Information upper bounds in composite quantum systems

• URL: http://arxiv.org/abs/2411.09150v4
• Date: Thu, 24 Jul 2025 17:36:06 GMT
• Title: Information upper bounds in composite quantum systems
• Authors: Zhaoyang Dong, Yuexian Hou, Chenguang Zhang, Yingjie Gao,
• Abstract summary: We prove the information upper bound of the 2-qubits system by analyzing the fundamental correlation structure among the parameters of quantum systems.<n>Our core conclusion is: the information-carrying capacity (information upper bound) of an $n$-qubits system is $n$ classical bits.
• Score: 11.005712568346414
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Pusey-Barrett-Rudolph (PBR) no go theorem provides arguments for the reality of quantum states, indicating that quantum states ought to be ontic. For $\psi$-ontology, a $n$-qubits system is specified by $2^n$ complex parameters. However, subject to the Holevo bound, an $n$-qubits system can only encode at most $n$ bits of classical information. The two form an inexplicable contradiction. Therefore, based on a posterior statistical inference framework compatible with the $\psi$-ontology perspective, we generally proved the information upper bound of the 2-qubits system by analyzing the fundamental correlation structure among the parameters of quantum systems. And we extended it to the $n$-qubits system based on the convex optimization process. Our core conclusion is: the information-carrying capacity (information upper bound) of an $n$-qubits system is $n$ classical bits. The reason of the scale contrast is that the high degree of correlation among the parameters of the quantum system causes the amount of information that the system can carry to only reach the order of $O(n)$.

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