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arXiv:1211.3794 · New Journal of Physics

Nondeterministic noiseless amplification via non-symplectic phase space transformations

Nathan Walk, Austin P. Lund, Timothy C. Ralph

Published Jul 5, 2013• 29 citations
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Abstract

We analyse the action of an ideal noiseless linear amplifier operator, , 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 purity of the distilled entanglement, and for optimizing the use of the amplification in quantum information protocols.

DOI
10.1088/1367-2630/15/7/073014

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We analyse the action of an ideal noiseless linear amplifier operator, , 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 purity of the distilled entanglement, and for optimizing the use of the amplification in quantum information protocols.
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 attainable. The relation between input coherent states and gain of amplification for deterministic noiseless amplification is thus derived. Furthermore, we extend our result to more general situation and show that deterministic noiseless amplification of Gaussian states is also possible. As an example of application, we find that our amplification model can obtain better performance in homodyne detection to measure the phase of state selected from a certain set. Besides, other possible applications are also discussed.
We address quantum state engineering of single- and two-mode states by means of nondeterministic noiseless linear amplifiers (NLAs) acting on Gaussian states. In particular, we consider the optimal implementation of a NLA proposed by Pandey et al. [Phys. Rev. A 88, 033852 (2013)] and we show that it provides an effective scheme to generate highly non-Gaussian and nonclassical states, when used outside the regime of high-fidelity amplification. Additionally, we show that in this regime also the amplification of a two-mode squeezed vacuum state (twin-beam) highly increases entanglement.
Noiseless linear amplification (NLA), first proposed by Ralpha et al., is a nondeterministic amplification process which gives gain to the Fock state |n〉 → g n |n〉, with g being the amplification gain. We here give a general framework for improving the NLA scheme with arbitrary general local unitary operations. We derive the improvement in the amplification gain in 0–1 photon subspace. In particular, we study if the local unitary is composed of single mode squeezing and coherent displacement operation. Finally, numerical simulations show that local unitary operation could give a further enhancement in the amplification gain as well as the success probability, making the NLA more feasible in future optic quantum communications.
Traditionally, quantum amplification limit refers to the property of inevitable noise addition on canonical variables when the field amplitude of an unknown state is linearly transformed through a quantum channel. Recent theoretical studies have determined amplification limits for cases of probabilistic quantum channels or general quantum operations by specifying a set of input states or a state ensemble. However, it remains open how much excess noise on canonical variables is unavoidable and whether there exists a fundamental trade-off relation between the canonical pair in a general amplification process. In this paper we present an uncertainty-product form of amplification limits for general quantum operations by assuming an input ensemble of Gaussian-distributed coherent states. It can be derived as a straightforward consequence of canonical uncertainty relations and retrieves basic properties of the traditional amplification limit. In addition, our amplification limit turns out to give a physical limitation on probabilistic reduction of an Einstein-Podolsky-Rosen uncertainty. In this regard, we find a condition that probabilistic amplifiers can be regarded as local filtering operations to distill entanglement. This condition establishes a clear benchmark to verify an advantage of non-Gaussian operations beyond Gaussian operations with a feasible input set of coherent states and standard homodyne measurements.
Abstract 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 amplifier at the detection stage of a quantum illumination-based quantum target detection protocol. Such a non-Gaussian amplifier offers a means of probabilistically amplifying an incoming signal without the addition of noise. Considering symmetric hypothesis testing, the quantum Chernoff bound is derived and limits on detection error probability is analysed for both the two-mode squeezed vacuum state and the coherent state classical benchmark. Our findings show that in such a scheme the potential quantum advantage is amplified even in regimes where quantum illumination alone offers no advantage, thereby extending its potential use. The same cannot be said for coherent states, whose performances are generally bounded by that without amplification.
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 signal, but the energy required to amplify the signal originates from the stochastic fluctuations in the field itself. Applying our amplification scheme, we examine the amplifier gain and the success rate as well as the properties of the output states after successful and failed amplification processes. We also optimize the setup to find the maximum success rates in terms of the reflectivities of the beam splitters used in the setup. In addition, we discuss the nonidealities related to the operation of our setup and the relation of our setup with the previous setups.