Gaussian quantum information

Abstract

The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.

Quantifying entanglement in two-mode Gaussian states

“…For many quantum communication protocols, Gaussian channels describe the decoherence introduced by the environment to a quantum state and represent the basic models of communication lines such as optical fibers [19]. Let us assume that a single mode of a two-mode squeezed vacuum state, i.e., a = b = 1+χ 2 1−χ 2 and c 1 = −c 2 = 2χ 1−χ 2 , with χ = tanh r ∈ [0,1), is sent through a Gaussian channel.…”

“…Let us assume that a single mode of a two-mode squeezed vacuum state, i.e., a = b = 1+χ 2 1−χ 2 and c 1 = −c 2 = 2χ 1−χ 2 , with χ = tanh r ∈ [0,1), is sent through a Gaussian channel. One-mode Gaussian channels can be defined as the transformation of the covariance matrix of the mode γ , i.e., γ → Uγ U T + V [19]. Typically, these channels are phase invariant and so produce states with balanced correlations that saturate the lower bound, i.e., r − = r o .…”

Quantum cloning machines and the applications

“…The criteria of CV cloning and teleportation are studied in (Grosshans and Grangier, 2001). We remark again that the reviews of CV quantum information can be found in (Braunstein and van Loock, 2005;Wang et al, 2007;Weedbrook et al, 2012).…”

“…Most schemes and protocols of quantum computation and quantum information can be realized and demonstrated by photonic state of CV, it may possesses unique advantage other than other systems. The reviews of CV quantum information can be found in (Braunstein and van Loock, 2005;Wang et al, 2007;Weedbrook et al, 2012), see spin squeezing in (Ma et al, 2011). An example of continuous systems is simply to consider the position and momentum of a particle, or the two quadratures of a quantized electromagnetic field.…”

Physics: Unite to build a quantum Internet

“…Quantum informationmeasured in units known as quantum bits, or qubits -can be encoded either by the discrete properties of a pulse of light, such as its polarization state, or by the continuous aspects of an electromagnetic wave, such as the intensity and phase of the wave's electric field 4 . To teleport this information, both the sender and receiver must own one of a pair of entangled quantum systems (see 'Quantum teleportation').…”