Unsharp measurements, joint measurability and classical distributions for some qudits

• URL: http://arxiv.org/abs/2004.05547v1
• Date: Sun, 12 Apr 2020 05:26:46 GMT
• Title: Unsharp measurements, joint measurability and classical distributions for some qudits
• Authors: H S Smitha Rao, Swarnamala Sirsi and Karthik Bharath
• Abstract summary: For qudits in dimension $n$, where $n$ is prime or power of prime, we present a method to construct unsharp versions of projective measurement operators. We establish that the constructed operators are jointly measurable for states given by a family of concentric spheres inscribed within a regular polyhedron.
• Score: 2.9005223064604078
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Classicality associated with joint measurability of operators manifests through a valid classical joint probability distribution on measurement outcomes. For qudits in dimension $n$, where $n$ is prime or power of prime, we present a method to construct unsharp versions of projective measurement operators which results in a geometric description of the set of quantum states for which the operators engender a classical joint probability distribution, and are jointly measurable. Specifically, within the setting of a generalised Bloch sphere in $n^2-1$ dimensions, we establish that the constructed operators are jointly measurable for states given by a family of concentric spheres inscribed within a regular polyhedron, which represents states that lead to classical probability distributions. Our construction establishes a novel perspective on links between joint measurability and optimal measurement strategies associated with Mutually Unbiased Bases (MUBs), and formulates a necessary condition for the long-standing open problem of existence of MUBs in dimension $n=6$.

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