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arXiv:2412.01892 · Quantum Science and Technology

Prospects for quantum process tomography at high energies

Clelia Altomonte, Alan J. Barr, Michał Eckstein, Paweł Horodecki, Kazuki Sakurai

Published Sep 24, 2025• 11 citations
arXivHTMLPDF

Abstract

Abstract In quantum information theory, the evolution of an open quantum system—a unitary evolution followed by a measurement—is described by a quantum channel or, more generally, a quantum instrument. In this work, we formulate spin and flavour measurements in collider experiments as quantum instruments. We demonstrate that the Choi matrix, which completely determines input-output transitions, can be both theoretically computed from a given model and experimentally reconstructed from a set of final state measurements (quantum state tomography) using varied input states. The experimental reconstruction of the Choi matrix, known as quantum process tomography, offers a powerful new approach for probing potential extensions of the Standard Model, which predict different input-output transitions. In addition, the methodology constitutes a new foundational test of quantum mechanics itself. As an example, we outline the quantum process tomography approach applied to the e + e − → t t ¯ process at a polarised lepton collider.

DOI
10.1088/2058-9565/ae0af1

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Abstract In quantum information theory, the evolution of an open quantum system—a unitary evolution followed by a measurement—is described by a quantum channel or, more generally, a quantum instrument. In this work, we formulate spin and flavour measurements in collider experiments as quantum instruments. We demonstrate that the Choi matrix, which completely determines input-output transitions, can be both theoretically computed from a given model and experimentally reconstructed from a set of final state measurements (quantum state tomography) using varied input states. The experimental reconstruction of the Choi matrix, known as quantum process tomography, offers a powerful new approach for probing potential extensions of the Standard Model, which predict different input-output transitions. In addition, the methodology constitutes a new foundational test of quantum mechanics itself. As an example, we outline the quantum process tomography approach applied to the e + e − → t t ¯ process at a polarised lepton collider.
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The characterization of the evolution of a quantum system is one of the main tasks to accomplish to achieve quantum information processing. The standard quantum process tomography (SQPT) has the unique property that it can be applied without introducing any additional quantum resources. In present work, we shall focus on the following two topics about the SQPT. At first, in the SQPT protocol for a ddd-dimensional system, one should encounter a problem in solving of a set of d4d^4d4 linear equations in order to get the matrix containing the complete information about the unknown quantum channel. Until now, the general form of the solution is unknown. And a long existed conviction is that the solutions are not unique. Here, we shall develop a self-consistent scheme, in which bounded linear operators are presented by vectors, to construct the set of linear equations. With the famous Cramer's rule for the set of linear equations, we are able to give the general form of the solution and prove that it is unique. In second, the central idea of the SQPT is to prepare a set of linearly independent inputs and measuring the outputs via the quantum state tomography (QST). Letting the inputs and the measurements be prepared by two sets of the rank-one positive-operator-valued measures [POVMs], where each POVM is supposed to be linearly independent and informationally complete (IC), we observe that SQPT now is equivalent to deciding a unknown state with a set of product IC-POVM in the d2d^2d2-dimensional Hilbert space. Following the general linear state tomography theory, we show that the product symmetric IC-POVM should minimize the mean-square Hilbert-Schmidt distance between the estimator and the true states. So, an optimal SQPT can be realized by preparing both the inputs and the measurements as the symmetric IC-POVM.
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Abstract The characterization of a quantum device is a crucial step in the development of quantum experiments. This is accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to deliver a possible reconstruction of the underlying process. The tomography is typically performed by processing an overcomplete set of measurements and extracting the process matrix from maximum-likelihood estimation. Here, we introduce Fourier Quantum Process Tomography, a technique which requires a reduced number of measurements, and benchmark its performance against the standard maximum-likelihood approach. Fourier Quantum Process Tomography is based on measuring probability distributions in two conjugate spaces for different state preparations and projections. Exploiting the concept of phase retrieval, our scheme achieves a complete and robust characterization of the setup by processing a near-minimal set of measurements. We experimentally test the technique on different space-dependent polarization transformations, reporting average fidelities higher than 90% and significant computational advantage.
Quantum tomography is a cornerstone of quantum information science, enabling the reconstruction of states and channels from experimental data. Here we introduce a new paradigm, temporal state tomography (TST), for reconstructing quantum processes across multiple times. Our approach is based on temporal quasiprobability distributions (TQDs), which, in the informationally complete setting, provide a complete description of multi-time quantum processes and uniquely determine temporal states. We formulate TST as a unified framework for reconstructing both density operators and quantum channels within a single scheme. We show that any TQD can be obtained via classical post-processing of measurement outcomes generated by a fixed set of quantum instruments, thereby establishing a direct operational route to accessing TQDs experimentally. For informationally complete TQDs, the associated temporal state can be reconstructed via a temporal Bloch-type representation. Leveraging this correspondence, we derive the sample complexity of TST, thereby quantifying its statistical efficiency.