Optimal processing of reversible quantum channels
arXiv:1308.3254 · doi:10.1016/j.physleta.2014.04.042
Abstract
We consider the general problem of the optimal transformation of N uses of (possibly different) unitary channels to a single use of another unitary channel in any finite dimension. We show how the optimal transformation can be fully parallelized, consisting in a preprocessing channel followed by a parallel action of all the N unitaries and a final postprocessing channel. Our techniques allow to achieve an exponential reduction in the number of the free parameters of the optimization problem making it amenable to an efficient numerical treatment. Finally, we apply our general results to find the analytical solution for special cases of interest like the cloning of qubit phase gates.
14 pages, 2 figures
References in corpus (14)
- Quantum correlations with no causal order
- Informational derivation of Quantum Theory
- Transforming quantum operations: quantum supermaps
- A derivation of quantum theory from physical requirements
- Continuous Variable Quantum Cryptography using Two-Way Quantum Communication
- Quantum computation with programmable connections between gates
- Quantum Teleportation of Optical Quantum Gates
- Optimal quantum tomography for states, measurements, and transformations
- Quantum information becomes classical when distributed to many users
- Quantum Networks: general theory and applications
- Quantum learning algorithms for quantum measurements
- Information - Disturbance Tradeoff in the Estimation of a Unitary Transformation
- Minimal computational-space implementation of multi-round quantum protocols
- Memory cost of quantum protocols
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