Abstract
We propose a scheme of repeated generalized Bell state measurement (GBSM) for probabilistic quantum teleportation of single qubit state of a particle (say, 0) using 3-qubit non-maximally entangled (NME) GHZ state as a quantum channel. Alice keeps two qubits (say, 1 and 2) of the 3-qubit resource and the third qubit (say, 3) goes to Bob. Initially, Alice performs GBSM on qubits 0 and 1 which may lead to either success or failure. On obtaining success, Alice performs projective measurement on qubit 2 in the eigen basis of σx. Both these measurement outcomes are communicated to Bob classically, which helps him to perform a suitable unitary transformation on qubit 3 to recover the information state. On the other hand, if failure is obtained, the next attempt of GBSM is performed on qubits 0 and 2. This process of repeating GBSM on alternate pair of qubits may continue until perfect teleportation with unit fidelity is achieved. We have obtained analytical expressions for success probability up to three repetitions of GBSM. The success probability is shown to be a polynomial function of bipartite concurrence of the NME resource. The variation of success probability with the bipartite concurrence has been plotted which shows the convergence of success probability to unity with GBSM repetitions.
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Acknowledgements
SJ, RKP, PSY dedicate this paper in the memory of Prof. Ranjana Prakash and Prof. Hari Prakash. May their soul rest in peace. We are thankful to Prof. N Chandra, Dr. V Verma and Dr. O N Verma for valuable suggestions. SJ is thankful to UGC scheme of Maulana Azad National Fellowship for providing financial support. RKP is thankful to UGC for providing financial assistance under CSIR-UGC SRF fellowship.
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Javed, S., Pandey, R.K., Yadav, P.S. et al. Probabilistic Quantum Teleportation via 3-Qubit Non-maximally Entangled GHZ State by Repeated Generalized Measurements. Int J Theor Phys 62, 11 (2023). https://doi.org/10.1007/s10773-022-05266-9
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DOI: https://doi.org/10.1007/s10773-022-05266-9