  Concurrence introduced by Hill and Wootters [Phys. Rev. Lett. 78, 5022
(1997)], provides an important measure of entanglement for a general pair of
qubits that is strictly positive entangled states and vanishes for all
separable states. We present an extension of entanglement measure to general
continuous variable states of multiple degrees of freedom by generalizing the
Lagrange's identity and wedge product framework proposed by Bhaskara et al.
[Quantum Inf. Process. 16, 118 (2017)] for pure discrete variable systems in
arbitrary dimensions. A family of faithful entanglement measures is constructed
that admit necessary and sufficient conditions for separability across
arbitrary bipartitions presented by Vedral et al. [Phys. Rev. Lett. 16 2275
(1997)]. The computed entanglement measure in the present approach for general
Gaussian states, pair coherent states and non Gaussian continuous variable Bell
states, matches with known results. We also quantify entanglement of phase
randomized squeezed states and superposition of squeezed states. Our results
also simplify several results in quantum entanglement theory.

Quantum Physics