On-chip implementation of the probabilistic quantum optical state comparison amplifier
David W. Canning, Ross J. Donaldson, Sebabrata Mukherjee, Robert John Collins, Luca Mazzarella, Ugo Zanforlin, John Jeffers, Robert R. Thomson, Gerald S. Buller
Propagation losses in transmission media limit the transmission distance of optical signals. In the case where the signal is made up of quantum optical states, conventional deterministic optical amplification schemes cannot be used to increase the transmission distance as the copying of an arbitrary and unknown quantum state is forbidden. One strategy that can offset propagation loss is the use of probabilistic, or non-deterministic, amplification schemes - an example of which is the state comparison amplifier. Here we report a state comparison amplifier implemented in a compact, fiber-coupled femtosecond laser-written waveguide chip as opposed to the large, bulk-optical components of previous designs. This pathfinder on-chip implementation of the quantum amplifier has resulted in several performance improvements: the polarization integrity of the written waveguides has resulted in improved visibility of the amplifier interferometers; the potential of substantially-reduced losses throughout the amplifier configuration; and a more compact and environmentally-stable amplifier which is scalable to more complex networks.
Propagation losses in transmission media limit the transmission distance of optical signals. In the case where the signal is made up of quantum optical states, conventional deterministic optical amplification schemes cannot be used to increase the transmission distance as the copying of an arbitrary and unknown quantum state is forbidden. One strategy that can offset propagation loss is the use of probabilistic, or non-deterministic, amplification schemes - an example of which is the state comparison amplifier. Here we report a state comparison amplifier implemented in a compact, fiber-coupled femtosecond laser-written waveguide chip as opposed to the large, bulk-optical components of previous designs. This pathfinder on-chip implementation of the quantum amplifier has resulted in several performance improvements: the polarization integrity of the written waveguides has resulted in improved visibility of the amplifier interferometers; the potential of substantially-reduced losses throughout the amplifier configuration; and a more compact and environmentally-stable amplifier which is scalable to more complex networks.
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.
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.
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.
Quantum mechanics imposes 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. Linear and noiseless amplification is allowed in principle provided that it only works probabilistically. Here we present a probabilistic amplifier that combines two quantum state comparison amplifiers (SCAMP) together with a feed-forward state correction strategy. Our system outperforms the unambiguous state discrimination (USD) measure-and-resend based amplifier in terms of the success probability-fidelity product and requires a more complex experimental setting.
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 and a deterministic linear amplifier. The concatenation of two amplifiers introduces the flexibility that allows one to tune between the regimes of high-gain or high noise-reduction, and control the trade-off of these performances against a finite heralding probability. We demonstrate an amplification signal transfer coefficient of Ts>1 with no statistical distortion of the output state. By partially relaxing the demand of output Gaussianity, we can obtain further improvement to achieve a Ts=2.55±0.08. Our amplification scheme only relies on linear optics and post-selection algorithm. We discuss the potential of using this amplifier as a building block in extending the distance of quantum communication.