Entanglement of multi-qubit states representing directed networks and its detection with quantum computing
arXiv:2407.09990 · doi:10.1016/j.physleta.2024.129815
Abstract
We consider quantum graph states that can be mapped to directed weighted graphs, also known as directed networks. The geometric measure of entanglement of the states is calculated for the quantum graph states corresponding to arbitrary graphs. We find relationships between the entanglement and the properties of the corresponding graphs. Namely, we obtain that the geometric measure of entanglement of a qubit with other qubits in the graph state is related to the weights of ingoing and outgoing arcs with respect to the vertex representing the qubit, outdegree and indegree of the corresponding vertex in the graph. For unweighted and undirected graphs, the entanglement depends on the degree of the corresponding vertex. Quantum protocol for quantifying of the entanglement of the quantum graph states is constructed. As an example, a quantum graph state corresponding to a chain is examined, and the entanglement of the state is calculated on AerSimulator.
References in corpus (30)
- Quantum entanglement
- Experimental quantum teleportation
- Multi-party entanglement in graph states
- Quantum Cryptography with Entangled Photons
- Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
- Graph States for Quantum Secret Sharing
- Quantum error-correcting codes associated with graphs
- Chip-to-chip quantum teleportation and multi-photon entanglement in silicon
- Bell Inequalities for Graph States
- 16-qubit IBM universal quantum computer can be fully entangled
- Experimental demonstration of a graph state quantum error-correction code
- Entanglement in a 20-Qubit Superconducting Quantum Computer
- Graph States as a Resource for Quantum Metrology
- Demonstration of Entanglement Purification and Swapping Protocol to Design Quantum Repeater in IBM Quantum Computer
- Pairwise thermal entanglement in Ising-XYZ diamond chain structure in an external magnetic field
- Quantum circuits for maximally entangled states
- Entanglement in eight-qubit graph states
- Quantum error correction codes and absolutely maximally entangled states
- Efficient quantum pseudorandomness with simple graph states
- Quantifying geometric measure of entanglement by mean value of spin and spin correlations for pure and mixed states
- Identification of networking quantum teleportation on 14-qubit IBM universal quantum computer
- Entanglement of graph states of spin system with Ising interaction and its quantifying on IBM's quantum computer
- Detecting entanglement by the mean value of spin on a quantum computer
- Geometric measure of entanglement of multi-qubit graph states and its detection on a quantum computer
- Unveiling the geometric meaning of quantum entanglement: discrete and continuous variable systems
- Efficient Entanglement Measure for Graph States
- Two-colorable graph states with maximal Schmidt measure
- Measuring entanglement of a rank-2 mixed state prepared on a quantum computer
- Correlations and projective measurements in maximally entangled multipartite states
- Geometric properties of evolutionary graph states and their detection on a quantum computer