158 research outputs found
Compatibility conditions on local and global spectra for -mode Gaussian states
Compatibility conditions between the (global) spectrum of an -mode
Gaussian state and the spectra of the individual modes are presented, making
optimal use of beam splitter and (two-mode) squeezing transformations. An
unexpected bye-product of our elementary approach is the result that every
two-mode Gaussian state is uniquely determined, modulo local transformations,
by its global spectrum and local spectra -- a property shared not even by a
pair of qubits.Comment: 10 Page
Entanglement of Formation for Gaussian States
The entanglement of formation (EOF) is computed for arbitrary two-mode
Gaussian states. Apart from a conjecture, our analysis rests on two main
ingredients. The first is a four-parameter canonical form we develop for the
covariance matrix, one of these parameters acting as a measure of EOF, and the
second is a generalisation of the EPR correlation, used in the work of Giedke
{\em et al} [Phys. Rev. Lett. {\bf 91}, 107901 (2003)], to noncommuting
variables. The conjecture itself is in respect of an extremal property of this
generalized EPR correlation.Comment: 4 page
Entanglement and nonclassicality for multi-mode radiation field states
Nonclassicality in the sense of quantum optics is a prerequisite for
entanglement in multi-mode radiation states. In this work we bring out the
possibilities of passing from the former to the latter, via action of
classicality preserving systems like beamsplitters, in a transparent manner.
For single mode states, a complete description of nonclassicality is available
via the classical theory of moments, as a set of necessary and sufficient
conditions on the photon number distribution. We show that when the mode is
coupled to an ancilla in any coherent state, and the system is then acted upon
by a beamsplitter, these conditions turn exactly into signatures of NPT
entanglement of the output state. Since the classical moment problem does not
generalize to two or more modes, we turn in these cases to other familiar
sufficient but not necessary conditions for nonclassicality, namely the Mandel
parameter criterion and its extensions. We generalize the Mandel matrix from
one-mode states to the two-mode situation, leading to a natural classification
of states with varying levels of nonclassicality. For two--mode states we
present a single test that can, if successful, simultaneously show
nonclassicality as well as NPT entanglement. We also develop a test for NPT
entanglement after beamsplitter action on a nonclassical state, tracing
carefully the way in which it goes beyond the Mandel nonclassicality test. The
result of three--mode beamsplitter action after coupling to an ancilla in the
ground state is treated in the same spirit. The concept of genuine tripartite
entanglement, and scalar measures of nonclassicality at the Mandel level for
two-mode systems, are discussed. Numerous examples illustrating all these
concepts are presented.Comment: Latex, 46 page
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