Imperfect Single-photon Sources Research Articles

Measurement-device-independent quantum random number generation over 23 Mbps with imperfect single-photon sources

Quantum randomness relies heavily on the accurate characterization of the generator implementation, where the device imperfection or inaccurate characterization can lead to incorrect entropy estimation and practical bias, significantly affecting the reliability of the generated randomness. Measurement-device-independent (MDI) quantum random number generation (QRNG) endeavors to produce certified randomness, utilizing uncharacterized and untrusted measurement devices that are vulnerable to numerous attack schemes targeting measurement loopholes. However, existing implementations have shown insufficient performance thus far. Here, we propose a high-speed MDI-QRNG scheme based on a robust measurement tomography approach against the imperfection of single-photon sources. Compared with the conventional approach, the decoy-state method is introduced to obtain more accurate tomography results and a tighter lower bound of randomness. Finally, by using a high-speed time-bin encoding system, we experimentally demonstrated the scheme and obtained a reliable min-entropy lower bound of 7.37×10−2 bits per pulse, corresponding to a generation rate over 23 Mbps, which substantially outperforms the existing realizations and makes a record in discrete-variable semi-device-independent QRNGs.

Measurement-Device-Independent Verification of Quantum Channels.

The capability to reliably transmit and store quantum information is an essential building block for future quantum networks and processors. Gauging the ability of a communication link or quantum memory to preserve quantum correlations is therefore vital for their technological application. Here, we experimentally demonstrate a measurement-device-independent protocol for certifying that an unknown channel acts as an entanglement-preserving channel. Our results show that, even under realistic experimental conditions, including imperfect single-photon sources and the various kinds of noise-in the channel or in detection-where other verification means would fail or become inefficient, the present verification protocol is still capable of affirming the quantum behavior in a faithful manner with minimal trust on the measurement device.

Security of two-state and four-state practical quantum bit-commitment protocols

We study cheating strategies against a practical four-state quantum bit-commitment protocol and its two-state variant when the underlying quantum channels are noisy and the cheating party is constrained to using single-qubit measurements only. We show that simply inferring the transmitted photons' states by using the Breidbart basis, optimal for ambiguous (minimum-error) state discrimination, does not directly produce an optimal cheating strategy for this bit-commitment protocol. We introduce a new strategy, based on certain post-measurement processes, and show it to have better chances at cheating than the direct approach. We also study to what extent sending forged geographical coordinates helps a dishonest party in breaking the binding security requirement. Finally, we investigate the impact of imperfect single-photon sources in the protocols. Our study shows that, in terms of the resources used, the four-state protocol is advantageous over the two-state version. The analysis performed can be straightforwardly generalised to any finite-qubit measurement, with the same qualitative results.

Simulating single photons with realistic photon sources

Quantum information processing provides remarkable advantages over its classical counterpart. Quantum optical systems are proved to be sufficient for realizing general quantum tasks, which however often rely on single photon sources. In practice, imperfect single photon sources, such as weak coherent state source, are used instead, which will inevitably limit the power in demonstrating quantum effects. For instance, with imperfect photon sources, the key rate of the BB84 quantum key distribution protocol will be very low, which fortunately can be resolved by utilizing the decoy state method. As a generalization, we investigate an efficient way to simulate single photons with imperfect ones to an arbitrary desired accuracy when the number of photonic inputs is small. Based on this simulator, we can thus replace the tasks that involve only a few single photon inputs with the ones that only make use of imperfect photon sources. In addition, our method also provides a quantum simulator to quantum computation based on quantum optics. In the main context, we take phase randomized coherent state as an example for analysis. A general photon source applies similarly and may provide some further advantages for certain tasks.

Long-Distance Trust-Free Quantum Key Distribution

The feasibility of trust-free long-haul quantum key distribution (QKD) is addressed. We combine measurement-device-independent QKD, as an access technology, with a quantum repeater setup, at the core of future quantum communication networks. This will provide a quantum link none of whose intermediary nodes need to be trusted, or, in our terminology, a trust-free QKD link. As the main figure of merit, we calculate the secret key generation rate when a particular probabilistic quantum repeater protocol is in use. We assume the users are equipped with imperfect single photon sources, which can possibly emit two single photons, or laser sources to implement decoy-state techniques. We consider apparatus imperfection, such as quantum efficiency and dark count of photodetectors, path loss of the channel, and writing and reading efficiencies of quantum memories. By optimizing different system parameters, we estimate the maximum distance over which users can share secret keys when a finite number of memories are employed in the repeater setup.

Protecting single-photon entanglement with imperfect single-photon source

Photon noiseless linear amplification (NLA) is a powerful way to protect the single photon or single-photon entanglement (SPE) from photon loss. However, current NLA protocols for single photon or SPE usually require the local auxiliary single photon, but the ideal single-photon source is unavailable in current technology. In this paper, we investigate the NLA protocols for both single photon and SPE with imperfect single-photon source. We show that the quality of amplified quantum state greatly depends on the imperfect single-photon sources. The upper bound of the fidelity of the amplified quantum state is the fidelity of the single-photon source. In this way, in order to realize the amplification, we should require the fidelity of the single-photon source to be greater than the fidelity of the initial degraded state.

Measurement-Device-Independent Quantum Key Distribution With Ensemble-Based Memories

Quantum memories are enabling devices for extending the reach of quantum key distribution (QKD) systems. The required specifications for memories are, however, often considered too demanding for available technologies. One can change this mindset by introducing memory-assisted measurement-device-independent QKD (MDI-QKD), which imposes less stringent conditions on the memory modules. It has been shown that, in the case of {\em fast} single-qubit memories, we can reach rates and distances not attainable by single no-memory QKD links. Single-qubit memories, such as single atoms or ions, have, currently, too slow of an access time to offer an advantage in practice. Here, we relax that assumption, and consider ensemble-based memories, which satisfy the main two requirements of having short access times and large storage-bandwidth products. Our results, however, suggest that the multiple-excitation effects in such memories can be so detrimental that they may wash away the scaling improvement offered by memory-equipped systems. We then propose an alternative setup that can in principle remedy the above problem. As a prelude to our main problem, we also obtain secret key generation rates for MDI-QKD systems that rely on imperfect single-photon sources with nonzero probabilities of emitting two photons.

Linear optics schemes for entanglement distribution with realistic single-photon sources

We study the operation of linear optics schemes for entanglement distribution based on nonlocal photon subtraction when input states, produced by imperfect single-photon sources, exhibit both vacuum and multiphoton contributions. Two models for realistic photon statistics with radically different properties of the multiphoton "tail" are considered. The first model assumes occasional emission of double photons and linear attenuation, while the second one is motivated by heralded sources utilizing spontaneous parametric down-conversion. We find conditions for the photon statistics that guarantee generation of entanglement in the relevant qubit subspaces and compare it with classicality criteria. We also quantify the amount of entanglement that can be produced with imperfect single-photon sources, optimized over setup parameters, using as a measure entanglement of formation. Finally, we discuss verification of the generated entanglement by testing Bell's inequalities. The analysis is carried out for two schemes. The first one is the well-established one-photon scheme, which produces a photon in a delocalized superposition state between two nodes, each of them fed with one single photon at the input. As the second scheme, we introduce and analyze a linear-optics analog of the robust scheme based on interfering two Stokes photons emitted by atomic ensembles, which does not require phase stability between the nodes.

Noise and measurement errors in a practical two-state quantum bit commitment protocol

We present a two-state practical quantum bit commitment protocol, the security of which is based on the current technological limitations, namely the nonexistence of either stable long-term quantum memories or nondemolition measurements. For an optical realization of the protocol, we model the errors, which occur due to the noise and equipment (source, fibers, and detectors) imperfections, accumulated during emission, transmission, and measurement of photons. The optical part is modeled as a combination of a depolarizing channel (white noise), unitary evolution (e.g., systematic rotation of the polarization axis of photons), and two other basis-dependent channels, namely the phase- and bit-flip channels. We analyze quantitatively the effects of noise using two common information-theoretic measures of probability distribution distinguishability: the fidelity and the relative entropy. In particular, we discuss the optimal cheating strategy and show that it is always advantageous for a cheating agent to add some amount of white noise---the particular effect not being present in standard quantum security protocols. We also analyze the protocol's security when the use of (im)perfect nondemolition measurements and noisy or bounded quantum memories is allowed. Finally, we discuss errors occurring due to a finite detector efficiency, dark counts, and imperfect single-photon sources, and we show that the effects are the same as those of standard quantum cryptography.

Second-order superposition operations via Hong-Ou-Mandel interference

We propose an experimental scheme to implement a second-order nonlocal superposition operation ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}^{\ifmmode\dagger\else\textdagger\fi{}2}+{e}^{i\ensuremath{\varphi}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}}^{\ifmmode\dagger\else\textdagger\fi{}2}$ and its variants by way of Hong-Ou-Mandel interference. The second-order coherent operations enable us to generate a NOON state with high particle number in a heralded fashion and also can be used to enhance the entanglement properties of continuous variable states. We discuss the feasibility of our proposed scheme considering realistic experimental conditions such as on-off photodetectors with nonideal efficiency and imperfect single-photon sources.

Linear-Optical Processing Cannot Increase Photon Efficiency

We answer the question whether linear-optical processing of the states produced by one or multiple imperfect single-photon sources can improve the single-photon fidelity. This processing can include arbitrary interferometers, coherent states, feedforward, and conditioning on results of detections. We show that without introducing multiphoton components, the single-photon fraction in any of the single-mode states resulting from such processing cannot be made to exceed the efficiency of the best available photon source. If multiphoton components are allowed, the single-photon fidelity cannot be increased beyond 1/2. We propose a natural general definition of the quantum-optical state efficiency, and show that it cannot increase under linear-optical processing.

Heralded single-photon generation using imperfect single-photon sources and a two-photon-absorbing medium

We propose a setup for a heralded, i.e., announced generation of a pure single-photon state given two imperfect sources whose outputs are represented by mixtures of the single-photon Fock state $\ensuremath{\mid}1⟩$ with the vacuum $\ensuremath{\mid}0⟩$. Our purification scheme uses beam splitters, photodetection, and a two-photon-absorbing medium. The admixture of the vacuum is fully eliminated. We discuss two potential realizations of the scheme.