Table 1 The classification of catalysts

From: Teleportation with embezzling catalysts

Constraints

Exact catalyst

Approximate catalyst

  

Correlated

Embezzling

Error on the target state σA

× 

✓

✓

Correlation between systems A and C

× 

✓

✓

Error on the catalyst τC

× 

× 

✓

  1. An exact catalyst56,62,63,64,65,66,67 is a state that facilitates an otherwise impossible transformation, without undergoing any change itself or becoming correlated with other systems. We can relax the conditions for exact catalysts and define a more general notion of approximate catalysts, as given in Def. 1. Approximate catalysts can be further classified into two types: correlated catalysts57,68,69,70,71,72,73,74,75,76,77 and embezzling catalysts11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34. A correlated catalyst is one in which no errors occur during its use, while an embezzling catalyst is characterized by small errors occurring during its utilization.
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