Quantum catalyst

<p>In <a href="/facts/Quantum_information_theory/Bl9QIvHj">quantum information theory</a>, a quantum catalyst is a special <a href="/facts/Ancilla_bit/pDfqX9DJ">ancillary</a> <a href="/facts/Quantum_state/7jbxd7Dx">quantum state</a> whose presence enables certain local <a href="/facts/Transformation_(function)/Yr2J3o8H">transformations</a> that would otherwise be impossible. Quantum catalytic behaviour has been shown to arise from the phenomenon of catalytic <a href="/facts/Majorization/RSSsgWTP">majorization</a>.
</p><p>The catalytic majorization relation can be used to find which transformations of jointly held pure quantum states are possible via local <a href="/facts/Operation_(mathematics)/Yplv602Q">operations</a> and classical communication (LOCC); particularly when an additional jointly held state is optionally specified to facilitate the transformation without being consumed. In the process sometimes referred to as <a href="/facts/Quantum_entanglement/afzslwN0">entanglement</a> catalysis, the catalyst can be understood as that temporarily involved entangled state. For <a href="/facts/Bipartite_graph/xWcXV9MB">bipartite</a> pure entangled states that can be transformed in this way with <a href="/facts/Unitarity_(physics)/x2gXDAsS">unit probability</a>, the respective Schmidt coefficients are said to satisfy the trumping relation, a mathematical relation which is an extension of the majorization relation. If correlations between the system and the catalyst are allowed, catalytic transformations between bipartite pure states are characterized via the <a href="/facts/Entanglement_entropy/yLSXsIMA">entanglement entropy</a>. Others have shown how quantum catalytic behaviour arises under a probabilistic approach via <a href="/facts/Stochastic_dominance/HAsIHbEB">stochastic dominance</a> with respect to the <a href="/facts/Convolution/PVPrdz9J">convolution of measures</a>.
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Quantum catalyst open-in-new

Quantum catalyst