A multilevel approach for a class of semidefinite programs

Author(s):  
Fu Lin ◽  
Zichao Di ◽  
Sven Leyffer
2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mark Girard ◽  
Martin Plávala ◽  
Jamie Sikora

AbstractGiven two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.


Author(s):  
Ismael Esteban Lozano ◽  
Yanina Grisel Piazza ◽  
Paola Babay ◽  
Emanuel Sager ◽  
Fernando Román de la Torre ◽  
...  

2012 ◽  
Vol 50 (9) ◽  
pp. 1847-1856 ◽  
Author(s):  
Margherita Brondino ◽  
Silvia A. Silva ◽  
Margherita Pasini

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