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We investigate properties of charge detection and detection-induced dephasing of a charge qubit interacting with an electron beam collider composed of a quantum point contact. We predict that the interference of the qubit is fully restored when the two inputs are identically biased so that all the electrons suffer two-electron collision, unlike the case without collision. This phenomenon is related to Fermi statistics and illustrates the peculiar nonlocality of dephasing. We also describe the detection properties of entangled electron pairs. For singlet pairs, the sensitivity of charge detection is enhanced which originates from the bunching behavior of electrons. This demonstrates that control of exchange statistics of particles can help sensitive charge detection.