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  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  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  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.
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 R. Donaldson et al., Phys. Rev. Lett. 114, 120505 (2015).
 R. Donaldson et al., in preparation.
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 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.
We describe a protocol in which we detect intercept-resend jamming of imaging and can reverse its effects. The security is based on control of the polarization states of photons that are sent to interrogate an object and form an image at a camera. The scheme presented here is a particular implementation of a general anti-jamming protocol established by Roga and Jeffers in Ref. 5. It is applied here to imaging by photons with partially distinguishable polarisation states. The protocol in this version is easily applicable as only single photon states are involved, however the efficiency is traded off against the intrusion detectability because of a leak of information to the intruder.
Imaging technologies working at very low light levels acquire data by attempting to count the number of photons impinging on each pixel. Especially in cases with, on average, less than one photocount per pixel the resulting images are heavily corrupted by Poissonian noise and a host of successful algorithms trying to reconstruct the original image from this noisy data have been developed. Here we review a recently proposed scheme that complements these algorithms by calculating the full probability distribution for the local intensity distribution behind the noisy photocount measurements. Such a probabilistic treatment opens the way to hypothesis testing and confidence levels for conclusions drawn from image analysis.
Classical digital signatures are commonly used in e-mail, electronic financial transactions and other forms of electronic
communications to ensure that messages have not been tampered with in transit, and that messages are transferrable. The
security of commonly used classical digital signature schemes relies on the computational difficulty of inverting certain
mathematical functions. However, at present, there are no such one-way functions which have been proven to be hard to
invert. With enough computational resources certain implementations of classical public key cryptosystems can be, and
have been, broken with current technology. It is nevertheless possible to construct information-theoretically secure
signature schemes, including quantum digital signature schemes. Quantum signature schemes can be made information theoretically
secure based on the laws of quantum mechanics, while classical comparable protocols require additional
resources such as secret communication and a trusted authority.
Early demonstrations of quantum digital signatures required quantum memory, rendering them impractical at present.
Our present implementation is based on a protocol that does not require quantum memory. It also uses the new technique
of unambiguous quantum state elimination, Here we report experimental results for a test-bed system, recorded with a
variety of different operating parameters, along with a discussion of aspects of the system security.
As society becomes more reliant on electronic communication and transactions, ensuring the security of these interactions becomes more important. Digital signatures are a widely used form of cryptography which allows parties to certify the origins of their communications, meaning that one party, a sender, can send information to other parties in such a way that messages cannot be forged. In addition, messages are transferrable, meaning that a recipient who accepts a message as genuine can be sure that if it is forwarded to another recipient, it will again be accepted as genuine. The classical digital signature schemes currently employed typically rely on computational complexity for security. Quantum digital signatures offer the potential for increased security. In our system, quantum signature states are passed through a network of polarization maintaining fiber interferometers (a multiport) to ensure that recipients will not disagree on the validity of a message. These signatures are encoded in the phase of photonic coherent states and the choice of photon number, signature length and number of possible phase states affects the level of security possible by this approach. We will give a brief introduction into quantum digital signatures and present results from our experimental demonstration system.
Digital signature schemes are often used in interconnected computer networks to verify the origin and authenticity of messages. Current classical digital signature schemes based on so-called “one-way functions” rely on computational complexity to provide security over sufficiently long timescales. However, there are currently no mathematical proofs that such functions will always be computationally complex. Quantum digital signatures offers a means of confirming both origin and authenticity of a message with security verified by information theoretical limits. The message cannot be forged or repudiated. We have constructed, tested and analyzed the security of what is, to the best of our knowledge, the first example of an experimental quantum digital signature system.