Round 12: Tossup 6

Specific representations of these mathematical objects called “spiders” are generators of a string diagram in ZX-calculus. Quantum circuits are represented using these objects in networks that can be described using Penrose notation. A multi-particle Hilbert space is constructed by applying an operation named for these objects (10[1])that, when applied to spaces of dimensions m and n, produces one of dimension m times n. These objects (10[1])can be divided (-5[1])into covariant and contravariant (10[1])components. A generalization of trace on these objects called “contraction” applies when an index appears as both a subscript and superscript in Einstein notation. A product named for these objects is denoted by a times symbol inside a circle. (10[1])For 10 points, name these objects that correspond to multilinear maps (10[1])and whose rank-2 representations (10[1])are matrices. ■END■ (0[2])

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