近日，印度马德拉斯理工学院的Arul Lakshminarayan&Sourav Manna及其研究团队取得一项新进展。他们对纠缠能力、门典型性和测量诱导相变进行了研究。相关研究成果已于2024年12月23日在国际知名学术期刊《物理评论A》上发表。

在量子电路中，当量子比特经历非局域幺正演化时，它们之间的纠缠会逐渐增强。相反，对单个量子比特进行测量则会导致它们与整个系统的解纠缠。纠缠减少的程度取决于局部投影测量的频率。在增强纠缠的幺正演化和削弱纠缠的测量之间，存在着一种微妙的平衡。在热力学极限下，当测量频率达到某个临界值时，会发生从体积律纠缠到面积律纠缠的相变。这种在同时包含幺正门和测量的混合量子电路中出现的现象，被称为测量诱导相变（MIPT）。

该研究团队研究了由通过卡坦分解参数化的两量子比特幺正门构成的，电路中测量诱导相变（MIPT）的行为。研究表明，电路中使用的两量子比特局部幺正变换的纠缠能力和门典型性，可以用来解释电路所能维持的全局二体纠缠的行为。

当整个电路中的两量子比特门是恒等的，且测量是纠缠行为的唯一驱动因素时，研究人员获得了纠缠熵的解析估计，该估计与数值模拟结果高度一致。

研究人员还发现，纠缠能力和门典型性使得能够根据混合电路中，可能发生的相变的不同普适性类别，对两量子比特幺正变换进行分类。对于特定普适性类别中的所有幺正变换，从体积律到面积律的纠缠转变具有相同的指数，该指数表征了相变的特性。

附：英文原文

Title: Entangling power, gate typicality, and measurement-induced phase transitions

Author: Sourav Manna^*, Vaibhav Madhok, and Arul Lakshminarayan^†

Issue&Volume: 2024-12-23

Abstract: When subject to a nonlocal unitary evolution, qubits in a quantum circuit become increasingly entangled. Conversely, measurements applied to individual qubits lead to their disentanglement from the collective system. The extent of entanglement reduction depends on the frequency of local projective measurements. A delicate balance emerges between unitary evolution, which enhances entanglement, and measurements which diminish it. In the thermodynamic limit, there is a phase transition from volume law entanglement to area law entanglement at a critical value of measurement frequency. This phenomenon, occurring in hybrid quantum circuits with both unitary gates and measurements, is termed as measurement-induced phase transition (MIPT). We study the behavior of MIPT in circuits comprising of two-qubit unitary gates parameterized by Cartan decomposition. We show that the entangling power and gate typicality of the two-qubit local unitaries employed in the circuit can be used to explain the behavior of global bipartite entanglement the circuit can sustain. When the two-qubit gate throughout the circuit is the identity and measurements are the sole driver of the entanglement behavior, we obtain an analytical estimate for the entanglement entropy that shows remarkable agreement with numerical simulations. We also find that the entangling power and gate typicality enable the classification of the two-qubit unitaries by different universality classes of phase transitions that can occur in the hybrid circuit. For all unitaries in a particular universality class, the transition from volume to area law of entanglement occurs with the same exponent that characterizes the phase transition.

DOI: 10.1103/PhysRevA.110.062422

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.062422