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arXiv · 2008.04514

Anti-$\mathcal{PT}$-symmetric Qubit: Decoherence and Entanglement Entropy

Julia Cen·Avadh Saxena
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Abstract

We investigate a two-level spin system based anti-parity-time (anti-$\mathcal{PT}$)-symmetric qubit and study its decoherence as well as entanglement entropy properties. We compare our findings with that of the corresponding $\mathcal{PT}$-symmetric and Hermitian qubits. First we consider the time-dependent Dyson map to find the exact analytical dynamics for a general non-Hermitian qubit system coupled with a bath, then we specialize it to the case of the anti-$\mathcal{PT}$-symmetric qubit. We find that the decoherence function for the anti-$\mathcal{PT}$-symmetric qubit decays slower than the $\mathcal{PT}$-symmetric and Hermitian qubits. For the entanglement entropy we find that for the anti-$\mathcal{PT}$-symmetric qubit it grows more slowly compared to the $\mathcal{PT}$-symmetric and Hermitian qubits. Similarly, we find that the corresponding variance and area of Fisher information is much higher compared to the $\mathcal{PT}$-symmetric and Hermitian qubits. These results demonstrate that anti-$\mathcal{PT}$-symmetric qubits may be better suited for quantum computing and quantum information processing applications than conventional Hermitian or even $\mathcal{PT}$-symmetric qubits.

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Julia Cen, Avadh Saxena. 2020-08-11. Anti-$\mathcal{PT}$-symmetric Qubit: Decoherence and Entanglement Entropy. https://arxiv.org/abs/2008.04514

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