Quantum entanglement in multi-qubit systems

Martin Plesch, Vladimír Bužek

We study how bi-partite quantum entanglement (measured in terms of a concurrence) can be shared in multi-qubit systems. We introduce a concept of the entangled graph such that each qubit of a multi-partite system is associated with a vertex while a bi-partite entanglement between two specific qubits is represented by an edge. We prove that any entangled graph can be associated with a pure state of a multi-qubit system. We also derive bounds on the concurrence for some weighted entangled graphs (the weight corresponds to the value of concurrence associated with the given edge).

Mikko M. Ervasti

Aditi Sen

Xin-Wei Zha, Chenzhi Yuan, Yanpeng Zhang

We first present a generalized criterion for maximally entangled states of 2–8 and in theory to arbitrary-number qubits. By this criterion, some known highly entangled multi-qubit states are examined and a new genuine eight-qubit maximally entangled state is obtained. For the four-, seven- and eight-qubit system in which no perfect maximally multi-qubit entangled state (MMES) was thought to exist before, we find that the proven four- and eight-qubit MMESs and the suspected seven-qubit MMES, are not completely mixed in subsystems with two, four and three qubits, respectively, but are completely mixed in subsystems with fewer qubits. The new criterion and MMES can play important roles in quantum information technology, such as teleportation and dense coding.

X. Wang, Klaus Mølmer

Martin Plesch, Jaroslav Novotný, Zuzana Dzuráková +1 more

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.