  Direct measurement protocol allows reconstructing specific elements of the
density matrix of a quantum state without using quantum state tomography.
However, the direct measurement protocols to date are primarily based on weak
or strong measurements with ancillary pointers, which interacts with the
investigated system to extract information about the specified elements. Here
we present a new direct measurement protocol based on phase-shifting technique
which do not need ancillary pointers. In this protocol, at most six different
project measurements suffice to determine any specific element of an unknown
quantum density matrix. A concrete quantum circuit to implement the
phase-shifting measurement protocol for multi-qubit states is provided, where
the circuit is composed of just single-qubit gates and two multi-qubit
controlled-phase gates. This protocol is also extended to the
continuous-variable cases for directly measuring the Wigner function.
Furthermore, we show that the protocol has the advantage of reducing
measurement and device complexity in the task of measuring the complete density
matrix compared to quantum state tomography in some quantum experiments. Our
method provides an efficient way to characterize arbitrary quantum systems,
which may be used to predict various properties of a quantum system and find
applications in quantum information processing.
