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| | In [[quantum mechanics]], and especially [[quantum information processing]], the '''entropy exchange''' of a [[quantum operation]] <math>\phi \,</math> acting on the [[density matrix]] <math>\rho_Q \,</math> of a system <math>Q \,</math> is defined as |
| | :<math>S(\rho,\phi) \equiv S[Q',R'] = S(\rho_{QR}')</math> |
| | where <math>S(\rho_{QR}') \,</math> is the [[von Neumann entropy]] of the system <math>Q \,</math> and a fictitious [[Purification of quantum state|purifying]] auxiliary system <math>R \,</math> after they are operated on by <math>\phi \,</math>. Here, |
| | :<math>\rho_{QR} = |QR\rangle\langle QR| \quad </math> , |
| | :<math>\mathrm{Tr}_R[\rho_{QR}] = \rho_Q \quad </math> , |
| | and |
| | :<math>\rho_{QR}' = \phi[\rho_{QR}] \quad</math> . |
| | |
| | ==References== |
| | * Nielsen, Michael A. and [[Isaac L. Chuang]] (2000). ''Quantum Computation and Quantum Information'', Cambridge University Press, ISBN 0-521-63503-9 |
| | |
| | [[Category:Quantum information science]] |
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| | {{Quantum-stub}} |
In quantum mechanics, and especially quantum information processing, the entropy exchange of a quantum operation acting on the density matrix of a system is defined as
where is the von Neumann entropy of the system and a fictitious purifying auxiliary system after they are operated on by . Here,
- ,
- ,
and
- .
References
- Nielsen, Michael A. and Isaac L. Chuang (2000). Quantum Computation and Quantum Information, Cambridge University Press, ISBN 0-521-63503-9
Template:Quantum-stub