The text of this website is available for modification and reuse under the terms of the Creataive Commons and the GNU Free Documentation Licence (unversioned, with no invariant sections, front-cover texts, or back-cover texts). Permutationally Invariant Quantum Tomography Permutionally Invariant Quantum Tomography or PI Quantum Tomography is the process of reconstructing the permutationally invariant part of thequantum state (density matrix) of a multi-particle system by local measurements on the system [1]. It is a scaleable alternative of full quantum state tomography, which make density matrix reconstruction possible for systems with more than 10 particles for photons, cold trapped ions, and any other realization where the particles are locally accessible. The permutationally invariant part of the density matrixPI state tomography reconstructs the permutationally invariant part of the density matrix, which is defined as the equal mixture of all permutations of the density matrix, where The number of degrees of freedom of The measurementsIn order to determine these degrees of freedom, we need to measure local measurement settings. A single local measurement settings in this case means that at each particle operator Efficient fitting of a physical stateWhile the number of measurements scales polynomially with the number of qubits, as long as the state of the system is represented by a Characteristics of the methodPI tomography can be used typically in experiments in which permutationally invariant states are produced. If the density matrix obtained from PI tomography is entangled, the density matrix of the system was also entangled. Thus the PI density matrix reconstructed can be used as the input of any usual entanglement detection procedure. In order to detect entanglement this way, we do not need to assume that the quantum state was permutationally invariant. The expectation values of any permutationally invariant operator, including projectors to symmetric states, can be obtained exactly from the permutationally invariant density matrix. References
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