Efficient Toffoli Gates Using Qudits

The simplest decomposition of a Toffoli gate acting on three qubits requires {\em five} 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to six. We show that the number of controlled-sign gates required to implement a Toffoli gate can be reduced to just {\em three} if one of the three quantum systems has a third state that is accessible during the computation, i.e. is actually a qutrit. Such a requirement is not unreasonable or even atypical since we often artificially enforce a qubit structure on multilevel quantums systems (eg. atoms, photonic polarization and spatial modes). We explore the implementation of these techniques in optical quantum processing and show that linear optical circuits could operate with much higher probabilities of success

Compensating for Beamsplitter Asymmetries in Quantum Interference Experiments

The visibility of the quantum interference "dip" seen in the Hong-Ou-Mandel experiment is optimized when a symmetric 50/50 beamsplitter is used in the interferometer. Here we show that the reduction in visibility caused by an asymmetric beamsplitter can be compensated by manipulating the polarization states of the two input photons. We experimentally demonstrate this by using a highly asymmetric 10/90 beamsplitter, and converting an initial dip visibility of 22% to a compensated value of 99%.Comment: 3 pages, 4 figure

Quantum computing on encrypted data

The ability to perform computations on encrypted data is a powerful tool for protecting privacy. Recently, protocols to achieve this on classical computing systems have been found. Here we present an efficient solution to the quantum analogue of this problem that enables arbitrary quantum computations to be carried out on encrypted quantum data. We prove that an untrusted server can implement a universal set of quantum gates on encrypted quantum bits (qubits) without learning any information about the inputs, while the client, knowing the decryption key, can easily decrypt the results of the computation. We experimentally demonstrate, using single photons and linear optics, the encryption and decryption scheme on a set of gates sufficient for arbitrary quantum computations. Because our protocol requires few extra resources compared to other schemes it can be easily incorporated into the design of future quantum servers. These results will play a key role in enabling the development of secure distributed quantum systems

Manipulating biphotonic qutrits

Quantum information carriers with higher dimension than the canonical qubit offer significant advantages. However, manipulating such systems is extremely difficult. We show how measurement induced non-linearities can be employed to dramatically extend the range of possible transforms on biphotonic qutrits; the three level quantum systems formed by the polarisation of two photons in the same spatio-temporal mode. We fully characterise the biphoton-photon entanglement that underpins our technique, thereby realising the first instance of qubit-qutrit entanglement. We discuss an extension of our technique to generate qutrit-qutrit entanglement and to manipulate any bosonic encoding of quantum information.Comment: 4 pages, 4 figure

Coherent analysis of quantum optical sideband modes

We demonstrate a device that allows for the coherent analysis of a pair of optical frequency sidebands in an arbitrary basis. We show that our device is quantum noise limited and hence applications for this scheme may be found in discrete and continuous variable optical quantum information experiments.Comment: 3 pages, 3 figures, submitted to Optics Letter

Violation of Bell's Inequality with Photons from Independent Sources

We report a violation of Bell's inequality using one photon from a parametric down-conversion source and a second photon from an attenuated laser beam. The two photons were entangled at a beam splitter using the post-selection technique of Shih and Alley [Phys. Rev. Lett. 61, 2921 (1988)]. A quantum interference pattern with a visibility of 91% was obtained using the photons from these independent sources, as compared with a visibility of 99.4% using two photons from a central parametric down-conversion source.Comment: 4 pages, 5 figures; minor change

A conditional-phase switch at the single-photon level

We present an experimental realization of a two-photon conditional-phase switch, related to the ``$c$-$\phi$'' gate of quantum computation. This gate relies on quantum interference between photon pairs, generating entanglement between two optical modes through the process of spontaneous parametric down-conversion (SPDC). The interference effect serves to enhance the effective nonlinearity by many orders of magnitude, so it is significant at the quantum (single-photon) level. By adjusting the relative optical phase between the classical pump for SPDC and the pair of input modes, one can impress a large phase shift on one beam which depends on the presence or absence of a single photon in a control mode.Comment: 8 pages, 4 figure

Systematic Review and Meta-Analysis of the Incidence of Rupture, Repair, and Death of Small and Large Abdominal Aortic Aneurysms under Surveillance

Background: The ultimate goal of treating patients with abdominal aortic aneurysms (AAAs) is to repair them when the risk of rupture exceeds the risk of repair. Small AAAs demonstrate a low rupture risk, and recently, large AAAs just above the threshold (5.5–6.0 cm) seem to be at low risk of rupture as well. The present review aims to investigate the outcomes of AAAs under surveillance through a comprehensive systematic review and meta-analysis. Methods: PubMed, Embase, and the Cochrane Central Register were searched (22 March 2022; PROSPERO; #CRD42022316094). The Cochrane and PRISMA statements were respected. Blinded systematic screening of the literature, data extraction, and quality assessment were performed by two authors. Conflicts were resolved by a third author. The meta-analysis of prevalence provided estimated proportions, 95% confidence intervals, and measures of heterogeneity (I2). Based on I2, the heterogeneity might be negligible (0–40%), moderate (30–60%), substantial (50–90%), and considerable (75–100%). The primary outcome was the incidence of AAA rupture. Secondary outcomes included the rate of small AAAs reaching the threshold for repair, aortic-related mortality, and all-cause mortality. Results: Fourteen publications (25,040 patients) were included in the analysis. The outcome rates of the small AAA group (<55 mm) were 0.3% (95% CI 0.0–1.0; I2 = 76.4%) of rupture, 0.6% (95% CI 0.0–1.9; I2 = 87.2%) of aortic-related mortality, and 9.6% (95% CI 2.2–21.1; I2 = 99.0%) of all-cause mortality. During surveillance, 21.4% (95% CI 9.0–37.2; I2 = 99.0%) of the initially small AAAs reached the threshold for repair. The outcome rates of the large AAA group (>55 mm) were 25.7% (95% CI 18.0–34.3; I2 = 72.0%) of rupture, 22.1% (95% CI 16.5–28.3; I2 = 25.0%) of aortic-related mortality, and 61.8% (95% CI 47.0–75.6; I2 = 89.1%) of all-cause mortality. The sensitivity analysis demonstrated a higher rupture rate in studies including <662 subjects, patients with a mean age > 72 years, >17% of female patients, and >44% of current smokers. Conclusion: The rarity of rupture and aortic-related mortality in small AAAs supports the current conservative management of small AAAs. Surveillance seems indicated, as one-fifth reached the threshold for repair. Large aneurysms had a high incidence of rupture and aortic-related mortality. However, these data seem biased by the sparse and heterogeneous literature overrepresented by patients unfit for surgery. Specific rupture risk stratified by age, gender, and fit-for-surgery patients with large AAAs needs to be further investigated