Extension of Noether's theorem in PT-symmetry systems and its experimental demonstration in an optical setup

Noether’s theorem is one of the fundamental laws in physics,relating the symmetry of a physical system to its constant of motion and conservation law.On the other hand,there exist a variety of non-Hermitian parity-time(PT)-symmetric systems,which exhibit novel quantum properties and have attracted increasing interest.In this work,we extend Noether’s theorem to a class of significant PT-symmetry systems for which the eigenvalues of the PT-symmetry Hamiltonian HPTchange from purely real numbers to purely imaginary numbers,and introduce a generalized expectation value of an operator based on biorthogonal quantum mechanics.We find that the generalized expectation value of a time-independent operator is a constant of motion when the operator presents a standard symmetry in the PT-symmetry unbroken regime,or a chiral symmetry in the PT-symmetry broken regime.In addition,we experimentally investigate the extended Noether’s theorem in PT-symmetry single-qubit and two-qubit systems using an optical setup.Our experiment demonstrates the existence of the constant of motion and reveals how this constant of motion can be used to judge whether the PT-symmetry of a system is broken.Furthermore,a novel phenomenon of masking quantum information is first observed in a PT-symmetry two-qubit system.This study not only contributes to full understanding of the relation between symmetry and conservation law in PT-symmetry physics,but also has potential applications in quantum information theory and quantum communication protocols.

Transferring entangled states of photonic cat-state qubits in circuit QED

We propose a method for transferring quantum entangled states of two photonic cat-state qubits(cqubits)from two microwave cavities to the other two microwave cavities.This proposal is realized by using four microwave cavities coupled to a superconducting flux qutrit.Because of using four cavities with different frequencies,the inter-cavity crosstalk is significantly reduced.Since only one coupler qutrit is used,the circuit resource is minimized.The entanglement transfer is completed with a singlestep operation only,thus this proposal is quite simple.The third energy level of the coupler qutrit is not populated during the state transfer,therefore decoherence from the higher energy level is greatly suppressed.Our numerical simulations show that high-fidelity transfer of two-cqubit entangled states from two transmission line resonators to the other two transmission line resonators is feasible with current circuit QED technology.This proposal is universal and can be applied to accomplish the same task in a wide range of physical systems,such as four microwave or optical cavities,which are coupled to a natural or artificial three-level atom.

Transfer of quantum entangled states between superconducting qubits and microwave field qubits

Transferring entangled states between matter qubits and microwave-field(or optical-field)qubits is of fundamental interest in quantum mechanics and necessary in hybrid quantum information processing and quantum communication.We here propose a way for transferring entangled states between superconducting qubits(matter qubits)and microwave-field qubits.This proposal is realized by a system consisting of multiple superconducting qutrits and microwave cavities.Here,“qutrit”refers to a three-level quantum system with the two lowest levels encoding a qubit while the third level acting as an auxiliary state.In contrast,the microwave-field qubits are encoded with coherent states of microwave cavities.Because the third energy level of each qutrit is not populated during the operation,decoherence from the higher energy levels is greatly suppressed.The entangled states can be deterministically transferred because measurement on the states is not needed.The operation time is independent of the number of superconducting qubits or microwave-field qubits.In addition,the architecture of the circuit system is quite simple because only a coupler qutrit and an auxiliary cavity are required.As an example,our numerical simulations show that high-fidelity transfer of entangled states from two superconducting qubits to two microwave-field qubits is feasible with present circuit QED technology.This proposal is quite general and can be extended to transfer entangled states between other matter qubits(e.g.,atoms,quantum dots,and NV centers)and microwave-or optical-field qubits encoded with coherent states.