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

• URL: http://arxiv.org/abs/2008.04514v1
• Date: Tue, 11 Aug 2020 05:19:21 GMT
• Title: Anti-$\mathcal{PT}$-symmetric Qubit: Decoherence and Entanglement Entropy
• Authors: Julia Cen and Avadh Saxena
• Abstract summary: We investigate a two-level spin system based anti-parity-time (anti-$mathcalPT$)-symmetric qubit. We compare our findings with that of the corresponding $mathcalPT$-symmetric and Hermitian qubits.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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