Unavoidable decoherence in the quantum control of an unknown state

D. Kielpinski 1 , 2 , R.A. Briggs 2 , 3 , and H.M. Wiseman 1 , 2 , 4
  • 1 Centre for Quantum Dynamics, Griffith University, Nathan QLD 4111, Australia
  • 2 School of Biomolecular and Physical Sciences, Griffith University, Nathan QLD 4111, Australia
  • 3 School of Philosophy, Australian National University, Canberra ACT 0200, Australia
  • 4 ARC Centre of Excellence for Quantum Computation and Communication Technology, Griffith University, Nathan QLD 4111, Australia

Abstract

A common objective for quantum control is to force a quantum system, initially in an unknown state, into a particular target subspace. We show that if the subspace is required to be a decoherence-free subspace of dimension greater than 1, then such control must be decoherent. That is, it will take almost any pure state to a mixed state. We make no assumptions about the control mechanism, but our result implies that for this purpose coherent control offers no advantage, in principle, over the obvious measurement-based feedback protocol.

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