We establish and explore a new connection between quantum information theory and classical statistical mechanics by studying the problem of qubit losses in 2D topological color codes. We introduce a protocol to cope with qubit losses, which is based on the identification and removal of a twin qubit from the code, and which guarantees the recovery of a valid three-colorable and trivalent reconstructed color code lattice. Moreover, we show that determining the corresponding qubit loss error threshold is equivalent to a new generalized classical percolation process. We numerically compute the associated qubit loss thresholds for two families of 2D color code and find that these are close to satisfying the fundamental limit $p_\text{fund} = 0.461 \pm 0.005$ close to the 50% as imposed by the no-cloning theorem. Our findings reveal a new connection between topological color codes and percolation theory, show high robustness of color codes against qubit loss, and are relevant for implementations of quantum error correction in various physical platforms.
Quantum information theory has shown strong connections with classical statistical physics. For example, quantum error correcting codes like the surface and the color code present a tolerance to qubit loss that is related to the classical percolation threshold of the lattices where the codes are defined. Here we explore such connection to study analytically the tolerance of the color code when the protocol introduced in [Phys. Rev. Lett. $\textbf{121}$, 060501 (2018)] to correct qubit losses is applied. This protocol is based on the removal of the lost qubit from the code, a neighboring qubit,…
Quantum properties of light, which are crucial resources for Quantum Technologies, are quite fragile in nature and can be degraded and even concealed by the environment. We show, both theoretically and experimentally, that mesoscopic twin-beam states of light can preserve their nonclassicality even in the presence of major losses and different types of noise, thus suggesting their potential usefulness to encode information in Quantum Communication protocols. We develop a comprehensive general analytical model for a measurable nonclassicality criterion and find thresholds on noise and losses fo…
Twin-field (TF) quantum key distribution (QKD) is highly attractive because it can beat the fundamental limit of secret key rate for point-to-point QKD without quantum repeaters. Many theoretical and experimental studies have shown the superiority of TFQKD in long-distance communication. All previous experimental implementations of TFQKD have been done over optical channels with symmetric losses. But in reality, especially in a network setting, the distances between users and the middle node could be very different. In this paper, we perform a first proof-of-principle experimental demonstratio…
Improving the rates and distances over which quantum secure keys are generated is a major challenge. New source and detector hardware can improve key rates significantly, however it can require expensive cooling. We show that Twin Field Quantum Key Distribution (TF QKD) has an advantageous topology allowing the localisation of cooled detectors. This setup for a quantum network allows a fully connected network solution, i.e. one where every connection has non zero key rates, in a box with sides of length up to 110km with just 4 cooled nodes, while Decoy state BB84 is only capable of up to 80km …
A new and simple quantum key distribution scheme based on the quantum intensity correlation of optical twin beams and the directly local measurements of intensity noise of single optical beam is presented and experimentally demonstrated. Using the twin beams with the quantum intensity correlation of 5dB the effective bit rate of $2\times 10^7bits/s$ is completed. The noncloning of quantum systems and the sensitivity of the existing correlations to losses provide the physical mechamism for the security against eavesdropping. In the presented scheme the signal modulation and homodyne detection a…
We report on the absolute calibration of a CCD camera by exploiting quantum correlation. This novel method exploits a certain number of spatial pairwise quantum correlated modes produced by spontaneous parametric-down-conversion. We develop a measurement model taking into account all the possible source of losses and noise that are not related to the quantum efficiency,accounting for all the uncertainty contributions, and we reach the relative uncertainty of 0.3% in low photon flux regime. This represents a significant step forward for the characterizaion of (scientific) CCDs used in mesoscopi…
Motivated by the pursuit of a simple system to produce non-classical light sources for long- distance quantum communication, we generate for the first time an all-fiber source of pulsed twin beams in 1550 nm band by using a high gain fiber optical parametric amplifier. The noise of intensity difference of the twin beams is below the shot noise limit by 3.1 dB (10.4 dB after correction for losses). A detailed study reveals a number of limiting factors for higher noise reduction. Therefore, further noise reduction will be feasible once care is taken for these limiting factors.
We study how heralded qubit losses during the preparation of a two-dimensional cluster state, a universal resource state for one-way quantum computation, affect its computational power. Above the percolation threshold we present a polynomial-time algorithm that concentrates a universal cluster state, using resources that scale optimally in the size of the original lattice. On the other hand, below the percolation threshold, we show that single qubit measurements on the faulty lattice can be efficiently simulated classically. We observe a phase transition at the threshold when the amount of ent…
Twin-field quantum key distribution (TFQKD), using single-photon-type interference, offers a way to exceed the rate-distance limit without quantum repeaters. However, it still suffers from the photon losses and dark counts, which impose an ultimate limit on its transmission distance. In this letter, we propose a scheme to implement TFQKD with an entangled coherent state source in the middle to increase its range, as well as comparing its performance under coherent attacks with that of TFQKD variants. Simulations show that our protocol has a theoretical distance advantage of 400 kilometers. Mor…
Due to their strict photon-number correlation, the twin beams produced in parametric down-conversion (PDC) work well for heralded state generation. Often, however, this state manipulation is distorted by the optical losses in the herald and by the higher photon-number contributions inevitable in the PDC process. In order to find feasible figures of merit for characterizing the heralded states, we investigate their normalized factorial moments of the photon number that can be accessed regardless of the optical losses in the detection. We then perform a measurement of the joint photon statistics…
We present the experimental realization of a theoretical effect discovered by Olivares and Paris, in which a pair of entangled optical beams undergoing independent losses can see nonlocal correlations restored by the use of a nonlocal resource correlating the losses. Twin optical beams created in an entangled Einstein-Podolsky-Rosen (EPR) state by an optical parametric oscillator above threshold were subjected to 50% loss from beamsplitters in their paths. The resulting severe degradation of the signature quantum correlations observed between the two beams was then suppressed when another, ind…
Loss measurements are at the base of spectroscopy and imaging, thus perme- ating all the branches of science, from chemistry and biology to physics and material science. However, quantum mechanics laws set the ultimate limit to the sensitivity, constrained by the probe mean energy. This can be the main source of uncertainty, for example when dealing with delicate system such as biological samples or photosensitive chemicals. It turns out that ordinary (clas- sical) probe beams, namely with Poissonian photon number distribution, are fundamentally inadequate to measure small losses with the high…
Non-degenerate forward four-wave mixing in hot atomic vapors has been shown to produce strong quantum correlations between twin beams of light [McCormick et al, Opt. Lett. 32, 178 (2007)], in a configuration which minimizes losses by absorption. In this paper, we look at the role of the phase-matching condition in the trade-off that occurs between the efficiency of the nonlinear process and the absorption of the twin beams. To this effect, we develop a semi-classical model by deriving the atomic susceptibilities in the relevant double-lambda configuration and by solving the classical propagati…
Any quantum algorithm can be implemented by an adaptive sequence of single node measurements on an entangled cluster of qubits in a square lattice topology. Photons are a promising candidate for encoding qubits but assembling a photonic entangled cluster with linear optical elements relies on probabilistic operations. Given a supply of $n$-photon-entangled microclusters, using a linear optical circuit and photon detectors, one can assemble a random entangled state of photons that can be subsequently "renormalized" into a logical cluster for universal quantum computing. In this paper, we prove …
We develop a scheme for generating a universal qubit cluster state using probabilistic Bell measurements without the need for feed-forward or long-time quantum memories. Borrowing ideas from percolation theory we numerically show that using unambiguous Bell measurements that succeed with 75% success probability, one could build a cluster state with an underlying pyrochlore geometry such that the probability of having a spanning cluster in a chosen direction approaches unity in the limit of an infinite lattice size. The initial resources required for the generation of a universal state in our p…
Proof-of-principle long-distance Sagnac twin-field quantum key distribution network
University of Toronto（多伦多大学）；National Tsing Hua University（国立清华大学）；National University of Singapore（新加坡国立大学）；Quantum Bridge Technologies, Inc.（量子桥科技有限公司）
We explore the advantages offered by twin light beams produced in parametric down-conversion for precision measurement. The symmetry of these bipartite quantum states, even under losses, suggests that monitoring correlations between the divergent beams permits a high-precision inference of any symmetry-breaking effect, e.g. fiber birefringence. We show that the quantity of entanglement is not the key feature for such an instrument. In a lossless setting, scaling of precision at the ultimate `Heisenberg' limit is possible with photon counting alone. Even as photon losses approach 100% the preci…
We have built a compact light source for bright squeezed twin-beams at 795\,nm based on four-wave-mixing in atomic $^{85}$Rb vapor. With a total optical power of 400\,mW derived from a free running diode laser and a tapered amplifier to pump the four-wave-mixing process, we achieve 2.1\,dB intensity difference squeezing of the twin beams below the standard quantum limit, without accounting for losses. Squeezed twin beams generated by the type of source presented here could be used as reference for the precise calibration of photodetectors. Transferring the quantum correlations from the light t…
Twin-field quantum key distribution (TFQKD) systems have shown great promise for implementing practical long-distance secure quantum communication due to its measurement-device-independent nature and its ability to offer fundamentally superior rate-loss scaling than point-to-point QKD systems. A surge of research and development effort in the last two years has produced many variants of protocols and experimental demonstrations. In terms of hardware topology, TFQKD systems interfering quantum signals from two remotely phase-locked laser sources are in essence giant Mach-Zehnder interferometers…
Many proposals for quantum information processing are subject to detectable loss errors. In this paper, we show that topological error correcting codes, which protect against computational errors, are also extremely robust against losses. We present analytical results showing the maximum tolerable loss rate is 50 %, which is determined by the square-lattice bond percolation threshold. This saturates the bound set by the no-cloning theorem. Our numerical results support this, and show a graceful trade-off between computational and loss errors.
Many proposals for fault tolerant quantum computation (FTQC) suffer detectable loss processes. Here we show that topological FTQC schemes, which are known to have high error thresholds, are also extremely robust against losses. We demonstrate that these schemes tolerate loss rates up to 24.9%, determined by bond percolation on a cubic lattice. Our numerical results show that these schemes retain good performance when loss and computational errors are simultaneously present.
In the last years the exploitation of specific properties of quantum states has disclosed the possibility of realising tasks beyond classical limits, creating the new field of quantum technologies [1, 2, 3, 4, 5, 6, 7, 8, 9]. Among them, quantum metrology and imaging aim to improve the sensitivity and/or resolution of measurements exploiting non-classical features such as squeezing and quantum correlations (entanglement and discordant states) [10, 11, 12, 13, 14]. Nevertheless, in most of the realistic scenarios losses and noise are known to nullify the advantage of adopting quantum strategies…
We have studied theoretical un-symmetric multi-photon subtracted twin beam state and demonstrated a method for generating states that resembles to high photon number states with the increase in the number of subtracted photons through Wigner distribution function, which can be reconstructed experimentally by Homodyne measurement. A crucial point is high non-classicality is obtained by photon subtraction when mean photons per mode of twin beam state is low. We have calculated photon statistics from the phase space distribution function and found sub-poissonian behaviour in the same low mean pho…
