Decomposition of pure states of a quantum register

Ioannis Raptis; Roman R. Zapatrin

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Decomposition of pure states of a quantum register

Ioannis Raptis·Roman R. Zapatrin

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Abstract

Using the leading vector method, we show that any vector $h\in(C^2)^{\otimes l}$ can be decomposed as a sum of at most (and at least in the generic case) $2^l-l$ product vectors using local bitwise unitary transformations. The method is based on representing the vectors by chains of appropriate simplicial complex. This generalizes the Scmidt decomposition of pure states of a 2-bit register to registers of arbitrary length $l$.

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Ioannis Raptis, Roman R. Zapatrin. 2000-10-31. Decomposition of pure states of a quantum register. https://arxiv.org/abs/quant-ph/0010104

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