Quantum state tomography with informationally complete POVMs generated in the time domain

AbstractThe article establishes a framework for dynamic generation of informationally complete POVMs in quantum state tomography. Assuming that the evolution of a quantum system is given by a dynamical map in the Kraus representation, one can switch to the Heisenberg picture and define the measurements in the time domain. Consequently, starting with an incomplete set of positive operators, one can obtain sufficient information for quantum state reconstruction by multiple measurements. The framework has been demonstrated on qubits and qutrits. For some types of dynamical maps, it suffices to initially have one measurement operator. The results demonstrate that quantum state tomography is feasible even with limited measurement potential.

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Dynamic State Reconstruction of Quantum Systems Subject to Pure Decoherence

International Journal of Theoretical Physics ◽

10.1007/s10773-020-04625-8 ◽

2020 ◽

Vol 59 (11) ◽

pp. 3646-3661

Author(s):

Artur Czerwinski

Keyword(s):

Quantum State ◽

Open Systems ◽

Initial Density ◽

Quantum Tomography ◽

Dynamic State ◽

Reconstruction Method ◽

State Reconstruction ◽

Quantum State Tomography ◽

Phase Damping ◽

State Tomography

Abstract The article introduces efficient quantum state tomography schemes for qutrits and entangled qubits subject to pure decoherence. We implement the dynamic state reconstruction method for open systems sent through phase-damping channels, which was proposed in: Czerwinski and Jamiolkowski Open Syst. Inf. Dyn. 23, 1650019 (2016). In the present article we prove that two distinct observables measured at four different time instants suffice to reconstruct the initial density matrix of a qutrit with evolution given by a phase-damping channel. Furthermore, we generalize the approach in order to determine criteria for quantum tomography of entangled qubits. Finally, we prove two universal theorems concerning the number of observables required for quantum state tomography of qudits subject to pure decoherence. We believe that dynamic state reconstruction schemes bring advancement and novelty to quantum tomography since they utilize the Heisenberg representation and allow to define the measurements in time domain.

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Adaptive quantum state tomography with neural networks

npj Quantum Information ◽

10.1038/s41534-021-00436-9 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Yihui Quek ◽

Stanislav Fort ◽

Hui Khoon Ng

Keyword(s):

Machine Learning ◽

Quantum State ◽

The State ◽

Learning To Learn ◽

Seamless Integration ◽

Quantum State Tomography ◽

Flexible Machine ◽

Meta Learning ◽

Long Time ◽

State Tomography

AbstractCurrent algorithms for quantum state tomography (QST) are costly both on the experimental front, requiring measurement of many copies of the state, and on the classical computational front, needing a long time to analyze the gathered data. Here, we introduce neural adaptive quantum state tomography (NAQT), a fast, flexible machine-learning-based algorithm for QST that adapts measurements and provides orders of magnitude faster processing while retaining state-of-the-art reconstruction accuracy. As in other adaptive QST schemes, measurement adaptation makes use of the information gathered from previous measured copies of the state to perform a targeted sensing of the next copy, maximizing the information gathered from that next copy. Our NAQT approach allows for a rapid and seamless integration of measurement adaptation and statistical inference, using a neural-network replacement of the standard Bayes’ update, to obtain the best estimate of the state. Our algorithm, which falls into the machine learning subfield of “meta-learning” (in effect “learning to learn” about quantum states), does not require any ansatz about the form of the state to be estimated. Despite this generality, it can be retrained within hours on a single laptop for a two-qubit situation, which suggests a feasible time-cost when extended to larger systems and potential speed-ups if provided with additional structure, such as a state ansatz.

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