Abstract In this work, we analyze a number of noisy quantum channels on a family of qudit states. The channels studied are the dit-flip noise, phase flip noise, dit-phase flip noise, depolarizing noise, non-Markovian Amplitude Damping Channel (ADC), dephasing noise, and depolarization noise. To gauge the effect of noise, the fidelity between the original and the final states is studied. The change of coherence under the action of noisy channels is also studied, both analytically and numerically. Our approach is advantageous as it has an explicit relation to the original approach to the multi-qubit hypergraph states.
The family of quantum graph and hypergraph states are ubiquitous in quantum information. They have diverse applications ranging from quantum network protocols to measurement based quantum computing. The hypergraph states are a generalization of graph states, a well-known family of entangled multi-qubit quantum states. We can map these states to qudit states. In this work, we analyze a number of noisy quantum channels for qudits, on the family of qudit hypergraph states. The channels studied are the dit-flip noise, phase flip noise, dit-phase flip noise, depolarizing noise, non-Markovian Amplitude Damping Channel (ADC), dephasing noise, and depolarization noise. To gauge the effect of noise on quantum hypergraph states, the fidelity between the original and the final states is studied. The change of coherence under the action of noisy channels is also studied, both analytically and numerically.
The concept of quantum teleportation is fundamental in the theory of quantum communication. Developing models of quantum teleportation in different physical scenario is a modern trend of research in this direction. This work is at the interface of hypergraph theory and quantum teleportation. We propose a new teleportation protocol for qutrit states in a noisy environment. This protocol utilizes a shared quantum hypergraph state between parties as quantum channels, to carry quantum information. During the preparation of the shared state different quantum noise may act on it. In this article, we consider six types of noises which are generalized for qutrits using Wyel operators. They are the qutrit-flip noise, qutrit-phase-flip noise, depolarizing noise, Markovian and non-Markovian amplitude damping channel, Markovian and non-Markovian dephasing channel, and non-Markovian depolarization noise. There are only five qutrit hypergraph states which satisfies our requirements to be used as a channel. We consider all of them in this work. For different hypergraph states and different noises we work out the analytical expressions of quantum teleportation fidelity.
Noise is a major challenge in quantum computing, affecting the reliability of quantum protocols. In this work, we analytically study the impact of various noise processes, such as depolarization, bit flip, and phase flip, on the quantum state teleportation protocol. Each noise process is modeled as a quantum channel and is applied individually to all qubits after the corresponding unitary operations to simulate realistic conditions. We evaluate the fidelity between the ideal and noisy teleported states to quantify the effect of noise. Our analysis shows that the fidelity decreases polynomially, in general, as the noise strength increases for all noise types, highlighting the sensitivity of state teleportation to different noise mechanisms. However, in the low noise regime, the fidelity decreases only linearly, indicating the robustness of the teleportation protocol. These results provide insight into error characterization and can inform strategies for noise mitigation in practical quantum computing applications.
We study the protocol of qudit teleportation using quantum systems subjected to several kinds of noise for arbitrary dimensionality
d. We consider four classes of noise: dit-flip,
d-phase-flip, dit-phase-flip, and depolarizing noise, each of them corresponding to a family of Weyl operators, introduced via Kraus formalism. We derive a general expression for the average fidelity of teleportation in arbitrary dimension
d for any combination of noise on the involved qudits. Under a different approach we derive the average fidelity of teleportation for a more general scenario involving the
d-dimensional generalization of amplitude damping noise as well. We show that all possible scenarios may be classified in four different behaviors and discuss the cases in which it is possible to improve the fidelity by increasing the associated noise fractions. All our results are in agreement with previous analysis for the case of qubits [R. Fortes and G. Rigolin, Phys. Rev. A 92, 012338 (2015)].
In quantum information theory, effects of quantum noise on teleportation are undeniable. Hence,we investigate the effect of noisy channels including amplitude damping, phase damping, depolarizing and phase ip on the teleported state between Alice and Bob where they share an entangled state by using atom-eld interaction state. We analyze the delity and quantum correlations as a function of decoherence rates and time scale of a state to be teleported. We observe that the average delityand quantum correlations accurately depend on types of noise acting on quantum channels. It is found that atom-eld interaction states are affected by amplitude damping channel are more useful for teleportation than when the shared qubites are affected by noisy channels such as AD channel and phase ip. We also observe that if the quantum channels is subject to phase ip noise, the average delity reproduces initial quantum correlations to possible values. On the other hand,not only all the noisy quantum channels do not always destroy average delity but also they can yield the highest delity in noisy conditions. In the current demonstration, our results provide that the average delity can have larger than 2/3 in front of the noise of named other channels with increasing decoherenc strength. Success in quantum states transfer in the present noise establishes the important of studing noisy channels.
Unitary
t-designs have a wide variety of applications in quantum information theory, such as quantum data encryption and randomized benchmarking. However, experimental realizations of
t-designs are subject to noise. Here we investigate the effect of noise channels on the quality of single-qubit
t-designs. The noise channels we study are bit flips, phase flips, bit and phase flips, phase damping, amplitude damping, and depolarizing noise. We consider two noise models: The first has noise applied before the
t-design unitary operations, while the second has noise applied after the unitary operations. We show that the single-qubit 1-design is affected only by amplitude damping, while numeric results obtained for the 2-, 3-, 4-, and 5-designs suggest that a
2t-design is significantly more sensitive to noise than a $(2t\ensuremath{-}1)$-design and that, with the exception of amplitude damping, a
(2t+1)-design is as sensitive to noise as a
2t-design. Numeric results also reveal substantial variations in sensitivity to noise throughout the Bloch sphere. In particular,
t-designs appear to be most sensitive to noise when acting on pure states and least sensitive to noise for the maximally mixed state. For depolarizing noise, we show that our two noise models are equivalent, and for the other noise channels, numeric results obtained for the model where noise is applied after the unitaries reflect the transformation of the noise channel into a depolarizing channel, an effect exploited in randomized benchmarking with 2-designs.