Abstract Multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states, are examined. The geometric measure of entanglement of a qubit with other qubits is found for the graph states represented by arbitrary graphs. The entanglement depends on the degree of the vertex representing the qubit, the absolute values of the parameter of the phase shift gate and the parameter of state the gate is acting on. Also the geometric measure of entanglement of the graph states is quantified on the quantum computer . The results obtained on the quantum device are in good agreement with analytical ones.
Bi-partite entanglement in multi-qubit systems cannot be shared freely. The rules of quantum mechanics impose bounds on how multi-qubit systems can be correlated. In this paper we utilize a concept of entangled graphs with weighted edges in order to analyze pure quantum states of multi-qubit systems. Here qubits are represented by vertexes of the graph while the presence of bi-partite entanglement is represented by an edge between corresponding vertexes. The weight of each edge is defined to be the entanglement between the two qubits connected by the edge, as measured by the concurrence. We prove that each entangled graph with entanglement bounded by a specific value of the concurrence can be represented by a pure multi-qubit state. In addition we present a logic network with O(N2) elementary gates that can be used for preparation of the weighted entangled graphs of N qubits.
Distributed entanglement across multi-node quantum networks is essential for a wide range of quantum technologies, including modular quantum computers, distributed sensing and metrology, and multi-party secure communication protocols. Such large-scale quantum networks will require photonic interconnects to generate and sustain entangled states across localized nodes. Previously, three-node distributed Greenberger-Horne-Zeilinger (GHZ) states have been generated between solid-state qubits and atomic ensembles, but not yet in the platform of individual atomic qubits, which can be replicated, detected, and individually controlled with high fidelity. Here we report the first fully-distributed GHZ state of qubits across a three-node quantum network of single atomic memories, using photonic interconnects. We achieve a bounded fidelity of
0.841(17)≤F≤0.881(17) at an entanglement generation rate of 0.095(5)/sec and measure a clear violation of Mermin's inequality while closing the detection loophole for the first time in a fully-distributed multipartite entangled state.
We consider multi-qubit entangled quantum states known in the literature as one-layer variational quantum states. The states can also be considered as quantum graph states representing directed and weighted graphs. The corresponding variational quantum protocols include
RY,RZ, and entangling blocks with
RXXgates. We examine the general case in which the entangling blocks have an arbitrary structure, namely,
RXXgates are applied to arbitrary pairs of qubits. This case corresponds to an arbitrary structure of the associated weighted and directed graphs. Variational quantum states, as well as quantum graph states, have broad applications in various fields of quantum computing, including quantum machine learning, quantum error correction, and optimization algorithms, and others. One of the key resources in quantum computing is entanglement. We analytically calculate the entanglement distance for variational quantum states with entangling blocks of arbitrary structure. The dependence of entanglement on the parameters of the variational quantum state and on the characteristics of the corresponding weighted and directed graphs is investigated. We find that the entanglement of a qubit with other qubits in the state depends on the outdegree and indegree of the corresponding vertex in the graph, as well as on the weights of the incoming and outgoing arcs associated with that vertex. Quantum protocols for quantifying the entanglement distance of variational quantum states have been constructed. For particular cases of variational quantum states, the dependence of entanglement distance on the state parameters has been examined using quantum computation on the Aer simulator.