image: The dynamic encircling of the exceptional point for entangled states and realization. a, the schematic of the quantum walk evolution operator. b, Riemann energy surface for evolution operator Ui. Four stars with different colors represent different initial states. A green ball indicates the position of the exceptional point (EP). c, experimental setup. It consists of three parts, state preparation by the Source; the implementation of the encircling evolution around the exceptional point by the Evolution; and the results obtained by the Measurement. During the state preparation, the quantum states of the two particles are encoded in the horizontal and vertical polarization states of the two photons. In the evolution, the rotation operator R(θ) is implemented using a combination of a green HWP at 0° and a black HWP at θ . Two QWPs and one HWP together implement the conditional phase shift operator S. The partially polarizing beam splitters (PPBS) are used to implement the equivalent gain-loss operator. A combination of two QWPs and one HWP is placed at the end of each step to realize the symmetry-breaking operator ψ(φ) . For different Mn, by changing the parameters θ1 and φ, the loop around the EP is implemented experimentally. For the last operation CN, it is decomposed into the product of a SWAP gate, controlled-not (CNOT) gate, and the operator T. For the measurement, the output state is obtained through two-photon quantum state tomography. d and e, experimental results of the chiral entanglement switching with encircling an EP. The asymmetric convention of entangled states can be found with the clockwise encircling or the counter-clockwise encircling, respectively.
Credit: by Zan Tang, Tian Chen, Xing Tang, and Xiangdong Zhang
Quantum entanglement as the heart of quantum mechanics highlights the non-separability and nonlocality, which has been created experimentally in various physical systems. However, it is susceptible to influences of environment, which often appears decoherence. How to perform robust entanglement operations is crucial for applications in quantum information. Recent investigations have shown that the combination of topology and quantum states can bring hope to solve such a problem, but the fidelities of entangled states become very low without any efficient design of these topologically protected operations.
In a new paper published in Light Science & Application, a team of scientists, led by Professor Xiangdong Zhang from Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing, China, and co-workers have developed effective scheme to realize robust operation of quantum entanglement states with high fidelity by designing quadruple degeneracy exceptional points (EPs). Based on this design, the asymmetric conversion between the four entangled states has been realized by encircling the EP, which indicates the realization of a chirality switch for entangled states. The output entangled state in the conversion is determined by the direction of circling the EP, and the conversion efficiency is very high. More interestingly, such a switch for entangled states is topologically protected. Even the disorder is introduced into the encircled path, the fidelities for output entangled states with disorder also do not change much compared to the case without disorder. This means the chiral switching of the entangled states does indeed exhibit robustness against disorder in the path parameters. At the end, they have experimentally realized the above theoretical scheme by constructing the non-Hermitian quantum walk platform, and demonstrated the robustness of this chiral switch for entangled states. The reported design will open new avenues for future quantum information, computing, and communications.
The scheme to realize robust operation of quantum entanglement states with high fidelity strongly depends on the design of quadruple degeneracy EPs. Because the designed Riemann energy surfaces with degeneracy EPs have the same eigenstates as the entangled states, asymmetric conversion between the entangled states can be realized by encircling the EP. Such manipulation for the entangled states is topologically protected due to the topological properties of the Riemann surface structure. These scientists summarize the principle of their design:
“We design a topologically protected entanglement switching around EPs for three purposes in one: (1) to realize the full topological switch between all entangled Bell states; (2) to simplify the design of various parameters for the transformation between different entangled states; and (3) to find a way to be easily implemented in various real systems.”
“Since the fidelities for all entangled states undergoing the switch are larger than 84%, it indicates the output states are very close to the ideal entangled states, and robustness to the disorder” they added.
“The presented method can be used to efficiently switch between different quantum entangled states but also help people manipulate quantum information in the real world. This breakthrough could open a new venue for future distant quantum information transfer, robust quantum computation, and any other quantum technologies.” the scientists forecast.
Article Title
Topologically protected entanglement switching around exceptional points