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Assuming you are talking about starting from a pure state, your statement is true. There are two steps to the proof: Show that a system without entanglement can implement any classical computation. Show that a system that remains separable can be simulated by a classical computation, proving that there are no calculations it can implement that a classical ...


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The linked question in the comments is akin to "can we efficiently simulate a quantum computer without entanglement?", while the question of the OP is more akin to "if we handicap a quantum computer to not use entanglement, is such a quantum computer equivalent to a classical computer?" @DaftWullie's great answer already shows that such a weakened quantum ...


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