  Detection of entanglement in quantum states is one of the most important
problems in quantum information processing. However, it is one of the most
challenging tasks to find a universal scheme which is also desired to be
optimal to detect entanglement for all states of a specific class--as always
preferred by experimentalists. Although, the topic is well studied at least in
case of lower dimensional compound systems, e.g., two-qubit systems, but in the
case of continuous variable systems, this remains as an open problem. Even in
the case of two-mode Gaussian states, the problem is not fully solved. In our
work, we have tried to address this issue. At first, a limited number of
Hermitian operators is given to test the necessary and sufficient criterion on
the covariance matrix of separable two-mode Gaussian states. Thereafter, we
present an interferometric scheme to test the same separability criterion in
which the measurements are being done via Stokes-like operators. In such case,
we consider only single-copy measurements on a two-mode Gaussian state at a
time and the scheme amounts to the full state tomography. Although this latter
approach is a linear optics based one, nevertheless it is not an economic
scheme. Resource-wise a more economical scheme than the full state tomography
is obtained if we consider measurements on two copies of the state at a time.
However, optimality of the scheme is not yet known.
