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We present a random number generation scheme that uses broadband measurements of the vacuum field contained in the radio-frequency sidebands of a single-mode laser. Even though the measurements may contain technical noise, we show that suitable algorithms can transform the digitized photocurrents into a string of random numbers that can be made arbitrarily correlated to a subset of the quantum fluctuations (High Quantum Correlation regime) or arbitrarily immune to environmental fluctuations (High Environmental Immunity). We demonstrate up to 2 Gbps of real time random number generation that were verified using standard randomness tests.Reliable and unbiased random numbers (RNs) are needed for a range of applications spanning from numerical modeling to cryptographic communications. With the numerous improvements in quantum key distribution (QKD) protocols 1,2 , fast and reliable RN generation is now one of the main technical impediment to highspeed QKD. Whilst there are algorithms that can generate pseudo-RNs, they can never be perfectly random nor indeterministic. True RNs from physical processes may offer a surefire solution.Several physical RN generation schemes have been proposed and demonstrated 3-5 , including schemes based on single photon detections 6-11 . The limit in speed of these systems are in the dead time of photon counters. An alternative quantum approach to photon counting is to use the vacuum fluctuations of an electromagnetic field for RN generation 12,13 . In this letter, we demonstrate a simple scheme to measure and convert vacuum field fluctuations into RNs.The schematic of the quantum RN generator is shown in Fig. 1. A single-mode laser beam at 1550 nm is used as the light source. A few mW of light is split into two equal intensity beams and detected by a pair of photodetectors in a balanced homodyne scheme. When the average laser field amplitude α is significantly larger than the vacuum field fluctuation the subtracted photo-current from the pair of detectors is proportional to αX v (ω), where X v is the quadrature amplitude of the vacuum field. The balanced homodyne setup therefore measures the amplified quadrature amplitude of the vacuum field fluctuations. Only sideband frequencies well above the technical noise frequencies of the laser are used for RN generation (shaded region of the radio frequency (RF) spectrum of Fig. 1(a)). This is achieved by demodulating the photocurrent with an RF frequency (1.6 GHz) followed by a low pass filter. The undulations in the spectra are due to non-uniform RF electronic gain in the photodetectors amplification stages (Fig. 1(b)). Nevertheless, the quantum noise has a constant clearance above the electronic a) Electronic mail: Ping.Lam@anu.edu.au noise level of 8.5 dB. Using a Field-programmable Gate Array (FPGA) a filter function can be programmed to neutralize the non-uniform electronic gain as shown in Fig. 1(c). Finally, using suitable numerical processes, the quantum noise is converted into a sequence of random digital bits as depicted by the 8-bit...

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The generation of random numbers via quantum processes is an efficient and reliable method to obtain true indeterministic random numbers that are of vital importance to cryptographic communication and large-scale computer modeling. However, in realistic scenarios, the raw output of a quantum random-number generator is inevitably tainted by classical technical noise. The integrity of the device can be compromised if this noise is tampered with, or even controlled by some malicious party. To safeguard against this, we propose and experimentally demonstrate an approach that produces side-information independent randomness that is quantified by min-entropy conditioned on this classical noise. We present a method for maximizing the conditional min-entropy of the number sequence generated from a given quantum-to-classical-noise ratio. The detected photocurrent in our experiment is shown to have a real-time random-number generation rate of 14 (Mbit/s)/MHz. The spectral response of the detection system shows the potential to deliver more than 70 Gbit/s of random numbers in our experimental setup.

Nonlocal correlations, a longstanding foundational topic in quantum information, have recently found application as a resource for cryptographic tasks where not all devices are trusted, for example, in settings with a highly secure central hub, such as a bank or government department, and less secure satellite stations, which are inherently more vulnerable to hardware "hacking" attacks. The asymmetric phenomena of Einstein-Podolsky-Rosen (EPR) steering plays a key role in one-sided device-independent (1sDI) quantum key distribution (QKD) protocols. In the context of continuous-variable (CV) QKD schemes utilizing Gaussian states and measurements, we identify all protocols that can be 1sDI and their maximum loss tolerance. Surprisingly, this includes a protocol that uses only coherent states. We also establish a direct link between the relevant EPR steering inequality and the secret key rate, further strengthening the relationship between these asymmetric notions of nonlocality and device independence. We experimentally implement both entanglement-based and coherent-state protocols, and measure the correlations necessary for 1sDI key distribution up to an applied loss equivalent to 7.5 and 3.5 km of optical fiber transmission, respectively. We also engage in detailed modeling to understand the limits of our current experiment and the potential for further improvements. The new protocols we uncover apply the cheap and efficient hardware of CV-QKD systems in a significantly more secure setting.

Entanglement distillation is an indispensable ingredient in extended quantum communication networks. Distillation protocols are necessarily non-deterministic and require advanced experimental techniques such as noiseless amplification. Recently it was shown that the benefits of noiseless amplification could be extracted by performing a post-selective filtering of the measurement record to improve the performance of quantum key distribution. We apply this protocol to entanglement degraded by transmission loss of up to the equivalent of 100km of optical fibre. We measure an effective entangled resource stronger than that achievable by even a maximally entangled resource passively transmitted through the same channel. We also provide a proof-of-principle demonstration of secret key extraction from an otherwise insecure regime. The measurement-based noiseless linear amplifier offers two advantages over its physical counterpart: ease of implementation and near optimal probability of success. It should provide an effective and versatile tool for a broad class of entanglement-based quantum communication protocols.The impossibility of determining all properties of a system, as exemplified by Heisenberg's uncertainty principle [1] is a well known signature of quantum mechanics. It results in phase and amplitude fluctuations in the vacuum, enables applications such as quantum key distribution and is at the heart of fundamental results such as the no-cloning theorem [2], quantum limited metrology [3], and the unavoidable addition of noise during amplification [4,5]. This last constraint means even an ideal quantum amplifier cannot be used for entanglement distillation [6][7][8] which is a critical step in the creation of large scale quantum information networks [9,10].Distillation protocols, originally conceived for discrete variables [6,7], proved initially more elusive in the continuous variable (CV) regime. The most experimentally feasible, and theoretically well studied, class of CV states and operations are the Gaussian states and the operations that preserve their Gaussianity [11]. Protocols that distill Gaussian states were discovered [8,12] involving an initial non-Gaussian operation that increases the entanglement followed by a 'Gaussification' step that iteratively drives the output towards a Gaussian state. More recently noiseless linear amplification has been identified as a simpler method of distilling Gaussian entanglement [13][14][15].The noiseless linear amplifier (NLA) avoids the unavoidable noise penalty by moving to a non-deterministic protocol. This ingenious concept and a linear optics implementation have been proposed [13,16,17] and experimentally realised for the case of amplifying coherent states [18][19][20][21], qubits [22][23][24], and the concentration of phase information [25]. All of these were extremely challenging experiments, with only Ref.[18] demonstrating entanglement distillation and none directly showing an increase in Einstein-Podolsky-Rosen (EPR) correlations [26]. Moreover the succe...

Although quantum metrology allows us to make precision measurements beyond the standard quantum limit, it mostly works on the measurement of only one observable due to the Heisenberg uncertainty relation on the measurement precision of noncommuting observables for one system. In this paper, we study the schemes of joint measurement of multiple observables which do not commute with each other using the quantum entanglement between two systems. We focus on analyzing the performance of a SU(1,1) nonlinear interferometer on fulfilling the task of joint measurement. The results show that the information encoded in multiple noncommuting observables on an optical field can be simultaneously measured with a signal-to-noise ratio higher than the standard quantum limit, and the ultimate limit of each observable is still the Heisenberg limit. Moreover, we find a resource conservation rule for the joint measurement.

Entanglement distillation is an indispensable ingredient in extended quantum communication networks. Distillation protocols are necessarily non-deterministic and require advanced experimental techniques such as noiseless amplification. Recently it was shown that the benefits of noiseless amplification could be extracted by performing a post-selective filtering of the measurement record to improve the performance of quantum key distribution. We apply this protocol to entanglement degraded by transmission loss of up to the equivalent of 100km of optical fibre. We measure an effective entangled resource stronger than that achievable by even a maximally entangled resource passively transmitted through the same channel. We also provide a proof-of-principle demonstration of secret key extraction from an otherwise insecure regime. The measurement-based noiseless linear amplifier offers two advantages over its physical counterpart: ease of implementation and near optimal probability of success. It should provide an effective and versatile tool for a broad class of entanglement-based quantum communication protocols.The impossibility of determining all properties of a system, as exemplified by Heisenberg's uncertainty principle [1] is a well known signature of quantum mechanics. It results in phase and amplitude fluctuations in the vacuum, enables applications such as quantum key distribution and is at the heart of fundamental results such as the no-cloning theorem [2], quantum limited metrology [3], and the unavoidable addition of noise during amplification [4,5]. This last constraint means even an ideal quantum amplifier cannot be used for entanglement distillation [6][7][8] which is a critical step in the creation of large scale quantum information networks [9,10].Distillation protocols, originally conceived for discrete variables [6,7], proved initially more elusive in the continuous variable (CV) regime. The most experimentally feasible, and theoretically well studied, class of CV states and operations are the Gaussian states and the operations that preserve their Gaussianity [11]. Protocols that distill Gaussian states were discovered [8,12] involving an initial non-Gaussian operation that increases the entanglement followed by a 'Gaussification' step that iteratively drives the output towards a Gaussian state. More recently noiseless linear amplification has been identified as a simpler method of distilling Gaussian entanglement [13][14][15].The noiseless linear amplifier (NLA) avoids the unavoidable noise penalty by moving to a non-deterministic protocol. This ingenious concept and a linear optics implementation have been proposed [13,16,17] and experimentally realised for the case of amplifying coherent states [18][19][20][21], qubits [22][23][24], and the concentration of phase information [25]. All of these were extremely challenging experiments, with only Ref.[18] demonstrating entanglement distillation and none directly showing an increase in Einstein-Podolsky-Rosen (EPR) correlations [26]. Moreover the succe...