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 attenuator is only possible due to the probabilistic nature of the device.
We propose a method to improve the performance of two entanglement-based continuous-variable quantum key distribution protocols using noiseless linear amplifiers. The two entanglement-based schemes consist of an entanglement distribution protocol with an untrusted source and an entanglement swapping protocol with an untrusted relay. Simulation results show that the noiseless linear amplifiers can improve the performance of these two protocols, in terms of maximal transmission distances, when we consider small amounts of entanglement, as typical in realistic setups.
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…
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…
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 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…
We address quantum $M$-ary phase-shift keyed (PSK) communication channels in the presence of phase diffusion, and analyze the use of probabilistic noiseless linear amplifiers (NLA) to enhance performance of coherent signals. We consider both static and dynamical phase diffusion and assess the performances of the channel for ideal and realistic phase receivers. Our results show that NLA employed at the stage of signal preparations is a useful resource, especially in the regime of weak signals. We also discuss the interplay between the use of NLA, and the memory effects occurring with dynamical …
We demonstrate that a phase-insensitive parametric amplifier, coupled to a quantum correlated source, can be used as a quantum information tap for noiseless three-way signal splitting. We find that the output signals are amplified noiselessly in two of the three output ports while the other can more or less keep its original input size without adding noise. This scheme is able to cascade and scales up for efficient information distribution in an optical network. Furthermore, we find this scheme satisfies the criteria for a non-ideal quantum non-demolition (QND) measurement and thus can serve a…
Attenuating a quantum state using a beam splitter will introduce noise and decoherence. Here we show that heralding techniques can be used to attenuate Schrödinger cat states and squeezed vacuum states without any noise or decoherence [Mičuda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Noiseless attenuation also preserves quantum interference effects in nonclassical states such as squeezed vacuum states.
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…
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 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…
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
We determine the maximum squashed entanglement achievable between sender and receiver of the noiseless quantum Gaussian attenuators and amplifiers and we prove that it is achieved sending half of an infinitely squeezed two-mode vacuum state. The key ingredient of the proof is a lower bound to the squashed entanglement of the quantum Gaussian states obtained applying a two-mode squeezing operation to a quantum thermal Gaussian state tensored with the vacuum state. This is the first lower bound to the squashed entanglement of a quantum Gaussian state and opens the way to determine the squashed e…
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)…
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.
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…
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 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…
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 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…
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" …
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…
The no-cloning theorem states that an unknown quantum state cannot be cloned exactly and deterministically due to the linearity of quantum mechanics. Associated with this theorem is the quantitative no-cloning limit that sets an upper bound to the quality of the generated clones. However, this limit can be circumvented by abandoning determinism and using probabilistic methods. Here, we report an experimental demonstration of probabilistic cloning of arbitrary coherent states that clearly surpasses the no-cloning limit. Our scheme is based on a hybrid linear amplifier that combines an ideal det…
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…
In fundamental papers from 1962 [1, 2], Heffener and Haus showed that it is not possible to construct a linear noiseless amplifier. The implies that the amplifier intrinsic noise sources induce random perturbations on the phase of the incoming optical signal which translates into spectral broadening. To achieve the minimum (quantum noise limited) induced phase fluctuation, and the corresponding minimum spectral broadening, an optimum phase measurement method is needed. We demonstrate that a measurement method based on the heterodyne detection and the extended Kalman filtering approaches an opt…
Due to the pervasive nature of decoherence, protection of quantum information during transmission is of critical importance for any quantum network. A linear amplifier that can enhance quantum signals stronger than their associated noise while preserving quantum coherence is therefore of great use. This seemingly unphysical amplifier property is achievable for a class of probabilistic amplifiers that does not work deterministically. Here we present a linear amplification scheme that realises this property for coherent states by combining a heralded measurement-based noiseless linear amplifier …
Degenerate parametric amplifiers (DPAs) exhibit the unique property of phase-sensitive gain and can be used to noiselessly amplify small signals or squeeze field fluctuations beneath the vacuum level. In the microwave domain, these amplifiers have been utilized to measure qubits in elementary quantum processors, search for dark matter, facilitate high-sensitivity spin resonance spectroscopy and have even been proposed as the building blocks for a measurement based quantum computer. Until now, microwave DPAs have almost exclusively been made from nonlinear Josephson junctions, which exhibit hig…
We determine the p->q norms of the Gaussian one-mode quantum-limited attenuator and amplifier and prove that they are achieved by Gaussian states, extending to noncommutative probability the seminal theorem "Gaussian kernels have only Gaussian maximizers" (Lieb in Invent Math 102(1):179-208, 1990). The quantum-limited attenuator and amplifier are the building blocks of quantum Gaussian channels, which play a key role in quantum communication theory since they model in the quantum regime the attenuation and the noise affecting any electromagnetic signal. Our result is crucial to prove the longs…
We analyse a system composed of a qubit coupled to electromagnetic fields of two high quality quantum oscillators. Particular realization of such a system is the superconducting qubit coupled to a transmission-line resonator driven by two signals with frequencies close to the resonator's harmonics. One strong signal is used for exciting the system to a high energetic state while the second weak signal is applied for probing effective eigenstates of the system. We demonstrate that a description of the system dynamics as doubly dressed qubit is applicable. Experiments show that in the case of hi…
