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Quantum teleportation scheme using entangled two ququads and its noise effects

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Abstract

We present a quantum teleportation scheme for single qubits, qutrits, and ququads using maximally entangled pairs of two ququads. Additionally, we demonstrate that, under a specific mapping, single ququad teleportation is equivalent to two-qubit teleportation using generalized Bell states. Furthermore, we establish a dense (superdense) coding scheme for sending four bits of classical information using a single ququad state. We also investigate the efficiency of the single ququad quantum teleportation scheme by studying the fidelity of teleportation when subjected to noise, such as amplitude damping, depolarizing channel, phase damping, and bit flip. Finally, we investigate noise effects in two qubit teleportation and compare its results with the ququad case. We observe that in both cases, adding more noise increases the fidelity of teleportation. Additionally, we show that qubit teleportation is more resilient to noise than ququad teleportation.

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Authors and Affiliations

  1. Department of Physics, Government Arts and Science College, Meenchanda, Calicut, Kerala, 673018, India

    N. C. Randeep

  2. Department of Physics, SARBTM Government College, Koyilandy, Kerala, 673307, India

    C. Anukrishna

  3. Department of Physics, AVAH Arts and Science College, Kuluppa, Kozhikode, Kerala, 673523, India

    A. K. Neha Raj

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Appendix A:Quantum circuit for creating generalized Bell states

Appendix A:Quantum circuit for creating generalized Bell states

Figure 9 shows the quantum circuit for creating generalized Bell states. For a given set of input states \(\{|0000\rangle , |1000\rangle , |0100\rangle , |1100\rangle , |0001\rangle , |1001\rangle , |0101\rangle , |1101\rangle ,|0010\rangle , |1010\rangle , |0110\rangle , |1110\rangle , |0011\rangle , |1011\rangle , |0111\rangle , |1111\rangle \} \), this quantum circuit produces 16 maximally entangled four qubit states given by Eq. (15). By applying the mapping described in Eq. (13), the aforementioned four qubit states becomes computational basis state for two ququads denoted by \(\{ \vert aa \rangle , \vert ca \rangle , \vert ba \rangle , \vert da \rangle , \vert ab \rangle , \vert cb \rangle , \) \( \vert bb \rangle , \vert db \rangle , \vert ac \rangle , \vert cc \rangle , \vert bc \rangle , \vert dc \rangle , \vert ad \rangle , \vert cd \rangle , \vert bd \rangle , \vert dd \rangle \}\). Then, applying a unitary transformation equivalent to the quantum circuit shown in Fig. 9 converts the computational basis states of two ququads into maximally entangled states as given by Eq. (4). The inverse circuit (unitary transformation) is useful for generalized Bell measurements.

Fig. 9
figure 9

The quantum circuit for creating four qubit entangled states

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Randeep, N.C., Anukrishna, C. & Neha Raj, A.K. Quantum teleportation scheme using entangled two ququads and its noise effects. Quantum Inf Process 23, 192 (2024). https://doi.org/10.1007/s11128-024-04381-2

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