We propose a straightforward method to determine the maximal entanglement of pure states using the criterion of maximal I-concurrence, a measure of entanglement. The square of concurrence for a bipartition $X|X^\prime$ of a pure state is defined as $E^2_{X| X ^\prime}=2[1-tr({ρ_X}^2)]$ . From this, we can infer that the concurrence $E_{X| X ^\prime}$ reaches its maximum when $tr({ρ_X}^2)$ is minimized. Using this approach, we identify numerous Absolutely Maximally Entangled (AME) pure states that exhibit maximal entanglement across all possible bipartitions. Conditions are derived for pure states to achieve maximal mixedness in all bipartitions, revealing that any pure state with an odd number of subsystem coefficients does not meet the AME criterion. Furthermore, we obtain equal maximal multipartite entangled pure states across all bipartitions using our maximal concurrence criterion.We propose a straightforward method to determine the maximal entanglement of pure states using the criterion of maximal I-concurrence, a measure of entanglement. The square of concurrence for a bipartition $X|X^\prime$ of a pure state is defined as $E^2_{X| X ^\prime}=2[1-tr({ρ_X}^2)]$. From this, we can infer that the concurrence $E_{X| X ^\prime}$ reaches its maximum when $tr({ρ_X}^2)$ is minimized. Using this approach, we identify numerous Absolutely Maximally Entangled (AME) pure states that exhibit maximal entanglement across all possible bipartitions. Conditions are derived for pure states to achieve maximal mixedness in all bipartitions, revealing that any pure state with an odd number of subsystem coefficients does not meet the AME criterion. Furthermore, we obtain equal maximal multipartite entangled pure states across all bipartitions using our maximal concurrence criterion.

arXiv:2501.15477Jan 26, 20250 citations

Universal maximally entangled states

M. Revzen

Quantum Studies Mathematics and FoundationsSep 23, 20142 citations

A Criterion to identify maximally entangled nine-qubit state

Xinwei Zha, Irfan Ahmed, Da Zhang +1 more

Abstract We present a generalized criterion for maximally entangled nine-qubit states, whose minimum averaged subsystem purity should be equal to 1/14. In this note, we prove that the absolutely maximally entangled state for nine qubits does not exist. In other words, we pronounce that the pure (9, 1, 5) 2 quantum error-correcting code does not exist. Further, we construct a new genuine nine-qubit maximally entangled states of 110,15 and 1 balanced purities equal to 1/16, 1/8 and 1/4, respectively. We found that the marginal density matrices for subsystems of 1,2,3- qubits all completely mixed in these states; therefore, maximally entangled nine-qubit state is a 3-uniform state.Abstract We present a generalized criterion for maximally entangled nine-qubit states, whose minimum averaged subsystem purity should be equal to 1/14. In this note, we prove that the absolutely maximally entangled state for nine qubits does not exist. In other words, we pronounce that the pure (9, 1, 5) 2 quantum error-correcting code does not exist. Further, we construct a new genuine nine-qubit maximally entangled states of 110,15 and 1 balanced purities equal to 1/16, 1/8 and 1/4, respectively. We found that the marginal density matrices for subsystems of 1,2,3- qubits all completely mixed in these states; therefore, maximally entangled nine-qubit state is a 3-uniform state.

arXiv:1907.05612Laser Physics LettersJan 28, 20209 citations

Multilinear monogamy relations for multiqubit states

Xian Shi, Lin Chen, Mengyao Hu

The monogamy of entanglement means that entanglement cannot be freely shared. In 2014, Oliveira et al. [T. R. de Oliveira, M. F. Cornelio, and F. F. Fanchini, Phys. Rev. A 89, 034303 (2014)] proposed a monogamy relation in the linear version and considered it in terms of entanglement of formation. Here we generalize the above version and consider a multilinear monogamy relation for a multiqubit system in terms of entanglement of formation and concurrence. Based on the above results, we present an entanglement criterion for genuine entangled states; also we consider the absolutely maximally entangled states and present what an absolutely maximally entangled state is for a three-qubit system. Last, we apply our results to a three-qubit pure state in terms of quantum discord.The monogamy of entanglement means that entanglement cannot be freely shared. In 2014, Oliveira et al. [T. R. de Oliveira, M. F. Cornelio, and F. F. Fanchini, Phys. Rev. A 89, 034303 (2014)] proposed a monogamy relation in the linear version and considered it in terms of entanglement of formation. Here we generalize the above version and consider a multilinear monogamy relation for a multiqubit system in terms of entanglement of formation and concurrence. Based on the above results, we present an entanglement criterion for genuine entangled states; also we consider the absolutely maximally entangled states and present what an absolutely maximally entangled state is for a three-qubit system. Last, we apply our results to a three-qubit pure state in terms of quantum discord.

arXiv:1810.09926Physical Review AJul 28, 20217 citations

X|X^\prime

of a pure state is defined as

E^2_{X| X ^\prime}=2[1-tr({ρ_X}^2)]

. From this, we can infer that the concurrence

E_{X| X ^\prime}

reaches its maximum when

tr({ρ_X}^2)

is minimized. Using this approach, we identify numerous Absolutely Maximally Entangled (AME) pure states that exhibit maximal entanglement across all possible bipartitions. Conditions are derived for pure states to achieve maximal mixedness in all bipartitions, revealing that any pure state with an odd number of subsystem coefficients does not meet the AME criterion. Furthermore, we obtain equal maximal multipartite entangled pure states across all bipartitions using our maximal concurrence criterion.