We introduce the concept of non-deterministic noiseless linear amplification. We propose a linear optical realization of this transformation that could be built with current technology. We discuss two applications; ideal probabilistic cloning of coherent states and distillation of continuous variable entanglement. For the latter example we demonstrate that highly pure entanglement can be distilled from transmission over a lossy channel.
Probabilistic amplification through photon addition, at the output of an Mach-Zehnder interferometer is discussed for a coherent input state. When a metric of signal to noise ratio is considered, nondeterministic, noiseless amplification of a coherent state shows improvement over a standard coherent state, for the general addition of $m$ photons. The efficiency of realizable implementation of photon addition is also considered and shows how the collected statistics of a post selected state, depend on this efficiency. We also consider the effects of photon loss and inefficient detectors.
A universal deterministic noiseless quantum amplifier has been shown to be impossible. However, probabilistic noiseless amplification of a certain set of states is physically permissible. Regarding quantum state amplification as quantum state transformation, we show that deterministic noiseless amplification of coherent states chosen from a proper set is possible. The relation between input coherent states and gain of amplification for deterministic noiseless amplification is thus derived. Besides, the potential applications of amplification of coherent states in quantum key distribution (QKD)…
In this work we study the use of noiseless attenuation and noiseless amplification, in terms of multi-mode Continuous-Variable (CV) Quantum Key Distribution (QKD) over satellite-to-ground channels. We propose an improved multi-mode CV-QKD protocol where noiseless attenuation and noiseless amplification operations are applied at the transmitter and the receiver, respectively. Our results show that consistent with single-mode CV-QKD, the noiseless amplification operation, when applied at the receiver, can increase the transmission distance and the channel noise tolerance of multi-mode CV-QKD. Di…
We examine the behavior of non-Gaussian states of light under the action of probabilistic noiseless amplification and attenuation. Surprisingly, we find that the mean field amplitude may decrease in the process of noiseless amplification -- or increase in the process of noiseless attenuation, a counterintuitive effect that Gaussian states cannot exhibit. This striking phenomenon could be tested with experimentally accessible non-Gaussian states, such as single-photon added coherent states. We propose an experimental scheme, which is robust with respect to the major experimental imperfections s…
We discuss the recently introduced concept of non-deterministic noiseless linear amplification, demonstrating that such an operation can only be performed perfectly with vanishing probability of success. We show that a weak measurement, which imprints the weak value of an observable of a pre-selected and post-selected system onto a probe system, can be used to approximate probabilistic noiseless amplification. This result may be applied to various tasks in continuous variable quantum information, including entanglement concentration, probabilistic cloning, and in quantum repeaters. We discuss …
The noiseless amplification or attenuation are two heralded filtering operations that enable respectively to increase or decrease the mean field of any 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 performance 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 data post-processing stage. Hence, virtual noiseless amplification or attenuation am…
We generalize the concept of optical state truncation and noiseless linear amplification to enable truncation of the Fock-state expansion of an optical state to higher order and to simultaneously amplify it using linear optics. The resulting generalized quantum scissors are more efficient for noiseless linear amplification than employing multiple scissors in parallel and are experimentally practical. As a particular example, we focus on a third-order scissor device and demonstrate advantages in terms of fidelity with the target state, probability of success, distillable entanglement, and the a…
We address quantum state engineering of single- and two-mode states by means of non-deterministic noiseless linear amplifiers (NLAs) acting on Gaussian states. In particular, we show that NLAs provide an effective scheme to generate highly non-Gaussian and non-classical states. Additionally, we show that the amplification of a two-mode squeezed vacuum state (twin-beam) may highly increase entanglement.
Most of the schemes for "noiseless" amplification of coherent states, which have recently been attracting theoretical and experimental interest, share a common trait: the amplification is not truly noiseless, or perfect, for non-zero success probability. While this must hold true for all phase-independent amplification schemes, in this work we point out that truly noiseless amplification is indeed possible, provided that the states which we wish to amplify come from a finite set. Perfect amplification with unlimited average gain is then possible with finite success probability, for example usi…
Non-deterministic noiseless amplification of a single mode can circumvent the unique challenges to amplifying a quantum signal, such as the no-cloning theorem, and the minimum noise cost for deterministic quantum state amplification. However, existing devices are not suitable for amplifying the fundamental optical quantum information carrier, a qubit coherently encoded across two optical modes. Here, we construct a coherent two-mode amplifier, to demonstrate the first heralded noiseless linear amplification of a qubit encoded in the polarization state of a single photon. In doing so, we increa…
Quantum optics dictates that amplification of a pure state by any linear deterministic amplifier always introduces noise in the signal and results in a mixed output state. However, it has recently been shown that noiseless amplification becomes possible if the requirement of a deterministic operation is relaxed. Here we propose and analyze a noiseless amplification scheme where the energy required to amplify the signal originates from the stochastic fluctuations in the field itself. In contrast to previous amplification setups, our setup shows that a signal can be amplified even if no energy i…
The idea of signal amplification is ubiquitous in the control of physical systems, and the ultimate performance limit of amplifiers is set by quantum physics. Increasing the amplitude of an unknown quantum optical field, or more generally any harmonic oscillator state, must introduce noise. This linear amplification noise prevents the perfect copying of the quantum state, enforces quantum limits on communications and metrology, and is the physical mechanism that prevents the increase of entanglement via local operations. It is known that non-deterministic versions of ideal cloning and local en…
We analyse the action of an ideal noiseless linear amplifier operator, $g^\hat{n}$, using the Wigner function phase space representation. In this setting we are able to clarify the gain $g$ for which a physical output is produced when this operator is acted upon inputs other than coherent states. We derive compact closed form expressions for the action of $N$ local amplifiers, with potentially different gains, on arbitrary $N$-mode Gaussian states and provide several examples of the utility of this formalism for determining important quantities including amplification and the strength and puri…
Polarization dependent loss (PDL) is a serious problem that hinders the transfer of polarization qubits through quantum networks. Recently it has been shown that the detrimental effects of PDL on qubit fidelity can be compensated for with the introduction of an additional passive PDL element that rebalances the polarization modes of the transmitted qubit. This procedure works extremely well when the output of the system is postselected on photon detection. However, in cases where the qubit might be needed for further analysis this procedure introduces unwanted vacuum terms into the state. Here…
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 r…
Photon loss is one of the main obstacles in current long-distance quantum communications. The approach of noiseless linear amplification (NLA) is one of the powerful way to distill the single-photon state (SPS) from a mixed state, which comprises both the SPS and vacuum state. However, existing NLA protocol can only perform the amplification for one time. That is the fidelity of the SPS cannot be increased anymore. In this paper, We put forward an efficient cascaded NLA protocol for both the SPS and single-photon entanglement (SPE), respectively, with the help of some auxiliary single photons.…
We address de-Gaussification of continuous variables Gaussian states by optimal non-deterministic noiseless linear amplifier (NLA) and analyze in details the properties of the amplified states. In particular, we investigate the entanglement content and the non-Gaussian character for the class of non-Gaussian entangled state obtained by using NL-amplification of two-mode squeezed vacua (twin-beam, TWB). We show that entanglement always increases, whereas improved EPR correlations are observed only when the input TWB has low energy. We then examine a Braunstein-Kimble-like protocol for the telep…
The viability of quantum communication schemes rely on sending quantum states of light over long distances. However, transmission loss can degrade the signal strength, adding noise. Heralded noiseless amplification of a quantum signal can provide a solution by enabling longer direct transmission distances and by enabling entanglement distillation. The central idea of heralded noiseless amplification---a conditional modification of the probability distribution over photon number of an optical quantum state---is suggestive of a parallel with weak measurement: in a weak measurement, learning part…
A general framework of quantum state amplification using the language of quantum state transformation is given systematically for the first time. The concept of amplification of quantum states is defined specifically and the amplification of a set of quantum states is formulated generally as the transformation of quantum states. Three different kinds of important quantum amplifications, i.e., deterministic noisy quantum amplification, probabilistic noiseless quantum amplification, and deterministic noiseless quantum amplification are identified and discussed. For deterministic quan- tum amplif…
The employ of a noiseless linear amplifier (NLA) has been proven as a useful tool for mitigating imperfections in quantum channels. Its analysis is usually conducted within specific frameworks, for which the set of input states for a given protocol is fixed. Here we obtain a more general description by showing that a noisy and lossy Gaussian channel followed by a NLA has a general description in terms of effective channels. This has the advantage of offering a simpler mathematical description, best suitable for mixed states, both Gaussian and non-Gaussian. We investigate the main properties of…
We examine heralded nondeterministic noiseless amplification based on the quantum scissors device, which has been shown to increase the one-photon amplitude of a state at the expense of the vacuum-state amplitude. Here we propose using the same basic design to perform perfect amplification in a basis set of up to two photons. The device is much more efficient than several one-photon amplifiers working in tandem. When used to amplify coherent states this advantage is shown using either fidelity or in terms of probability of sucessful action, or more strikingly in a combination of the two.
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 s…
Theoretical results are presented which show that noiseless phase quadrature amplification is possible, and limited experimentally only by the efficiency of the phase detection system. Experimental results obtained using a Nd:YAG laser show a signal gain of 10dB and a signal transfer ratio of T_s=0.9. This result easily exceeds the standard quantum limit for signal transfer. The results also explicitly demonstrate the phase sensitive nature of the amplification process.
Einstein-Podolsky-Rosen (EPR) steering is one of the most intriguing features of quantum mechanics and an important resource for quantum communication. For practical applications, it remains a challenge to protect EPR steering from decoherence due to its intrinsic difference from entanglement. Here, we experimentally demonstrate the distillation of Gaussian EPR steering and entanglement in lossy and noisy environments using measurement-based noiseless linear amplification. Different from entanglement distillation, the extension of steerable region happens in the distillation of EPR steering be…
We suggest and investigate a scheme for non-deterministic noiseless linear amplification of coherent states using successive photon addition, $(\hat a^{\dagger})^2$, where $\hat a^\dagger$ is the photon creation operator. We compare it with a previous proposal using the photon addition-then-subtraction, $\hat a \hat a^\dagger$, where $\hat a$ is the photon annihilation operator, that works as an appropriate amplifier only for weak light fields. We show that when the amplitude of a coherent state is $|α| \gtrsim 0.91$, the $(\hat a^{\dagger})^2$ operation serves as a more efficient amplifier co…
Heralded noiseless amplifcation of photons has recently been shown to provide a means to overcome losses in complex quantum communication tasks. In particular, to overcome transmission losses that could allow for the violation of a Bell inequality free from the detection loophole, for Device Independent Quantum Key Distribution (DI-QKD). Several implementations of a heralded photon amplifier have been proposed and the first proof of principle experiments realised. Here we present the first full characterisation of such a device to test its functional limits and potential for DI-QKD. This devic…
Quantum target detection aims to utilise quantum technologies to achieve performances in target detection not possible through purely classical means. Quantum illumination is an example of this, based on signal-idler entanglement, promising a potential 6 dB advantage in error exponent over its optimal classical counterpart. So far, receiver designs achieving this optimal reception remain elusive with many proposals based on Gaussian processes appearing unable to utilise quantum information contained within Gaussian state sources. This paper considers the employment of a noiseless linear amplif…
Quantum mechanics imposes that any amplifier that works independently on the phase of the input signal has to introduce some excess noise. The impossibility of such a noiseless amplifier is rooted into unitarity and linearity of quantum evolution. A possible way to circumvent this limitation is to interrupt such evolution via a measurement, providing a random outcome able to herald a successful - and noiseless - amplification event. Here we show a successful realisation of such an approach; we perform a full characterization of an amplified coherent state using quantum homodyne tomography, and…
Amplification of quantum states is inevitably accompanied with the introduction of noise at the output. For protocols that are probabilistic with heralded success, noiseless linear amplification in theory may still possible. When the protocol is successful, it can lead to an output that is a noiselessly amplified copy of the input. When the protocol is unsuccessful, the output state is degraded and is usually discarded. Probabilistic protocols may improve the performance of some quantum information protocols, but not for metrology if the whole statistics is taken into consideration. We calcula…
Utility of noiseless linear amplification and attenuation in single-rail discrete-variable quantum communications
University of Queensland（昆士兰大学）；The Australian National University（澳大利亚国立大学）；A*STAR Quantum Innovation Centre (Q.InC), Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局量子创新中心）；Q-CTRL
Noise is the price to pay when trying to clone or amplify arbitrary quantum states. The quantum noise associated to linear phase-insensitive amplifiers can only be avoided by relaxing the requirement of a deterministic operation. Here we present the experimental realization of a probabilistic noiseless linear amplifier that is able to amplify coherent states at the highest level of effective gain and final state fidelity ever reached. Based on a sequence of photon addition and subtraction, and characterized by a significant amplification and low distortions, this high-fidelity amplification sc…
We analytically show that probabilistic amplification of a weak coherent state stored inside an atomic medium can be achieved via detection of coherently scattered photons. We show that this is because of collective excitations created among atoms in the ensemble. We describe the physics of the amplification and identify the failure events, which occur during the amplification process. The amplification is realized by coherently mapping a weak coherent state in an ensemble of $Λ$-level atoms followed by detection of multiple Raman scattered photons, conditionally projecting the coherent state …
The entanglement structure between different frequency components within broadband quantum light pulses, forged at entanglement creation, represents a promising route to the practical delivery of many multipartite quantum information applications. However, the scalability of such applications is largely limited by the entanglement decoherence caused by photon loss. One promising method to combat such losses is noiseless linear amplification. However, while there have been various procedures that implement noiseless linear amplification on single-mode states, no realization has thus far been pr…
We study the operational regime of a noiseless linear amplifier based on quantum scissors that can nondeterministically amplify the one photon component of a quantum state with weak excitation. It has been shown that an arbitrarily large quantum state can be amplified by first splitting it into weak excitation states using a network of beamsplitters. The output states of the network can then be coherently recombined. In this paper, we analyse the performance of such a device for distilling entanglement after transmission through a lossy quantum channel, and look at two measures to determine th…
Loss and decoherence are a major problem in the transmission of non-classical states of light over large distances. It was recently shown that the effects of decoherence can be reduced by applying a probabilistic noiseless attenuator before transmitting a quantum state through a lossy channel, followed by probabilistic noiseless amplification (M. Micuda et al, Phys. Rev. Lett. 109, 180503 (2012)). Here we show that similar results can be obtained for certain kinds of macroscopic quantum states by squeezing the signal before transmission, followed by deterministic amplification and anti-squeezi…
The process of heralded noiseless amplification, and the inverse process of heralded noiseless attenuation, have potential applications in the context of quantum communications. Although several different physical implementations of heralded noiseless amplifiers have now been demonstrated, the research on heralded noiseless attenuators has been largely confined to a beam-splitter based approach. Here we show that an optical parametric amplifier (OPA), combined with appropriate heralding, can also serve as a heralded noiseless attenuator. The counterintuitive use of an optical amplifier as an a…
We propose a protocol for conditional suppression of losses in direct quantum state transmission over a lossy quantum channel. The method works by noiselessly attenuating the input state prior to transmission through a lossy channel followed by noiseless amplification of the output state. The procedure does not add any noise hence it keeps quantum coherence. We experimentally demonstrate it in the subspace spanned by vacuum and single-photon states, and consider its general applicability.
The investigation of the ultimate limits imposed by quantum mechanics on amplification represents an important topic both on a fundamental level and from the perspective of potential applications. We propose here a novel setup for an optomechanical amplifier, constituted by a mechanical resonator dispersively coupled to an optomechanical cavity asymmetrically driven around both mechanical sidebands. We show that, on general grounds, the present amplifier operates in a novel regime-- which we here call phase-mixing amplification. At the same time, for a suitable choice of parameters, the amplif…
Quantum optical amplification that beats the noise addition limit for deterministic amplifiers has been realized experimentally using several different nondeterministic protocols. These schemes either require single-photon sources, or operate by noise addition and photon subtraction. Here we present an experimental demonstration of a protocol that allows nondeterministic amplification of known sets of coherent states with high gain and high fidelity. The experimental system employs the two mature quantum optical technologies of state comparison and photon subtraction and does not rely on elabo…
We show the possibility of noiseless amplification of an optical image in cavities containing a parametric oscillator. We consider a confocal ring cavity with plane mirrors and compare with the case of planar cavity. In the latter case the system operates with severe spatial limitations, while in the confocal case, there is the possibility of preserving the signal-to-noise ratio while amplifying uniformely the entire image.
A process which strongly amplifies both quadrature amplitudes of an oscillatory signal necessarily adds noise. Alternatively, if the information in one quadrature is lost in phase-sensitive amplification, it is possible to completely reconstruct the other quadrature. Here we demonstrate such a nearly perfect phase-sensitive measurement using a cavity optomechanical scheme, characterized by an extremely small noise less than 0.2 quanta. We also observe microwave radiation strongly squeezed by 8 dB below vacuum. A source of bright squeezed microwaves opens up applications in manipulations of qua…
It is a fundamental principle of quantum theory that an unknown state cannot be copied or, as a consequence, an unknown optical signal cannot be amplified deterministically and perfectly. Here we describe a protocol that provides nondeterministic quantum optical amplification in the coherent state basis with high gain, high fidelity and which does not use quantum resources. The scheme is based on two mature quantum optical technologies, coherent state comparison and photon subtraction. The method compares favourably with all previous nondeterministic amplifiers in terms of fidelity and success…
Heralded noiseless amplification based on single-photon sources and linear optics is ideally suited for long-distance quantum communication tasks based on discrete variables. We experimentally demonstrate such an amplifier, operating at telecommunication wavelengths. Coherent amplification is performed with a gain of G=1.98+/-0.2, for a state with a maximum expected gain G=2. We also demonstrate that there is no need for a stable phase reference between the initial signal state and the local auxiliary photons used by the amplifier. These results highlight the potential of heralded quantum ampl…
We show that the use of probabilistic noiseless amplification in entangled coherent state-based schemes for the test of quantum non locality provides substantial advantages. The threshold amplitude to falsify a Bell-CHSH non locality test, in fact, is significantly reduced when amplification is embedded into the test itself. Such a beneficial effect holds also in the presence of detection-inefficiency. Our study helps in affirming noiseless amplification as a valuable tool for coherent information processing and the generation of strongly non classical states of bosonic systems.
Through simultaneous but unequal electromechanical amplification and cooling processes, we create a method for nearly noiseless pulsed measurement of mechanical motion. We use transient electromechanical amplification (TEA) to monitor a single motional quadrature with a total added noise $-8.5\pm2.0$ dB relative to the zero-point motion of the oscillator, or equivalently the quantum limit for simultaneous measurement of both mechanical quadratures. We demonstrate that TEA can be used to resolve fine structure in the phase-space of a mechanical oscillator by tomographically reconstructing the d…
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" …
We address the characterization of the gain parameter of a non-deterministic noiseless linear amplifier (NLA) and compare the performances of different estimation strategies using tools from quantum estimation theory. At first, we show that, contrary to naive expectations, post-selecting only the amplified states does not offer the most accurate estimate. We then focus on minimal implementations of a NLA, i.e. those obtained by coupling the input state to a two-level system, and show that the maximal amount of information about the gain of the NLA is obtained by measuring the whole composite s…
Single-photon entanglement is of major importance in current quantum communications. However, it is sensitive to photon loss. In this paper, we discuss the protection of single-photon multi-mode W state with noiseless linear amplification. It is shown that the amplification factor is only decided with the transmission coefficient of the variable fiber beam splitters, and it does not change with the number of the spatial mode. This protocol may be useful in current quantum information processing.
