Multipartite secure state distribution

Dür, W.; Calsamiglia, John; Briegel, Hans J.

doi:10.1103/physreva.71.042336

Cited by 36 publications

(37 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Most prominently, the graph states that correspond to a two dimensional square lattice, also known as the 2D cluster states [2], are known to be universal resources for measurement based quantum computation [3,4]. Other graph states serve as algorithmic specific resources for measurement based quantum computation, are codewords of error correcting codes known as Calderbank-Shor-Steane codes [6,7], or are used in multiparty communication schemes [8,9,10]. Graph states are specific instances of stabilizer states, which allows for an efficient description and manipulation of the states by making use of the stabilizer formalism [5].…”

Section: Introductionmentioning

confidence: 99%

Graph states as ground states of many-body spin-1∕2Hamiltonians

et al. 2008

Self Cite

View full text Add to dashboard Cite

We consider the problem whether graph states can be ground states of local interaction Hamiltonians. For Hamiltonians acting on n qubits that involve at most two-body interactions, we show that no n-qubit graph state can be the exact, non-degenerate ground state. We determine for any graph state the minimal d such that it is the non-degenerate ground state of a d-body interaction Hamiltonian, while we show for d ′ -body Hamiltonians H with d ′ < d that the resulting ground state can only be close to the graph state at the cost of H having a small energy gap relative to the total energy. When allowing for ancilla particles, we show how to utilize a gadget construction introduced in the context of the k-local Hamiltonian problem, to obtain n-qubit graph states as non-degenerate (quasi-)ground states of a two-body Hamiltonian acting on n ′ > n spins.

show abstract

Section: Introductionmentioning

confidence: 99%

Graph states as ground states of many-body spin-1∕2Hamiltonians

et al. 2008

Self Cite

View full text Add to dashboard Cite

show abstract

“…[109], three different solutions to the secure-state distribution problem were put forward (see Fig. 17).…”

Section: Secure State Distributionmentioning

confidence: 99%

Entanglement purification and quantum error correction

2007

View full text Add to dashboard Cite

Abstract. We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context of quantum communication, where we emphasize its close relation to quantum error correction. Various bipartite and multipartite entanglement purification protocols are discussed, and their performance under idealized and realistic conditions is studied. Several applications of entanglement purification in quantum communication and computation are presented, which highlights the fact that entanglement purification is a fundamental tool in quantum information processing.

show abstract

“…proportional to the area of the surface of the block). The fact that the sensitivity to noise of a cluster state does not scale with the number of (physical) qubits [21], is of due to the fact that it is effectively made up by local singlet pairs. This insight also enables to construct distillation protocols for cluster states by translating bipartite distillation protocols to the valence bond picture [22].…”

mentioning

confidence: 99%

Valence-bond states for quantum computation

2004

View full text Add to dashboard Cite

Cluster states are entangled multipartite states which enable to do universal quantum computation with local measurements only. We show that these states have a very simple interpretation in terms of valence bond solids, which allows to understand their entanglement properties in a transparent way. This allows to bridge the gap between the differences of the measurement-based proposals for quantum computing, and we will discuss several features and possible extensions.

show abstract

Multipartite secure state distribution

Cited by 36 publications

References 15 publications

Graph states as ground states of many-body spin-1∕2Hamiltonians

Graph states as ground states of many-body spin-1∕2Hamiltonians

Entanglement purification and quantum error correction

Valence-bond states for quantum computation

Contact Info

Product

Resources

About