Quantum information entropy and multi-qubit entanglement

Zixuan Hu, Sabre Kais

Abstract A “qubit information logic” (QIL) theory is developed that uses the “qubit information equation” (QIE) and logic to describe the correlation behaviors of multi‐qubit entanglement. Introducing the “global information status” and “local information availability”, the QIL gives an alternative and natural interpretation of the “spooky action” and the quantum no‐communication theorem. Compared to the conventional entropy‐based entanglement theories, the QIL directly describes the correlation of each possible pair of qubits and how the correlation changes when other qubits are measured. This makes the QIL more advantageous in describing the correlation properties of multi‐qubit entanglement, which is illustrated by studying the dormant entanglement phenomenon. The QIL theory's usefulness is further demonstrated by understanding and designing an exotic quantum state where two qubits can be entangled but not correlated in any arbitrary basis. Overall the QIL provides an alternative and intuitive understanding of multi‐qubit entanglement that is, compared to the conventional theories, directly focused on the correlation behaviors between qubits and thus more suitable for designing exotic quantum states that may be used in quantum computing and information processing.

V. P. Belavkin, Masanori Ohya

Jincheng Zhang

This paper proposes a novel information encoding scheme, termed Quantum Information Entropy Encoding (QIE), leveraging quantum entanglement and coherence to potentially surpass the entropy limits established by classical information theory. QIE utilizes multi-qubit entanglement states, precisely manipulating their coherence, to establish highly correlated information representations between quantum bits. The encoding process employs quantum gate operations to transform these entangled states, facilitating information compression and transmission. Decoding relies on measurements of the entangled states to recover the original information. The core claim is the potential for QIE to achieve higher compression rates and faster transmission speeds compared to conventional entropy coding methods. This approach represents a departure from traditional information theory, exploring the utilization of quantum mechanical phenomena for enhanced information processing. The theoretical framework presented here lays the groundwork for future investigations into the feasibility and limitations of QIE.

John Cardy

Jeong San Kim

We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order $q$, we first provide a generalized monogamy inequality of multi-qubit entanglement for $q=2$ or $3$. This generalization encapsulates multi-qubit CKW-type inequality as a special case. We further provide a generalized polygamy inequality of multi-qubit entanglement in terms of Tsallis-$q$ entropy for $1 \leq q \leq2$ or $3 \leq q \leq 4$, which also contains the multi-qubit polygamy inequality as a special case.

Andrew G. White, Daniel F. V. James, William J. Munro +1 more