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Register a new userQuantum state engineering by non-deterministic noiseless linear amplification
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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.
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We address the characterization of the gain parameter of a non-deterministic noiseless linear amplifier (NLA) and compare the performances of different estimation strategies using tools from quantum estimation theory. At first, we show that, contrary to naive expectations, post-selecting only the amplified states does not offer the most accurate estimate. We then focus on minimal implementations of a NLA, i.e. those obtained by coupling the input state to a two-level system, and show that the maximal amount of information about the gain of the NLA is obtained by measuring the whole composite system. The quantum Fisher information (QFI) of this best-case scenario is analysed in some details, and compared to the QFI of the post-selected states, both for successful and unsuccessful amplification. Eventually, we show that full extraction of the available information is achieved when the non-deterministic process is implemented by a Luders instrument. We also analyse the precision attainable by probing NLAs by single-mode pure states and measuring the field or the number of quanta, and discuss in some details the specific cases of squeezed vacuum and coherent states.
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.
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
Quantum mechanics imposes that any amplifier that works independently on the phase of the input signal has to introduce some excess noise. The impossibility of such a noiseless amplifier is rooted into unitarity and linearity of quantum evolution. A possible way to circumvent this limitation is to interrupt such evolution via a measurement, providing a random outcome able to herald a successful - and noiseless - amplification event. Here we show a successful realisation of such an approach; we perform a full characterization of an amplified coherent state using quantum homodyne tomography, and observe a strong heralded amplification, with about 6dB gain and a noise level significantly smaller than the minimal allowed for any ordinary phase-independent device.
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.
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