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...

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...

A Bell inequality is a fundamental test to rule out local hidden variable model descriptions of correlations between two physically separated systems. There have been a number of experiments in which a Bell inequality has been violated using discrete-variable systems. We demonstrate a violation of Bells inequality using continuous variable quadrature measurements. By creating a four-mode entangled state with homodyne detection, we recorded a clear violation with a Bell value of B = 2.31 ± 0.02. This opens new possibilities for using continuous variable states for device independent quantum protocols.A Bell test is a fundamental demonstration of quantum mechanics. It is made up of a family of inequalities that test the hypothesis of local realism [1]. Violation of a Bell inequality between spatially separated sub-systems demonstrates that there exist non local correlations between them. Only entangled quantum systems can violate a Bell inequality in this way. This has application in quantum technologies where one can be faced with the verification of quantum devices. For quantum key distribution (QKD) and quantum random number generators (QRNG) a violation of a loop-hole free Bell inequality can rule out a compromise of the quantum source or measurement devices by a third party. This allows the users to achieve device independent (DI) protocols [2].In quantum optics there are two ways to decompose the optical field. One is to quantize the optical field into discrete photon numbers. This allows information to be encoded in discrete variables (DV). These systems can have very low bandwidths from photon generation and high detection losses at room temperature [3] but they are relatively robust to channel losses and noise. Bell inequalities have been violated with DV systems for over 35 years [4] with ever increasing efficiency. These violations have relied on the "fair-sampling" assumption -a loop-hole that could be exploited by an adversary. With the recent improvement in photon detection efficiencies at cryogenic temperatures there have been three significant demonstrations of a loophole free Bell test [5][6][7]. These experiments will allow for true DV DI-QRNG [8] and DI-QKD [9] protocols.The second approach, used in this letter, is to consider a decomposition into the continuous variable (CV) amplitude and phase quadratures of the optical field. The advantages of CV systems are that high detection efficiency is much easier to achieve and the resource states are deterministically generated. For CV quantum optics a Bell test is harder to realize. Bell argued that Quan-