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. As our protocol requires few extra resources compared with 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.

Detection-loophole-free test of quantum nonlocality, and applications.

We present a source of entangled photons that violates a Bell inequality free of the "fair-sampling" assumption, by over 7 standard deviations. This violation is the first reported experiment with photons to close the detection loophole, and we demonstrate enough "efficiency" overhead to eventually perform a fully loophole-free test of local realism. The entanglement quality is verified by maximally violating additional Bell tests, testing the upper limit of quantum correlations. Finally, we use the source to generate "device-independent" private quantum random numbers at rates over 4 orders of magnitude beyond previous experiments.

Squeezing and over-squeezing of triphotons.

Quantum mechanics places a fundamental limit on the accuracy of measurements. In most circumstances, the measurement uncertainty is distributed equally between pairs of complementary properties; this leads to the 'standard quantum limit' for measurement resolution. Using a technique known as 'squeezing', it is possible to reduce the uncertainty of one desired property below the standard quantum limit at the expense of increasing that of the complementary one. Squeezing is already being used to enhance the sensitivity of gravity-wave detectors and may play a critical role in other high precision applications, such as atomic clocks and optical communications. Spin squeezing (the squeezing of angular momentum variables) is a powerful tool, particularly in the context of quantum light-matter interfaces. Although impressive gains in squeezing have been made, optical spin-squeezed systems are still many orders of magnitude away from the maximum possible squeezing, known as the Heisenberg uncertainty limit. Here we demonstrate how an optical system can be squeezed essentially all the way to this fundamental bound. We construct spin-squeezed states by overlapping three indistinguishable photons in an optical fibre and manipulating their polarization (spin), resulting in the formation of a squeezed composite particle known as a 'triphoton'. The symmetry properties of polarization imply that the measured triphoton states can be most naturally represented by quasi-probability distributions on the surface of a sphere. In this work we show that the spherical topology of polarization imposes a limit on how much squeezing can occur, leading to the quasi-probability distributions wrapping around the sphere-a phenomenon we term 'over-squeezing'. Our observations of spin-squeezing in the few-photon regime could lead to new quantum resources for enhanced measurement, lithography and information processing that can be precisely engineered photon-by-photon.

Multiparticle state tomography: hidden differences.

We address the problem of completely characterizing multiparticle states including loss of information to unobserved degrees of freedom. In systems where nonclassical interference plays a role, such as linear-optics quantum gates, such information can degrade interference in two ways, by decoherence and by distinguishing the particles. Distinguishing information, often the limiting factor for quantum optical devices, is not correctly described by previous state-reconstruction techniques, which account only for decoherence. We extend these techniques and find that a single modified density matrix can completely describe partially coherent, partially distinguishable states. We use this observation to experimentally characterize two-photon polarization states in single-mode optical fiber.