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Register a new userNoiseless Linear Amplification and Distillation of Entanglement
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The idea of signal amplification is ubiquitous in the control of physical systems, and the ultimate performance limit of amplifiers is set by quantum physics. Increasing the amplitude of an unknown quantum optical field, or more generally any harmonic oscillator state, must introduce noise. This linear amplification noise prevents the perfect copying of the quantum state, enforces quantum limits on communications and metrology, and is the physical mechanism that prevents the increase of entanglement via local operations. It is known that non-determinist
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Despite an extensive research on protecting entanglement from decoherence, it remains a challenge to protect Einstein-Podolsky-Rosen (EPR) steering due to its intrinsic difference from entanglement. We experimentally demonstrate the distillation of Gaussian EPR steering and entanglement in lossy and noisy environment using measurement-based noiseless linear amplification (NLA). Different from entanglement distillation, the extension of steerable region is observed in the distillation of EPR steering besides the enhancement of steerability. We recover the two-way steerability from one-way in certain region of loss and enhance steerablilities for both directions when the NLA based on Bobs measurement results is implemented. The one-way steering can even be recovered from non-steerable region in a certain extent in a noisy environment by implementing the NLA based on Alices measurement results. As an application, the distilled EPR steering is used to extract secret key in one-sided device-independent quantum key distribution.
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 the efficacy of the noiseless linear amplifier. The measures used are the amount of entanglement achievable and the final purity of the output amplified entangled state. We study the performances of both a single and a two-element noiseless linear amplifier for amplifying weakly excited states. Practically, we show that it may be advantageous to work with a limited number of stages.
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 $|alpha| gtrsim 0.91$, the $(hat a^{dagger})^2$ operation serves as a more efficient amplifier compared to the $hat a hat a^dagger$ operation in terms of equivalent input noise. Using $hat a hat a^dagger$ and $(hat a^{dagger})^2$ as basic building blocks, we compare combinatorial amplifications of coherent states using $(hat a hat a^dagger)^2$, $hat a^{dagger 4}$, $hat a hat a^daggerhat a^{dagger 2}$, and $hat a^{dagger 2}hat a hat a^dagger$, and show that $(hat a hat a^dagger)^2$, $hat a^{dagger 2}hat a hat a^dagger$, and $hat a^{dagger 4}$ exhibit strongest noiseless properties for $|alpha| lesssim 0.51$, $0.51 lesssim |alpha| lesssim 1.05 $, and $|alpha|gtrsim 1.05 $, respectively. We further show that the $(hat a^{dagger})^2$ operation can be used for amplifying superpositions of the coherent states. In contrast to previous studies, our work provides efficient schemes to implement a noiseless amplifier for light fields with medium and large amplitudes.
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), noisy channel and non-ideal detection are also discussed.
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