  In neutrino oscillation with non-standard interactions (NSI) the system is
enriched with CP violation caused by phases due to NSI in addition to the
standard lepton Kobayashi-Maskawa phase \delta. In this paper we show that it
is possible to disentangle the two CP violating effects by measurement of muon
neutrino appearance by a near-far two detector setting in neutrino factory
experiments. Prior to the quantitative analysis we investigate in detail the
various features of the neutrino oscillations with NSI, but under the
assumption that only one of the NSI elements, \epsilon_{e \mu} or \epsilon_{e
\tau}, is present. They include synergy between the near and the far detectors,
the characteristic differences between the \epsilon_{e \mu} and
\epsilon_{e\tau} systems, and in particular, the parameter degeneracy. Finally,
we use a concrete setting with the muon energy of 50 GeV and magnetized iron
detectors at two baselines, one at L=3000 km and the other at L=7000 km, each
having a fiducial mass of 50 kton to study the discovery potential of NSI and
its CP violation effects. We demonstrate, by assuming 4 \times 10^{21} useful
muon decays for both polarities, that one can identify non-standard CP
violation down to | epsilon_{e \mu} | \simeq \text{a few} \times 10^{-3}, and |
\epsilon_{e \tau} | \simeq 10^{-2} at 3\sigma CL for \theta_{13} down to \sin^2
2\theta_{13} = 10^{-4} in most of the region of \delta. The impact of the
existence of NSI on the measurement of \delta and the mass hierarchy is also
worked out.
