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 and 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 favorably with all previous nondeterministic amplifiers in terms of fidelity and success probability.
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 and 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 favorably with all previous nondeterministic amplifiers in terms of fidelity and success probability.
We present an experimental demonstration of a practical nondeterministic quantum optical amplification scheme that employs two mature technologies, state comparison and photon subtraction, to achieve amplification of known sets of coherent states with high fidelity. The amplifier uses coherent states as a resource rather than single photons, which allows for a relatively simple light source, such as a diode laser, providing an increased rate of amplification. The amplifier is not restricted to low amplitude states. With respect to the two key parameters, fidelity and the amplified state production rate, we demonstrate significant improvements over previous experimental implementations, without the requirement of complex photonic components. Such a system may form the basis of trusted quantum repeaters in nonentanglement-based quantum communications systems with known phase alphabets, such as quantum key distribution or quantum digital signatures.
As light propagates through a transmission media, such as an optical fiber, it experiences a length-dependent loss which can reduce the communication efficiency as the transmission distance increases. In conventional telecommunications, optical signals can be transmitted over inter-continental distances, due to deterministic all-optical amplifiers. However, quantum communications are still limited to transmission distances of typically a few 100’s km since deterministic amplifiers cannot be used to amplify quantum signals. The use of deterministic amplification on a quantum signal will introduce noise that will mask the original quantum properties of the signal, introducing uncertainty or errors to any measurement. Nondeterministic methods for amplifying quantum signals via post-selection can be used instead, providing a solution to create a low noise quantum amplifier. Several methods for nondeterministic amplification have already been experimentally demonstrated. However, these devices rely on “quantum resources” which makes implementation challenging. Here we present an overview of experimental demonstrations for amplifying coherent states using a method called state comparison amplification. This is a nondeterministic protocol that performs amplification of known sets of phase-encoded coherent states using two modular stages. The outcome of each stage is recorded using single-photon detectors and time-stamped electronics to enable post-selection. State comparison amplification is a relatively simple technique, only requiring “off-the-shelf” components. The presentation will show several demonstrations of state comparison amplification including an amplifier which has high gain, fidelity, and success rate with the added advantage of being robust to channel noise and easily reconfigurable. Finally, we will discuss the effect of introducing a feedforward mechanism allowing for unsuccessful state amplifications.
Quantum optical coherent-state comparison amplifiers are nondeterministic devices which can amplify rather noiselessly a weak coherent state with an unknown phase from a finite discrete set. The high fidelity and high success probability of this amplifier are accomplished by a comparison stage and some photon subtraction stages. Due to the heralding nature of these amplifiers, they work part of the time. Here, we propose a feedforward protocol to increase the heralded times by correcting the incorrect guess. Hence, we enhance the fidelity and success probability more. Finally, the schematic experimental configuration of the feedforward-assisted coherent-state comparison amplifier is proposed.
Abstract Optical signals are subject to a distance-dependent loss as they propagate through transmission media. High-intensity, classical, optical signals can routinely be amplified to overcome the degradation caused by this loss. However, quantum optical states cannot be deterministically amplified and any attempt to do so will introduce intrinsic noise that spoils the desired quantum properties. Non-deterministic optical amplification, based on post-selection of the output depending on certain conditioning detection outcomes, is an emerging enabling technology in quantum measurement and quantum communications. Here we present an investigation into the properties of a simple, modular optical state comparison amplifier operating on weak coherent states. This amplifier requires no complex quantum resources and is based on linear optical components allowing for a high amplification rate at high gain and fidelity. We examine the amplifier’s performance in different configurations and develop an accurate analytical model that accounts for typical experimental scenarios.
The laws of quantum mechanics pose stringent constraints on the amplification of a quantum signal. Deterministic amplification of an unknown quantum state always implies the addition of a minimal amount of noise. In principle, linear and noiseless amplification is allowed provided it works only probabilistically [1,2]. The state comparison amplifier [3] is an approximate probabilistic amplifier that amplifies a coherent state chosen at random from a set of coherent states with known mean photon number. The amplification process works as follows: Alice picks uniformly at random an input state and passes it to Bob. He desires to amplify the state so he mixes it with a guess coherent state at a beam splitter in an attempt to achieve destructive interference in one of the output arms. This output is fed into an APD detector. The lack of trigger at the detector is an imperfect indication that Bob’s guess is right and that the output contains the correct amplified state. On the other hand, if the first detector fires Bob knows that his guess was wrong but he can still correct the output by changing the input state for a second amplification stage via a feed-forward loop. In summary, Bob declares success when both the detectors do not fire or when the first detector does fire and state correction is performed. We generalize this mechanism for an arbitrary number of input states and beam splitters, using an on-line learning strategy based on maximum a posteriori probability. The success probability-fidelity product [2] of the SCAMP is the joint probability of success and of passing a measurement test on the output comparing it to right amplified state. Our figures of merit compare favorably with other schemes. The success probability-fidelity product of the SCAMP is always bigger than that of a USD based amplifier [2] that, when inconclusive, delivers a conveniently chosen random output. The SCAMP can be realized with classical resources (i.e., lasers, linear optics and APD detectors), the ability to switch between input states on the fly requires delay lines and fast switching but it can still be achieved with classical resources and the loss introduced by the delay can be offset at the second stage. Similar systems, with no state correction, proved to achieve high-gain, high fidelity and high repetition rates, e.g. [4, 5]. Due to its simplicity, the system we propose might represent an ideal candidate either as a recovery station to counteract quantum signal degradation due to propagation in a lossy fibre or across the turbulent atmosphere or as a quantum receiver to improve the key-rate of continuous-variable quantum key distribution with discrete modulation. The system is also suitable for on-chip implementation. [1] T.C. Ralph & A.P. Lund, Proceedings of the 9th QCMC Conference 2009. [2] S. Pandey, et al., Phys. Rev. A 88, 033852 (2013). [3] E. Eleftheriadou et al., Phys. Rev. Lett. 111, 213601 (2013). [4] R. Donaldson et al., Phys. Rev. Lett. 114, 120505 (2015). [5] R. Donaldson et al., in preparation.
Fundamental laws of quantum mechanics impose that arbitrary quantum states cannot be perfectly cloned or amplified without introducing some unavoidable noise in the process. The quantum noise intrinsic to the functioning of a linear phase-insensitive amplifier can however be avoided by relaxing the requirement of a deterministic operation. Non-deterministic noiseless linear amplifiers that do not violate any fundamental quantum law are therefore possible and here we present the first experimental realization of a scheme that allows noiseless amplification of coherent states at the best level of effective gain and final state fidelity ever reached. This scheme, based on a sequence of photon addition and subtraction, and characterized by a significant amplification and low distortions, may become a useful tool for quantum communications and metrology, by enhancing the discrimination between partially overlapping quantum states or by recovering the information transmitted over lossy channels.