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

TL;DR

This paper analyzes an anti-$\mathcal{PT}$-symmetric qubit, revealing it exhibits slower decoherence and entanglement growth, suggesting potential advantages for quantum computing over traditional Hermitian or $\mathcal{PT}$-symmetric qubits.

Contribution

It provides an exact analytical solution for anti-$\mathcal{PT}$-symmetric qubits coupled with a bath, highlighting their superior decoherence and entanglement properties.

Findings

Decoherence decays slower in anti-$\mathcal{PT}$-symmetric qubits.

Entanglement entropy grows more slowly compared to other qubit types.

Higher Fisher information variance and area in anti-$\mathcal{PT}$-symmetric qubits.

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.