Abstract
In this chapter we investigate the joint measurability of the observables of a qubit system, that is, a quantum system whose relevant degrees of freedom are represented by a two-dimensional complex Hilbert space. We will give a full characterisation of the pairs of simple qubit observables that are jointly measurable. We also develop the theory of approximate joint measurements of incompatible pairs of sharp qubit observables. The resulting measurement uncertainty relations for mutually unbiased observables are found to be closely related to corresponding optimal preparation uncertainty relations.
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Notes
- 1.
We recall that an affine space over a vector space is a set such that any two points can be joined by a unique vector in a natural way. In special relativity, the elements of \(M_4\) are called point events and the vectors connecting them describe the possibility of joining the events with straight signals.
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Busch, P., Lahti, P., Pellonpää, JP., Ylinen, K. (2016). Qubits. In: Quantum Measurement. Theoretical and Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-43389-9_14
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DOI: https://doi.org/10.1007/978-3-319-43389-9_14
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