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OSA Trends in Optics and Photonics Series

Holography, vortices and qudits: Encoding quantum information in optical spatial modes

Nathan K. Langford, R. B. Dalton, Alexei Gilchrist, Jeremy L. O’Brien, Geoff J. Pryde, Andrew G. White, M. Harvey, Stephen D. Bartlett

Published Jan 1, 2004• 0 citations
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Abstract

Using quantum state tomography, we completely characterise entangled qubits and qutrits encoded in photons in different transverse spatial modes. We investigate using such entangled qutrits for quantum bit commitment, the basis of quantum coin flipping.

Related papers

Holography, vortices and qudits: encoding quantum information in optical spatial modes

Nathan K. Langford, R. B. Dalton, Alexei Gilchrist +5 more

Using quantum state tomography, we completely characterise entangled qubits and qutrits encoded in photons in different transverse spatial modes. We investigate using such entangled qutrits for quantum bit commitment, the basis of quantum coin flipping.

Conference on Lasers and Electro-Optics•Jan 1, 2004•0 citations

Holography, vortices and qudits: encoding quantum information in optical spatial modes

NK Langford, RB Dalton, Alexei Gilchrist +5 more

Using quantum state tomography, we completely characterise entangled qubits and qutrits encoded in photons in different transverse spatial modes. We investigate using such entangled qutrits for quantum bit commitment, the basis of quantum coin flipping

•May 21, 2004•0 citations

Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment

Nathan K. Langford, R. B. Dalton, M. Harvey +5 more

We produce and holographically measure entangled qudits encoded in transverse spatial modes of single photons. With the novel use of a quantum state tomography method that only requires two-state superpositions, we achieve the most complete characterization of entangled qutrits to date. Ideally, entangled qutrits provide better security than qubits in quantum bit commitment: we model the sensitivity of this to mixture and show experimentally and theoretically that qutrits with even a small amount of decoherence cannot offer increased security over qubits.

arXiv:quant-ph/0312072•Physical Review Letters•Jul 26, 2004•349 citations

Encoding, manipulating and measuring quantum information in optics

Nathan K. Langford

In this thesis, I present experimental and theoretical work which assesses and develops a range of tools that are required for performing quantum information processing, particularly in photonic systems. I investigate the three degrees of freedom of a single photon—its polarisation, spatialmomentum and time-frequency distributions. For polarisation, I show that using wave plates to implement arbitrary, single-qubit rotations is more complicated than is commonly appreciated. In the spatial-momentum and time-frequency domains, I develop ways to perform tomographic analysis of quantum states, and I report the first demonstrations of these techniques. In the time-frequency domain, the tomography technique utilises entanglement in the photon polarisation as a resource to store and provide access to the time-frequency information. In my first two experiments, I use spontaneous parametric down-conversion to produce entanglement between pairs of single photons in all three degrees of freedom. I demonstrate the first characterisation of entanglement in spatial modes and the time-frequency domain, the first quantitative measurement of entangled qutrit states, and the highest quality entangled states yet measured in both polarisation and spatial modes. I also report the first realisation of complete hyperentanglement, and a full, black-box tomography of a 36-dimensional two-photon state—the largest system to be characterised in this way to date. In my final experiment, I model and implement a new architecture for a controlled-Z gate which is much simpler to align than previous implementations. This gate requires only one non-classical interference condition, the visibility of which is the main limitation to its performance. I show that the gate operates effectively as a means of both creating entanglement and discriminating between the four elements in a basis of maximally entangled, Bell-type states. Indeed, its observed performance as a Bell analyser would be sufficient to build a quantum state teleporter which would guarantee that the recipient would be left with a better copy of an unknown input state than any eavesdropper. In a series of numerical simulations, I investigate some of the practicalities that arise when using tomographic reconstruction techniques, including how to estimate errors, which measurements to make and what is actually the optimal reconstruction. In particular, I show that tomographies perform better when based on the results from over-complete sets of measurements. Finally, I discuss the important issue of how to compare two processes, particularly when trying to assess the quality of a measured process by comparing it to some expected ideal. Judging possible candidate measures against a set of experimentally and theoretically motivated

•Jan 1, 2007•17 citations

Encoding Qubit-Qudit States in Photon Polarization and Picosecond Time-Bins

Y. Pilnyak, Y. Schechter, D. Pleban +5 more

We introduce a qubit-qutrit information system realized by two degrees of freedom in a single photon: polarization and picosecond time-bin. We demonstrate creation and reconstruction of states in this framework using quantum state tomography.

OSA Quantum 2.0 Conference•Jan 1, 2020•0 citations

Encoding qubit-qudit states in photon polarization and picosecond time-bins

Y. Pilnyak, Y. Schechter, D. Pleban +5 more

We introduce a qubit-qutrit information system realized by two degrees of freedom in a single photon: polarization and picosecond time-bin. We demonstrate creation and reconstruction of states in this framework using quantum state tomography.

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting•Jan 1, 2019•0 citations
We produce and holographically measure entangled qudits encoded in transverse spatial modes of single photons. With the novel use of a quantum state tomography method that only requires two-state superpositions, we achieve the most complete characterization of entangled qutrits to date. Ideally, entangled qutrits provide better security than qubits in quantum bit commitment: we model the sensitivity of this to mixture and show experimentally and theoretically that qutrits with even a small amount of decoherence cannot offer increased security over qubits.
In this thesis, I present experimental and theoretical work which assesses and develops a range of tools that are required for performing quantum information processing, particularly in photonic systems. I investigate the three degrees of freedom of a single photon—its polarisation, spatialmomentum and time-frequency distributions. For polarisation, I show that using wave plates to implement arbitrary, single-qubit rotations is more complicated than is commonly appreciated. In the spatial-momentum and time-frequency domains, I develop ways to perform tomographic analysis of quantum states, and I report the first demonstrations of these techniques. In the time-frequency domain, the tomography technique utilises entanglement in the photon polarisation as a resource to store and provide access to the time-frequency information. In my first two experiments, I use spontaneous parametric down-conversion to produce entanglement between pairs of single photons in all three degrees of freedom. I demonstrate the first characterisation of entanglement in spatial modes and the time-frequency domain, the first quantitative measurement of entangled qutrit states, and the highest quality entangled states yet measured in both polarisation and spatial modes. I also report the first realisation of complete hyperentanglement, and a full, black-box tomography of a 36-dimensional two-photon state—the largest system to be characterised in this way to date. In my final experiment, I model and implement a new architecture for a controlled-Z gate which is much simpler to align than previous implementations. This gate requires only one non-classical interference condition, the visibility of which is the main limitation to its performance. I show that the gate operates effectively as a means of both creating entanglement and discriminating between the four elements in a basis of maximally entangled, Bell-type states. Indeed, its observed performance as a Bell analyser would be sufficient to build a quantum state teleporter which would guarantee that the recipient would be left with a better copy of an unknown input state than any eavesdropper. In a series of numerical simulations, I investigate some of the practicalities that arise when using tomographic reconstruction techniques, including how to estimate errors, which measurements to make and what is actually the optimal reconstruction. In particular, I show that tomographies perform better when based on the results from over-complete sets of measurements. Finally, I discuss the important issue of how to compare two processes, particularly when trying to assess the quality of a measured process by comparing it to some expected ideal. Judging possible candidate measures against a set of experimentally and theoretically motivated