National Quantum Information Center of Gdansk, 81-824 Sopot, Poland and University of Gdansk, 80-952 Gdansk, Poland.
National Quantum Information Center of Gdansk, 81-824 Sopot, Poland and Faculty of Applied Physics and Mathematics, Technical University of Gdansk, 80-233 Gdansk, Poland.
Phys Rev Lett. 2014 Jan 31;112(4):040404. doi: 10.1103/PhysRevLett.112.040404. Epub 2014 Jan 29.
The problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension d and any measurement scenario consisting of projective measurements, (i) the measure of contextuality of a quantum state is entirely determined by its spectrum, so that pure and maximally mixed states represent the two extremes of contextual behavior, and that (ii) state-independent contextuality is equivalent to the contextuality of the maximally mixed state up to a global unitary transformation. We then derive a necessary and sufficient condition for a measurement scenario represented by an orthogonality graph to reveal state-independent contextuality. This condition is given in terms of the fractional chromatic number of the graph χf(G) and is shown to identify all state-independent contextual measurement scenarios including those that go beyond the original Kochen-Specker paradigm.
考虑识别在给定 Hilbert 空间维度中能够揭示状态无关的上下文的测量场景的问题。我们首先表明，对于任何给定的维度 d 和任何由投影测量组成的测量场景，(i) 量子态的上下文的度量完全由其谱决定，因此纯态和最大混合态代表了上下文行为的两个极端，并且 (ii) 状态无关的上下文与最大混合态的上下文是等价的，只是在全局幺正变换下有所不同。然后，我们推导出由正交图表示的测量场景揭示状态无关上下文的必要和充分条件。该条件是用图的分数色数 χf(G) 给出的，并证明它可以识别所有状态无关的上下文测量场景，包括那些超出原始 Kochen-Specker 范例的场景。
