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arXiv:1407.7702

Noise powered amplification in CV quantum key distribution

Petr Marek, Radim Filip

Published Jul 29, 2014• 0 citations
arXivHTMLPDF

Abstract

Amplification plays a key role in classical communication protocols, where it compensates the unavoidable loss of the signal. However, when we enter the quantum domain this approach starts being problematic as the standard kinds of amplifiers are usually accompanied by excess noise which detrimentally affects the quantum features of used states. Recently, several kinds of "noiseless" amplifiers that do not suffer from this feature have been proposed. Among these amplifiers, one that stands out is the noise powered amplifier, which acts incoherently, amplifying the signal by adding the "right" kind of noise. Here we show that despite the incoherence, which makes the amplifier unsuitable for protocols such as entanglement distillation, the added noise is not a big problem in quantum key distribution tasks and can be in some situations beneficial.

DOI
10.48550/arxiv.1407.7702

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Amplification plays a key role in classical communication protocols, where it compensates the unavoidable loss of the signal. However, when we enter the quantum domain this approach starts being problematic as the standard kinds of amplifiers are usually accompanied by excess noise which detrimentally affects the quantum features of used states. Recently, several kinds of "noiseless" amplifiers that do not suffer from this feature have been proposed. Among these amplifiers, one that stands out is the noise powered amplifier, which acts incoherently, amplifying the signal by adding the "right" kind of noise. Here we show that despite the incoherence, which makes the amplifier unsuitable for protocols such as entanglement distillation, the added noise is not a big problem in quantum key distribution tasks and can be in some situations beneficial.
The unavoidable addition of noise during amplification is a well known signature of quantum mechanics. It is at the heart of fundamental results such as the no-cloning theorem, quantum limited metrology, quantum key distribution and the impossibility of increasing entanglement by local operations. Nonetheless one can still avoid the unavoidable by moving to a non-deterministic protocol. This novel concept and a linear optics implementation have been proposed [1] and experimentally realised for the case of amplifying coherent states [2-4], qubits [5,6] and the concentration of phase information [7]. All these were extremely challenging experiments, with only [2] demonstrating entanglement distillation and none directly showing the EPR distillation necessary for application to CV QKD. Furthermore the success probability of these experiments was substantially worse than the theoretical considerations would imply. However as has been noted in [8,9] it is possible to virtually implement noiseless amplification (NLA) and hence entanglement distillation via post-selective measurements, achieving significant distillation with a much improved probability of success.
According to the fundamental laws of quantum optics, noise is necessarily added to the system when one tries to clone or amplify a quantum state. However, it has recently been shown that the quantum noise related to the operation of a linear phase-insensitive amplifier can be avoided when the requirement of a deterministic operation is relaxed. Nondeterministic noiseless linear amplifiers are therefore realizable. Usually nondeterministic amplifiers rely on using single photon sources. We have, in contrast, recently proposed an amplification scheme in which no external energy is added to the signal, but the energy required to amplify the signal originates from the stochastic fluctuations in the field itself. Applying our amplification scheme, we examine the amplifier gain and the success rate as well as the properties of the output states after successful and failed amplification processes. We also optimize the setup to find the maximum success rates in terms of the reflectivities of the beam splitters used in the setup. In addition, we discuss the nonidealities related to the operation of our setup and the relation of our setup with the previous setups.
Noiseless amplification or attenuation are two heralded filtering operations that enable amplifying or de-amplifying a quantum state of light with no added noise, at the cost of a small success probability. We show that inserting such noiseless operations in a transmission line improves the performances of continuous-variable quantum key distribution over this line. Remarkably, these noiseless operations do not need to be physically implemented but can simply be simulated in the classical data postprocessing stage. Hence, virtual noiseless amplification or attenuation amounts to performing a Gaussian postselection, which enhances the secure range or tolerable excess noise while keeping the benefits of Gaussian security proofs.
According to the fundamental laws of quantum optics, noise is necessarily added to the system when one tries to clone or amplify a quantum state. However, it has recently been shown that the quantum noise related to the operation of a linear phase-insensitive amplifier can be avoided when the requirement of a deterministic op-eration is relaxed. Nondeterministic noiseless linear amplifiers are therefore realizable. Usually nondeterministic amplifiers rely on using single photon sources. We have, in contrast, recently proposed an amplification scheme in which no external energy is added to the signal, but the energy required to amplify the signal originates from the stochastic fluctuations in the field itself. Applying our amplification scheme, we examine the amplifier gain and the success rate as well as the properties of the output states after successful and failed amplification processes. We also optimize the setup to find the maximum success rates in terms of the reflectivities of the beam splitters used in the setup. In addition, we discuss the nonidealities related to the operation of our setup and the relation of our setup with the previous setups.
Amplification of an entangled state is a matter of great significance in quantum communication. However, any parametric amplifier (PA) will introduce added noise into the system which unavoidably degrades the entanglement or even makes it disappear. Recently, it has been experimentally demonstrated that amplification of one half of a two-mode squeezed state is possible while preserving entanglement [Phys. Rev. Lett. 103, 010501 (2009)]. However, such entanglement cannot be maintained when the strength of the amplification is large. To solve this problem, we propose a correlation modulation scheme (CMS), which fully exploits the quantum correlation between the two output states from the PA process, to suppress the added noise from the parametric amplifications. For amplifying an entangled state using a PA, we demonstrate that the CMS not only better maintains but also always preserves the entanglement whatever the strength of the PA. Such a CMS may pave the way to low-noise amplification of an entangled state.
We compare the effect of different noise scenarios on the achievable rate of an ${\ensuremath{\varepsilon}}_{}$-secure key for the BB84 and the six-state protocol. We study the situation where quantum noise is added deliberately, and investigate the remarkable benefit for the finite key rate. We compare our results to the known case of added classical noise and the asymptotic key rate, i.e., in the limit of infinitely many signals. As a complementary interpretation, we show that under the realistic assumption that the noise which is unavoidably introduced by a real channel is not fully dedicated to the eavesdropper, the secret key rate increases significantly.