51 lines
1.7 KiB
Plaintext
51 lines
1.7 KiB
Plaintext
---
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title: concurrence
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description: API reference for qiskit.quantum_info.concurrence
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in_page_toc_min_heading_level: 1
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python_api_type: function
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python_api_name: qiskit.quantum_info.concurrence
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---
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<span id="qiskit-quantum-info-concurrence" />
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# qiskit.quantum\_info.concurrence
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<Function id="qiskit.quantum_info.concurrence" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.16/qiskit/quantum_info/states/measures.py" signature="concurrence(state)">
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Calculate the concurrence of a quantum state.
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The concurrence of a bipartite [`Statevector`](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector") $|\psi\rangle$ is given by
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$$
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C(|\psi\rangle) = \sqrt{2(1 - Tr[\rho_0^2])}
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$$
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where $\rho_0 = Tr_1[|\psi\rangle\!\langle\psi|]$ is the reduced state from by taking the $~qiskit.quantum_info.partial_trace$ of the input state.
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For density matrices the concurrence is only defined for 2-qubit states, it is given by:
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$$
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C(\rho) = \max(0, \lambda_1 - \lambda_2 - \lambda_3 - \lambda_4)
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$$
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where $\lambda _1 \ge \lambda _2 \ge \lambda _3 \ge \lambda _4$ are the ordered eigenvalues of the matrix $R=\sqrt{\sqrt{\rho }(Y\otimes Y)\overline{\rho}(Y\otimes Y)\sqrt{\rho}}$.
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**Parameters**
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**state** ([*Statevector*](qiskit.quantum_info.Statevector "qiskit.quantum_info.Statevector") *or*[*DensityMatrix*](qiskit.quantum_info.DensityMatrix "qiskit.quantum_info.DensityMatrix")) – a 2-qubit quantum state.
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**Returns**
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The concurrence.
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**Return type**
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float
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**Raises**
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* **QiskitError** – if the input state is not a valid QuantumState.
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* **QiskitError** – if input is not a bipartite QuantumState.
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* **QiskitError** – if density matrix input is not a 2-qubit state.
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</Function>
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