Measuring the parity of an $N$-qubit state

Abstract

We present a scheme for a projective measurement of the parity operator $P_z={\prod }_{i=1}^N{\sigma }_z^{(i)}$ of $N$-qubits. Our protocol uses a single ancillary qubit, or a probe qubit, and involves manipulations of the total spin of the $N$ qubits without requiring individual addressing. We illustrate our protocol in terms of an experimental implementation with atomic ions in a two-zone linear Paul trap, and further discuss its extensions to several more general cases.

4 pages, 2 figures