Noise-powered probabilistic concentration of phase information

Abstract

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...

Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier

“…Thus, when only considering its successful runs, the NLA can compensate the effect of losses and could therefore be useful for quantum communication [28], and to establish the nonlocal nature of quantum correlations thanks to a loophole-free Bell test [29]. The availability of such a device has stimulated intense experimental activity over the past years, demonstrating the implementation of approximated versions [18][19][20][21][22][23], which have provided solid proof of principle.…”

“…In this paper, we consider the use of a heralded noiseless linear amplifier (NLA) [17][18][19][20][21][22][23] on the detection stage as a way to increase the robustness of CV QKD protocols against losses and noise. First, it should be noted that while amplifiers can effectively recover classical signals, they only offer limited advantages when working on quantum signals, as amplification is bound to preserve the original signal to noise ratio (SNR) [19,24,25].…”

Heralded photon amplification for quantum communication

“…Of particular interest are those for which the success of the amplification process is heralded [3]. This includes techniques based on single-photon addition [4,5] or thermal noise addition followed by heralded photon subtraction [6,7].…”

Noiseless Loss Suppression in Quantum Optical Communication

“…Although this cannot be done perfectly because g n is unbounded, faithful noiseless amplification is possible in any finite subspace spanned by the Fock states |n with n ≤ N , albeit with a correspondingly low probability scaling as g −2N in the worst case of input vacuum state. With current technology, it has been proven possible to faithfully noiselessly amplify weak coherent states containing mostly vacuum and single-photon contributions [14][15][16][17].The noiseless amplifier can improve the performance of quantum key distribution protocols [18][19][20][21] and it can also be used to distribute high-quality entanglement over a lossy channel [13,22]. Beyond that, the noiseless amplifier is not useful to suppress losses in direct transmission of arbitrary quantum states because it is not the inverse map of a lossy channel L. As a matter of fact, any superposition of Fock states that is not a coherent state is mapped by L onto a mixed state, and this added noise cannot be eliminated by noiseless amplification.…”