13 Aug 2020
•
Sahoo Surya Narayan
•
Chakraborti Sanchari
•
Pati Arun K.
•
Sinha Urbasi
Quantum State Tomography (QST) has been the traditional method for
characterization of an unknown state. Recently, many direct measurement methods
have been implemented to reconstruct the state in a resource efficient way...In
this letter, we present an interferometric method, in which, any qubit state,
whether mixed or pure, can be inferred from the visibility, phase shift and
average intensity of an interference pattern using a single shot measurement --
hence, we call it Quantum State Interferography. This provides us with a "black
box" approach to quantum state estimation, wherein, between the incidence of
the photon and extraction of state information, we are not changing any
conditions within the set-up, thus giving us a true single shot estimation of
the quantum state. In contrast, standard QST requires at least two measurements
for pure state qubit and at least three measurements for mixed state qubit
reconstruction. We then go on to show that QSI is more resource efficient than
QST for quantification of entanglement in pure bipartite qubits. We
experimentally implement our method with high fidelity using the polarisation
degree of freedom of light. An extension of the scheme to pure states involving
$d-1$ interferograms for $d$-dimensional systems is also presented. Thus, the
scaling gain is even more dramatic in the qudit scenario for our method where
in contrast, standard QST, without any assumptions, scales roughly as $d^2$.(read more)