Extracting GHZ states from linear cluster states
Jarn de Jong, Frederik Hahn, Nikolay Tcholtchev, Manfred Hauswirth, Anna Pappa
Abstract
Quantum information processing architectures typically only allow for nearest-neighbor entanglement creation. In many cases, this prevents the direct generation of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>GHZ</a:mi></a:math> states, which are commonly used for many communication and computation tasks. Here, we show how to obtain <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>GHZ</b:mi></b:math> states between nodes in a network that are connected in a straight line, naturally allowing them to initially share linear cluster states. We prove a strict upper bound of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mo>⌊</c:mo><c:mo>(</c:mo><c:mi>n</c:mi><c:mo>+</c:mo><c:mn>3</c:mn><c:mo>)</c:mo><c:mo>/</c:mo><c:mn>2</c:mn><c:mo>⌋</c:mo></c:mrow></c:math> on the size of the set of nodes sharing a <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>GHZ</d:mi></d:math> state that can be obtained from a linear cluster state of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>n</e:mi></e:math> qubits, using local Clifford unitaries, local Pauli measurements, and classical communication. Furthermore, we completely characterize all selections of nodes below this threshold that can share a <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>GHZ</f:mi></f:math> state obtained within this setting. Finally, we demonstrate these transformations on the IBMQ Montreal quantum device for linear cluster states of up to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>n</g:mi><g:mo>=</g:mo><g:mn>19</g:mn></g:mrow></g:math> qubits. Published by the American Physical Society 2024