Abstract
The $\mathcal{PT}$-symmetric non-Hermitian systems have been widely studied and explored both in theory and in experiment these years due to various interesting features. In this work, we focus on the dynamical features of a triple-qubit system, one of which evolves under local $\mathcal{PT}$-symmetric Hamiltonian. A new kind of abnormal dynamic pattern in the entropy evolution process is identified, which presents a parameter-dependent stable state, determined by the non-Hermiticity of Hamiltonian in the broken phase of $\mathcal{PT}$-symmetry. The entanglement and mutual information of a two-body subsystem can increase beyond the initial values, which do not exist in the Hermitian and two-qubit $\mathcal{PT}$-symmetric systems. Moreover, an experimental demonstration of the stable states in non-Hermitian system with non-zero entropy and entanglement is realized on a four-qubit quantum simulator with nuclear spins. Our work reveals the distinctive dynamic features in the triple-qubit $\mathcal{PT}$-symmetric system and paves the way for practical quantum simulation of multi-party non-Hermitian system on quantum computers.
Highlights
In the conventional quantum mechanics, the Hamiltonian of a closed system requires it to be Hermitian [1], which guarantees the reality of the energy spectrum and the unitarity of the corresponding time evolution operators
Two kinds of dynamic pattern, named ADP and normal dynamic pattern (NDP), are found in this system, where entropy and entanglement tend to be stable at a non-Hermiticity-related nonzero value in the ADP which does not exist in the two-qubit counterparts
Twobody subsystems in ADP present a maximum entanglement increase at the exceptional point, and mutual information can increase beyond the initial values
Summary
In the conventional quantum mechanics, the Hamiltonian of a closed system requires it to be Hermitian [1], which guarantees the reality of the energy spectrum and the unitarity of the corresponding time evolution operators. Some previous research [9,11] focuses on the two-body nonHermitian system as shown, where two qubits (Alice and Bob) are entangled initially and one of them (Alice) evolves under a local PT -symmetric Hamiltonian Such a two-qubit model can lead to oscillations of entropy and entanglement in the unbroken phase of PT symmetry, which violates the property of entanglement monotonicity [10,11]. The entropy and entanglement of both qubits will decay exponentially to zero in the broken phase and form stable states which do not vary with time Such stable states, whose dynamic process is named a normal dynamic pattern (NDP) here, are related only to the quantum phase but are independent of the degree of non-Hermiticity. By enlarging the system with ancillary qubits and encoding the subsystem with the non-Hermitian Hamiltonian with postselection, an experimental demonstration of the stable states in ADP is realized on a four-qubit quantum simulator based on a quantum circuit algorithm
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