Reducing the detection of genuine entanglement of n qubits to two qubits
- URL: http://arxiv.org/abs/2110.01479v1
- Date: Mon, 4 Oct 2021 14:31:16 GMT
- Title: Reducing the detection of genuine entanglement of n qubits to two qubits
- Authors: Dafa Li
- Abstract summary: We show that all of the projected states of a pure product n-qubit state are pure product states provided that it cannot be written as a product of a single qubit state.
We also show that a pure n-qubit state is genuinely entangled provided that the state has at least two genuinely entangled (n-1)-qubit projected states.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose a criterion for the detection of genuine entanglement of pure
multiqubit states. To this aim, we define an operator called the losing one
qubit operator, which is different from the reduced density operator. The
states obtained from a multiqubit state by applying the losing one qubit
operator are referred to as its projected states. We show that all of the
projected states of a pure product n-qubit state are pure product states
provided that it cannot be written as a product of a single qubit state and a
genuinely entangled (n-1)-qubit state. We also show that a pure n-qubit state
is genuinely entangled provided that the state has at least two genuinely
entangled (n-1)-qubit projected states. By repeating the losing process, we
reduce the detection of entanglement of pure n-qubit states to the one of pure
two-qubit states. Also we write a LISP program for the reduction process.
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