Abstract We study feasible and effective techniques to improve the efficiency and fidelity of photon subtraction in order to enable practical quantum resource engineering based on it. We use thermal light for our investigation and consider non-negligible beam splitting beyond the conventional setup, also taking into account photon detection errors. We find that the output is still a photon-subtracted thermal state when a non-negligible amount of light is reflected from the input beam and measured by the photon detector, but it has an effective mean photon number different than that of the input. It enables a strategy for achieving a target photon-subtracted thermal state by employing a stronger input light and leads to substantial improvement in the probability of successful photon subtraction events. We calculate the fidelity of the output state and analyze how it worsens with larger beam splitting ratios and photon counting errors. Using our understanding of the limiting factors in the conventional routine, we propose a new method for photon subtraction that can achieve high-fidelity output with decent efficiency, and using only mediocre photon detectors. We experimentally verify our solutions that are valuable for improving photon subtraction and lowering the experimental barrier.
Abstract We study feasible and effective techniques to improve the efficiency and fidelity of photon subtraction in order to enable practical quantum resource engineering based on it. We use thermal light for our investigation and consider non-negligible beam splitting beyond the conventional setup, also taking into account photon detection errors. We find that the output is still a photon-subtracted thermal state when a non-negligible amount of light is reflected from the input beam and measured by the photon detector, but it has an effective mean photon number different than that of the input. It enables a strategy for achieving a target photon-subtracted thermal state by employing a stronger input light and leads to substantial improvement in the probability of successful photon subtraction events. We calculate the fidelity of the output state and analyze how it worsens with larger beam splitting ratios and photon counting errors. Using our understanding of the limiting factors in the conventional routine, we propose a new method for photon subtraction that can achieve high-fidelity output with decent efficiency, and using only mediocre photon detectors. We experimentally verify our solutions that are valuable for improving photon subtraction and lowering the experimental barrier.
Thermal radiation played a pivotal role in the preliminary development of quantum physics where it helped resolve the apparent incongruity of the ultraviolet catastrophe. In contemporary physics, thermal state generation and manipulation finds new application in fields such as quantum imaging and quantum illumination and as a practical realization of Maxwell's demon. These applications often go hand in hand with photon subtraction operations which probabilistically amplify the mean photon number (MPN) of thermal light as a result of its super-Poissonian photon statistics. In this article, we introduce an operation for thermal states of light based on a generalized photon subtraction scheme. Displaced-photon subtraction (DPS) makes use of coherent state displacement followed by a subsequent anti-displacement in combination with single-photon detection to probe the MPN of a thermal state. We find regimes in which the output of a successful DPS is amplified, unchanged, or attenuated relative to the unconditioned output state. The regime of operation is controlled via the magnitude of the coherent displacement. A theoretical description of generalized photon subtraction of a displaced thermal state is derived via a two-mode moment-generating function (MGF) and used to describe generalized DPS. We perform a proof of principle experimental implementation of DPS for the case of a balanced beam splitter for which results demonstrate good agreement with the model.
Subtracting photons from a two-mode squeezed state is a well-known method to increase entanglement. We analyze different strategies of local photon subtraction from a two-mode squeezed state in terms of entanglement gain and success probability. We develop a general framework that incorporates imperfections and losses in all stages of the process: before, during, and after subtraction. By combining all three effects into a single efficiency parameter, we provide analytical and numerical results for subtraction strategies using photon-number-resolving and threshold detectors. We compare the entanglement gain afforded by symmetric and asymmetric subtraction scenarios across the two modes. For a given amount of loss, we identify an optimized set of parameters, such as initial squeezing and subtraction beam splitter transmissivity, that maximize the entanglement gain rate. We identify regimes for which asymmetric subtraction of different Fock states on the two modes outperforms symmetric strategies. In the lossless limit, subtracting a single photon from one mode always produces the highest entanglement gain rate. In the lossy case, the optimal strategy depends strongly on the losses on each mode individually, such that there is no general optimal strategy. Rather, taking losses on each mode as the only input parameters, we can identify the optimal subtraction strategy and required beam splitter transmissivities and initial squeezing parameter. Finally, we discuss the implications of our results for the distillation of continuous-variable quantum entanglement.
Photon-number-resolving superconducting photon detectors promise to simplify detection schemes where only photon statistics matters in the few-photon regimes. Employed in one- and two-photon subtraction protocols, they allowed reconstruction of the photon number distribution for coherent and thermal states obtained from a pulsed laser at telecom wavelengths. The experimental setup is based on photon detection events recorded using a photon-number-resolving detector based on an array of eight superconducting NbN nanostrips working at 2.2 K. Photon subtraction was implemented using a low-reflectivity beam splitter and two superconducting nanostrip single photon detectors with an efficiency higher than 90% and a dark count rate of 1 cps. Our results confirm that our scheme accurately reproduces the theoretically expected effects of the annihilation operator on the states, achieving a fidelity higher than 99%.
Realistic non-Gaussian operations, which can be implemented by mixing a nonclassical Gaussian state with a Fock state at a beam splitter and then heralding on a photon-number-resolving detector, are known to improve phase estimation in a Mach-Zehnder interferometer. The existing studies have considered the single-mode squeezed vacuum for difference-intensity and parity detection, and the two-mode squeezed thermal state for parity detection alone as the initial Gaussian resources. However, a real squeezer in the lab actually produces single-mode squeezed thermal light, which has not been studied in a coherent-plus-resource interferometer. We take up this case and using the phase space Wigner picture, we obtain the heralded state produced by photon subtraction, addition and catalysis on a single-mode squeezed thermal resource, and evaluate the corresponding phase sensitivities. Single-photon catalysis, which is useless on squeezed vacuum, becomes a useful operation for any thermal occupation above $\nth\simeq0.2$, and since it heralds with a probability near one-half, it turns out to be the best success-weighted operation over the whole thermal range. In the vacuum limit our results reproduce the known hierarchy, where two-photon catalysis is the best operation. The quantum Fisher information computations confirms that thermal noise enhances the phase information encoded in the catalyzed state, demonstrating that difference-intensity detection closely approaches the ultimate precision bound across most operational regimes, and, together with a loss analysis, verifies the robustness of the effect.
Engineering quantum states of light represents a crucial task in the vast majority of photonic quantum technology applications. Direct manipulation of the number of photons in the light signal, such as single-photon subtraction and addition, proved to be an efficient strategy for the task. Here we propose an adaptive multi-photon subtraction scheme where a particular subtraction task is conditioned by all previous subtraction events in order to maximize the probability of successful subtraction. We theoretically illustrate this technique on the model example of conversion of Fock states via photon subtraction. We also experimentally demonstrate the core building block of the proposal by implementing a feedforward-assisted conversion of two-photon state to a single-photon state. Our experiment combines two elementary photon subtraction blocks where the splitting ratio of the second subtraction beam splitter is affected by the measurement result from the first subtraction block in real time using an ultra-fast feedforward loop. The reported optimized photon subtraction scheme applies to a broad range of photonic states, including highly nonclassical Fock states and squeezed light, advancing the photonic quantum toolbox.
We develop a method for generating a more squeezed than single-mode squeezed vacuum (SMSV) state by subtracting 2,4,6 photons from it. In general, the more photons are subtracted, the more gain of the squeezing (more of 3 dB) is observed in the measurement-induced continuous variable (CV) states of definite parity. However, the two-photon subtraction strategy is practically preferred. It can be implemented with higher success probability, wider squeezing gain width ~ 5 dB and least quadrature variance in the corresponding range of initial squeezing. We demonstrate the mitigating effect of a photon-number resolving (PNR) detector with non-unit quantum efficiency on the output characteristics of the measurement-induced CV states, resulting in their slight decrease compared to ideal photon subtraction. Use of a single photon in addition to the SMSV state at beam splitter (BS) input with subsequent registration of odd number of photons (say, 3 photons) allows the implementation of the measurement-induced even CV state which is several times brighter than the initial state and has lower quadrature noise.