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Phase insensitive optical amplification of an unknown quantum state is known to be a fundamentally noisy operation that inevitably adds noise to the amplified state [1][2][3][4][5]. However, this fundamental noise penalty in amplification can be circumvented by resorting to a probabilistic scheme as recently proposed and demonstrated in refs [6][7][8]. These amplifiers are based on highly non-classical resources in a complex interferometer. Here we demonstrate a probabilistic quantum amplifier beating the fundamental quantum limit utilizing a thermal noise source and a photon number subtraction scheme [9]. The experiment shows, surprisingly, that the addition of incoherent noise leads to a noiselessly amplified output state with a phase uncertainty below the uncertainty of the state prior to amplification. This amplifier might become a valuable quantum tool in future quantum metrological schemes and quantum communication protocols.Besides being the subject of a fundamental dicussion going back to Dirac [10], the measurement of phase is at the heart of many quantum metrological and quantum informational applications such as gravitational wave detection, global positioning, clock syncronization, quantum computing and quantum key distribution. In many of these applications the phase is most often imprinted onto a coherent state of light and subsequently estimated using an interferometric measurement scheme. Such a phase estimation process [11] is however hampered by the fundamental quantum noise of the coherent state which plays an increasingly devastating role as the excitation of the coherent state becomes smaller. Small coherent state excitations and associated large phase uncertainties are typical in real systems such as long distance coherent state communication and lossy interferometry.To reduce the phase uncertainty and thus concentrate the phase information, the state must be amplified noiselessly. This can be done probabilistically using either a highly complicated interferometric setup of single photon sources [6][7][8], a sophisticated sequence of photon addition and subtraction schemes [9,12] or a very strong cross-Kerr nonlinearity [13]. However, as we show in this letter, it is possible to amplify the phase information noiselessly without the use of any non-classical resources or any strong parametric interactions. Remarkably, the supply of energy in our amplifier is simply a thermal light source.A schematic diagram of the probabilistic amplifier [9] is shown in Fig. 1a. It is solely based on phase insensitive noise addition and photon subtraction. To explain in simple terms why the addition of noise can help amplifying a coherent state, we consider the phase space pictures in Fig. 1b. The addition of thermal noise induces random displacements to the coherent state, thus resulting in a Gaussian mixture of coherent states; some with excitations that are larger than the original excitation and some with smaller excitations. In the photon subtraction process, the coherent states with large excitations ar...

We present a concept of non-Gaussian measurement composed of a non-Gaussian ancillary state, linear optics and adaptive heterodyne measurement, and on the basis of this we also propose a simple scheme of implementing a quantum cubic gate on a traveling light beam. In analysis of the cubic gate in the Heisenberg representation, we find that nonlinearity of the gate is independent from nonclassicality; the nonlinearity is generated solely by a classical nonlinear adaptive control in a measurement-and-feedforward process while the nonclassicality is attached by the non-Gaussian ancilla that suppresses excess noise in the output. By exploiting the noise term as a figure of merit, we consider the optimum non-Gaussian ancilla that can be prepared within reach of current technologies and discuss performance of the gate. It is a crucial step towards experimental implementation of the quantum cubic gate.

Abstract:We develop an experimental scheme based on a continuouswave (cw) laser for generating arbitrary superpositions of photon number states. In this experiment, we successfully generate superposition states of zero to three photons, namely advanced versions of superpositions of two and three coherent states. They are fully compatible with developed quantum teleportation and measurement-based quantum operations with cw lasers. Due to achieved high detection efficiency, we observe, without any loss correction, multiple areas of negativity of Wigner function, which confirm strongly nonclassical nature of the generated states. Haroche, "Quantum Zeno dynamics of a field in a cavity," Phys. Rev. A 86, 032120 (2012).

We propose a probabilistic measurement-induced amplification for coherent states. The amplification scheme uses a counterintuitive architecture: a thermal noise addition (instead of a single-photon addition) followed by a feasible multiple-photon subtraction using a realistic photon-number-resolving detector. It allows one to substantially amplify weak coherent states and simultaneously reduce their phase uncertainty, which is impossible when using a deterministic Gaussian amplifier.