Compact set of invariants characterizing graph states of up to eight qubits

Abstract

The set of entanglement measures proposed by Hein, Eisert, and Briegel for n-qubit graph states [Phys. Rev. A 69, 062311 (2004)] fails to distinguish between inequivalent classes under local Clifford operations if n > 6. On the other hand, the set of invariants proposed by van den Nest, Dehaene, and De Moor (VDD) [Phys. Rev. A 72, 014307 (2005)] distinguishes between inequivalent classes, but contains too many invariants (more than 2 10^{36} for n=7) to be practical. Here we solve the problem of deciding which entanglement class a graph state of n < 9 qubits belongs to by calculating some of the state's intrinsic properties. We show that four invariants related to those proposed by VDD are enough for distinguishing between all inequivalent classes with n < 9 qubits.

arXiv commentREVTeX4, 9 pages, 1 figure

References in corpus (10)

• Three qubits can be entangled in two inequivalent ways
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Multi-party entanglement in graph states
• Quantum error-correcting codes associated with graphs
• Graphical description of the action of local Clifford transformations on graph states
• The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
• Local unitary versus local Clifford equivalence of stabilizer states
• Local unitary versus local Clifford equivalence of stabilizer and graph states
• Entanglement in eight-qubit graph states
• Finite set of invariants to characterize local Clifford equivalence of stabilizer states

Cited by in corpus (10)

• Measurement-based quantum repeaters
• Entanglement Witnesses for Graph States: General Theory and Examples
• Entanglement and nonclassical properties of hypergraph states
• Optimal preparation of graph states
• Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques
• Graph states and local unitary transformations beyond local Clifford operations
• Graphical description of unitary transformations on hypergraph states
• Shor-Laflamme distributions of graph states and noise robustness of entanglement
• Many-body quantum resources of graph states
• Small quantum networks in the qudit stabilizer formalism