Coherence of quantum states based on mutually unbiased bases in C4.
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Abstract: (FIZ Karlsruhe)
Recently, many measures have been put forward to quantify the coherence of quantum states relative to a given basis. We extend the relationship between mutually unbiased basis (MUBs) and quantum coherence to a higher dimension. Results include arbitrary complete sets of MUBs from C2 to C4, and the form of arbitrary 2×2 Unitary matrix and any density matrix of qubit states in respect of complete sets of MUBs. We construct a set of three MUBs by tensor product and further think of complete sets of five MUBs in C4. Taking the Bell diagonal state as an example, we analyze the coherence of quantum states under MUBs and calculate the corresponding upper and lower bounds. The results show that in addition to selecting the unbiased basis which is often used, we can consider more sets of MUBs, which may be helpful to the analysis of quantum states.For the entire collection see [Zbl 1516.68008].- coherence
- mutually unbiased bases
- coherence measure
- 81R30
- 81P55
- 51F25
- 81P65
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