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arXiv:2203.13771 · Physical Review A

Investigating the effect of noise channels on the quality of unitary t -designs

Conrad Strydom, Mark Tame

Published Nov 15, 2023• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.108.052414

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We investigate how the efficiency of the quantum teleportation protocol is affected when the qubits involved in the protocol are subjected to noise or decoherence. We study all types of noise usually encountered in real-world implementations of quantum communication protocols, namely, the bit-flip, phase-flip (phase damping), depolarizing, and amplitude-damping noise. Several realistic scenarios are studied in which a part or all of the qubits employed in the execution of the quantum teleportation protocol are subjected to the same or different types of noise. We find noise scenarios not yet known in which more noise or less entanglement lead to more efficiency. Furthermore, we show that if noise is unavoidable it is better to subject the qubits to different noise channels in order to obtain an increase in the efficiency of the protocol.
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