (4) to get output in one of the two possible operators 0 R and 1 R at the receiving end. ( ) Tr R E s b is the probability value in Bob's measurement, which depends on the bit value sent by Alice and the method of maximum likelihood that depends on the values of bits b and s to make ( ) Tr R E s b maximum. The average error probability is written asBob performs von Neumann measurement to get P e minimum, henceConcurrence is used to measure the entanglement amount, the entanglement strength and considered as an independent entanglement measure. Concurrence for a pure state ψ with bipartite two-level systems is defined ashere * ψ is the complex conjugate of pure state ψ , 2 σ is the Pauli y-matrix defined as. Concurrence for a given mixed state is written ashere i λ represents decreasing eigenvalues of the Hermitian matrix R = r r r  and ( ) ( ). THE EFFECT OF VARIOUS KINDS OF NOISES ON THE QUANTUM STATESHere we consider only some specific noise models like amplitude damping, phase-damping and two types of collective noises for the interaction with the quantum states transmitting between Alice and Bob. We follow the method used 13 for the information transfer under noisy environment. let the quantum density state is r = ψ ψ , here ψ is any n qubit initial pure quantum state before transmission. Under noisy conditions the transmitted pure state evolves as follows:where k E i j denotes Kraus operator for specific type of noisy channel under consideration applied on desired qubit of the travelling quantum state. The evolution of density matrix undercollective noise models can be written ashere k represents type of noisy channel used, and U i is a 2 x 2 matrix (it works on a single qubit) for collective dephasing andcollective rotation noises. After obtaining the transformed density matrix k r , the normalization can be achieved by calculating the trace to be 1. We can make it one by dividing it by the trace of the transformed matrix k r ....

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