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A Simple Algorithm for Complete Factorization of an N-Partite Pure Quantum State |
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PP: 73-77 |
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doi:10.18576/qpl/060110
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Author(s) |
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Dhananjay P. Mehendale,
Pramod S. Joag,
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Abstract |
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| We present a simple algorithm to completely factorize an arbitrary N-partite pure quantum state. This complete factorization of such a pure state also specifies its complete entanglement status : whether the given N-partite pure quantum state is completely separable (N factors), or completely entangled (no factors), or partially entangled having entangled factors of different sizes which cannot be factored further. The problem of deciding entanglement status of a bipartite pure quantum state is one of the initial problems encountered in quantum information research and this problem is usually tackled using the well known Schmidt decomposition procedure. One obtains Schmidt number of the state which decides the entanglement status of the state. In this paper we first develop a simple criterion which when fulfilled enables us to factorize given N-partite pure quantum state as tensor product of an m-partite pure quantum state and an n-partite pure quantum state where m+n = N. This criterion gives rise to an effective mechanical procedure in terms of an easy algorithm to perform complete factorization of given N-partite pure quantum state and thus provides an easy method to determine complete entanglement status of the state. In this paper we carry out our discussion for the case of N-qubit pure quantum state instead of N-qudit case for the sake of simplicity of presentation. The extension to the case of N-qudit pure quantum state is straightforward and follows by proceeding along similar lines. We just mention this extension to avoid repetition and only briefly demonstrate it with the help of one of the examples discussed at the end of the paper. |
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