Information upper bounds in composite quantum systems

• URL: http://arxiv.org/abs/2411.09150v2
• Date: Fri, 15 Nov 2024 08:10:52 GMT
• Title: Information upper bounds in composite quantum systems
• Authors: Zhaoyang Dong, Yuexian Hou, Chenguang Zhang, Yingjie Gao,
• Abstract summary: We decompose the quantum state and focus on the total amount of information contained in the components that constitute the legal quantum state itself. We analytically proved that the upper bound of the posterior information content of quantum pure states is exactly equal to 2.
• Score: 11.005712568346414
• License:
• Abstract: Quantum information entropy is regarded as a measure of coherence between the observed system and the environment or between many-body. It is commonly described as the uncertainty and purity of a mixed state of a quantum system. Different from traditional information entropy, we introduce a new perspective, aiming to decompose the quantum state and focus on the total amount of information contained in the components that constitute the legal quantum state itself. Based on $\chi^2$ divergence, we define the posterior information content of quantum pure states. We analytically proved that the upper bound of the posterior information of a 2-qubit system is exactly equal to 2. At the same time, we found that when the number of qubits n>2 in the quantum system, the process of calculating the upper bound of the posterior information can always be summarized as a standard semi-definite programming. Combined with numerical experiments, we generalized the previous hypothesis: A composite quantum system composed of n-qubits, the upper bound of the posterior information should be equal to n.

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