Quantum information with continuous variables

Abstract

Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or entanglement. We review the progress in quantum information based on continuous quantum variables, with emphasis on quantum optical implementations in terms of the quadrature amplitudes of the electromagnetic field.

Quantum entanglement and disentanglement of multi-atom systems

“…Apart from two qubit systems, various attempts have been made to produce entanglement in more complex systems. An extensive research have been done on generation of multipartite continuous variable entangled states of atomic ensembles form multi-mode squeezed light [50][51][52][53]. The reason for using atomic ensembles is twofold.…”

Privacy of a lossy bosonic memory channel

“…Quantum communications concern the study of quantum channels that also use continuous alphabets [1]. These can be modeled by bosonic field modes whose phase space quadratures enable for continuous variable encoding/decoding.…”

“…Since we deal with Gaussian states, it turns useful to work with Wigner distribution functions [1]. Let q k , p k be the quadrature variables ofâ k , i.e.…”

“…is the single kmode displacement operator, corresponding to the complex number µ k andŜ a (r) = exp 1 2 r â † 1â † 2 −â 1â2 denotes the two-mode squeeze operator [1], with r the entanglement parameter between the two inputs (r = 0 refers to input product states). Let us write the input (1) as a density operator…”

“…These can be modeled by bosonic field modes whose phase space quadratures enable for continuous variable encoding/decoding. Lossy bosonic channel, which consists of a collection of bosonic modes that lose energy en route from the transmitter to the receiver, belongs to the class of Gaussian channels which provide a fertile testing ground for the general theory of quantum channels' capacities [2] and are easy to implement experimentally with high accuracy level (beam splitters or squeezers are examples of Gaussian operations) [1]. Hence, the increasing attention devoted to channels with memory effects, where the noise may be strongly correlated between uses of the channel, has been extended to bosonic channels [3].…”