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Processing and measuring quantum information encoded in photons

Jeremy O'Brien

Centre for Quantum Computer Technology, University of Queensland

3.30pm, Monday 24 November 2003, AR103 Seminar Room, Graduate Research Centre

Quantum Information Science is concerned with storing and manipulating information quantum mechanically. The resources required include: physical systems to encode this quantum information; quantum gates to process it; measurement devices; and the capacity to characterise these quantum processes. Quantum information can be encoded in any quantum system, but usually two level systems - qubits. However, there exist quantum communication protocols where higher dimensional quantum systems - qudits - are proven to be more useful. I will describe some recent experimental results concerned with processing qubits and qudits encoded in the quantum state of light: (1) an all optical CNOT gate, (2) quantum process tomography of this gate, (3) a quantum non-demolition measurement of the polarisation of a single photon, and (4) quantum state tomography of spatially encoded qudits.

The polarisation state of a single photon is an attractive qubit since its good isolation from the environment makes decoherence inherently low. The usual gates required for quantum computation are single qubit rotations, and a controlled-NOT (CNOT) gate that flips a "target" qubit conditional on a "control" qubit being 1. Rotating the polarisation of a single photon is straightforward, however, the non-linear interactions between qubits, necessary for a CNOT gate, are difficult to realise. Following the ideas for measurement induced non-linearities we have demonstrated and completely characterised an all-optical CNOT gate suitable for scalable quantum computing, producing all four entangled Bell states with high fidelities.

A complete characterisation of any quantum process is fundamental to realising quantum information protocols - what does this black box do? We demonstrate how to definitely answer this question by performing quantum process tomography on our CNOT gate. We have generated the first physical process matrix for a measured quantum process, and it has an average process fidelity of 0.81 with an ideal CNOT gate.

Measuring the polarisation of a single photon typically results in its destruction. We demonstrate a quantum non-demolition (QND) scheme for realising such a measurement non-destructively. We vary this QND measurement continuously into the weak regime, and use it to perform a non-destructive test of complementarity in quantum mechanics. Our scheme realises the most advanced general measurement of a qubit: it is non-destructive, can be made in any basis, and with arbitrary strength.

An alternative to polarisation is to encoded quantum information in the transverse spatial mode of photons, which has the advantage of allowing arbitrarly higher dimensional qudits. We have demonstrated the first comprehensive characterisation of qudits encoded in this way through quantum state tomography, and shown how they can be used in an antagonistic bit commitment protocol.

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