Abstract
Quantum state tomography suffers from the measurement effort increasing exponentially with the number of qubits. Here, we demonstrate permutationally invariant tomography for which, contrary to conventional tomography, all resources scale polynomially with the number of qubits both in terms of the measurement effort as well as the computational power needed to process and store the recorded data. We demonstrate the benefits of combining permutationally invariant tomography with compressed sensing by studying the influence of the pump power on the noise present in a six-qubit symmetric Dicke state, a case where full tomography is possible only for very high pump powers.
Highlights
Quantum state tomography suffers from the measurement effort increasing exponentially with the number of qubits
We demonstrate the benefits of combining permutationally invariant tomography with compressed sensing by studying the influence of the pump power on the noise present in a six-qubit symmetric Dicke state, a case where full tomography is possible only for very high pump powers
The following question arises: how much information about a quantum state can be inferred without all the measurements a full quantum state tomography (QST) would require? Protocols have been proposed which need significantly fewer measurement settings if one has additional knowledge about a state, e.g., that it is of low rank, a matrix product state, or a permutationally invariant (PI) state [3,4,5,6,7,8]
Summary
Quantum state tomography suffers from the measurement effort increasing exponentially with the number of qubits. To fully characterize a multiqubit state via quantum state tomography (QST), the measurement effort scales exponentially with the number of qubits. We use these data as a reference for a detailed evaluation of different tomography schemes, which enable the state determination with significantly fewer measurements.
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