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Introduction to Quantum Information

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Exploring Quantum Foundations with Single Photons

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

Quantum information science views quantum mechanics as a theory that is fundamentally about information and information processing.

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Notes

  1. 1.

    Classical probabilistic mixtures in contrast would typically allow for a unique decomposition into pure states.

  2. 2.

    Note that this space is in fact isomorphic to the state-space of a single ququart with basis \(\{ | 0 \rangle , | 1 \rangle , | 2 \rangle , | 3 \rangle \}\), see also Chap. 4. Certain quantum superposition states in the ququart space correspond to entangled states in the bipartite qubit space.

  3. 3.

    Translated from the German term “Verschränkung”, coined by Erwin Schrödinger in 1935 [12].

  4. 4.

    This feature is reminiscent of the observation that quantum mechanics is impartial about how a certain quantum state was prepared (as a mixture of pure states) or how a certain transformation is implemented (as a mixture of unitary transformations), see Sect. 3.3 for more details.

  5. 5.

    Traditionally the strength of a von Neumann measurement is determined by the coupling strength g, the interaction time t, and the initial uncertainty in the meter \(\Delta \). A measurement is then considered “weak” if \(gt\ll \Delta \), see e.g. Ref. [42].

  6. 6.

    If the upgraded BICEP detector finds convincing evidence for polarization of the cosmic microwave background that would suggest a coherence time on the order of billions of years.

  7. 7.

    In fact, the waveplate still imparts a global phase of \(\pi \) or \(\pi {/}2\), which can be relevant if it is part of a multi-path interferometer.

  8. 8.

    In fact, \(\theta _0\) is the angle of either fast or slow axis, and determining which of the two it is requires more complicated methods, such as using Fresnel reflection from a metallic surface [59]. In practice, however, it is almost always sufficient to simply make sure that all axes within an experiment are aligned relative to one another, which merely requires analysing the behaviour of two consecutive waveplates.

  9. 9.

    At first sight it might seem obvious that photons that do not arrive at the same time cannot interfere, but, in fact, the interference can be restored by erasing the information about which photon was first [63].

  10. 10.

    In fact, the same is true for every input state which has a \( | VV \rangle \)-component.

  11. 11.

    A series of these gates can, however, be used in an overlapping ladder structure, as long as no two photons interfere twice [64].

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  1. School of Mathematics and Physics, The University of Queensland, Queensland, QLD, Australia

    Martin Ringbauer

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Ringbauer, M. (2017). Introduction to Quantum Information. In: Exploring Quantum Foundations with Single Photons. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-64988-7_1

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