Complexity analysis of quantum teleportation via different entangled channels in the presence of noise

Abstract

Quantum communication is an integral part of quantum computing, where teleportation of a quantum state has gained significant attention from researchers. Many teleportation schemes have been introduced in the recent past. In this study, the authors compare the teleportation of a single‐qubit message among different entangled channels such as the two‐qubit Bell channel, three‐qubit GHZ channel, two/three‐qubit cluster states, a highly entangled five‐qubit state (Brown et al.) and the six‐qubit state (Borras et al.). The authors calculate and compare the quantum costs for these channels. The authors also study the effects of six noise models: bit‐flip noise, phase‐flip noise, bit‐phase‐flip noise, amplitude damping, phase damping and depolarising error. These noise models may affect the communication channel used for teleportation. An investigation of the variation of the initial state's fidelity is performed for the teleported state in the presence of the noise model. It is observed that the fidelity decreases in all the entangled channels as the noise parameter η increases in the range [0, 0.5] for all the noise models. The fidelity shows an upward trend in the Bell, GHZ and three‐qubit cluster state channels, as η varies in the range [0.5, 1.0] for all the noise models. However, in the rest of the three channels, the fidelity substantially decreases in the case of amplitude damping, phase damping and depolarising noise, and even it reaches zero for η = 1 in Brown et al. and Borras et al. channels.

Entanglement Parallelization via Quantum Fourier Transform

“…Table 7 represents the compilation of the three fidelities for all the protocols seen so far. The reason for the performance degradation of the different protocols, from those at the top of the table to those at the bottom of the table, has to do with several factors: In all the experiments carried out so far, we have used a reduced version of all the protocols (including the example in the next subsection), [75,76] i.e., without quantum measurement modules, since the physical IBM Q machines do not support the if-then-else statement, nor the measurement modules in intermediate instances of quantum circuits. [47] For example, the simplified version of the quantum teleportation protocol used in Subsection 3.1 is that of Figure 13 and not that of Figure 5a.…”

“…In all the experiments carried out so far, we have used a reduced version of all the protocols (including the example in the next subsection), [ 75,76 ] i.e., without quantum measurement modules, since the physical IBM Q machines do not support the if‐then‐else statement, nor the measurement modules in intermediate instances of quantum circuits. [ 47 ] For example, the simplified version of the quantum teleportation protocol used in Subsection 3.1 is that of Figure 13 and not that of Figure 5a.…”

Quantum secret sharing protocol through noisy channel with application in visual cryptography

“…The security of quantum cryptography relies on the fundamental laws of quantum mechanics instead of the complex mathematical problems involved in classical cryptography. In the prospect of quantum cryptography, many branches have been established, such as quantum key distribution (QKD), [1][2][3] quantum secure direct communication (QSDC), 4,5 quantum private comparison protocol, 6 quantum teleportation, [7][8][9] quantum digital signature, 10,11 quantum image encryption, [12][13][14] and quantum visual secret sharing. 15,16 Similarly, quantum secret sharing (QSS) is one of the crucial research problems in secure communication.…”

High‐Fidelity and Low‐Cost Hyperparallel Quantum Gates for Photon Systems via Λ‐Type Systems

“…Therefore, building universal quantum gates with the least quantum resource overhead (cost) and the minimum external manipulation is crucial in quantum computing. [21,22] Notably, the number of gates used to construct the quantum circuits can be greatly reduced by auxiliary dimensions [23][24][25] or multiple degrees of freedom (DoFs) of photon system. For the former, Ralph et al introduced the qudit concept to build Toffoli gate with a set of two-qubit gates, [26] where the qudit takes advantage of ancillary higher-dimensional spaces.…”