Robert B. Adamson

Improving Quantum State Estimation with Mutually Unbiased Bases

When used in quantum state estimation, projections onto mutually unbiased bases have the ability to maximize information extraction per measurement and to minimize redundancy. We present the first experimental demonstration of quantum state tomography of two-qubit polarization states to take advantage of mutually unbiased bases. We demonstrate improved state estimation as compared to standard measurement strategies and discuss how this can be understood from the structure of the measurements we use. We experimentally compared our method to the standard state estimation method for three different states and observe that the infidelity was up to 1.84 ± 0.06 times lower by using our technique than it was by using standard state estimation methods.

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.

Detecting hidden differences via permutation symmetries

We present a method for describing and characterizing the state of

Optimal bounded-error strategies for projective measurements in nonorthogonal-state discrimination

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Preparation of pure and mixed polarization qubits and the direct measurement of figures of merit

particles that may be distinguishable in principle but not in practice due to experimental limitations. The technique relies upon a careful treatment of the exchange symmetry of the state among experimentally accessible and experimentally inaccessible degrees of freedom. The approach we present allows a formalization of the notion of indistinguishability and can be implemented easily using currently available experimental techniques. Our work is of direct relevance to current experiments in quantum optics, for which we provide a specific implementation.

Quantum process tomography and the search for decoherence-free subspaces

Research in nonorthogonal-state discrimination has given rise to two conventional optimal strategies: unambiguous discrimination (UD) and minimum error discrimination. We explore the experimentally relevant range of measurement strategies between the two, where the rate of inconclusive results is minimized for a bounded-error rate. We first provide some constraints on the problem that apply to generalized measurements [positive-operator-valued measurements (POVMs)]. We then provide the theory for the optimal projective measurement in this range. Through analytical and numerical results we investigate this family of projective, bounded-error strategies and compare it to the POVM family as well as to experimental implementation of UD using POVMs. We also discuss a possible application of these bounded-error strategies to quantum key distribution.

Experimental implementation of a three-party quantum key distribution protocol

Non-classical joint measurements can hugely improve the efficiency with which certain figures of merit of quantum systems are measured. We use such a measurement to determine a particular figure of merit, the purity, for a polarization qubit. In the process we highlight some of subtleties involved in common methods for generating decoherence in quantum optics.

Experimental quantum state estimation with mutually unbiased bases

We describe experiments with photon pairs to evaluate, correct for, and avoid sources of error in optical quantum information processing. It is well known that a simple beamsplitter can non-deterministicially prepare or select entangled polarization states. We use quantum process tomography (QPT) to fully characterize this effect, including loss and decoherence. The QPT results identify errors and indicate how well they can be corrected. To evade decoherence in a noisy quantum channel, we identify decoherence-free subspaces using experimental channel characterization, without need for a priori knowledge of the decoherence mechanism or simplifying assumptions. Working with pairs of polarization-encoded photonic qubits, we use tomographic and adaptive techniques to identify 2- and 3-state decoherence-free subspaces for encoding decoherence-free qubits and qutrits within the noisy channel.

Polarization-squeezed triphoton states and their Wigner representation on the Poincaré sphere

We present a proof-of-principle experimental implementation of provably secure three-party quantum key distribution. The protocols security relies on the quantum correlations of GHz states but it is implemented using bipartite entanglement.