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arXiv:2503.07999

Complete Measurement of Two-Photon Density Matrix by Single-Photon Detection

Salini Rajeev, Mayukh Lahiri

Published Mar 11, 2025• 1 citation
arXivHTMLPDF

Abstract

The reconstruction of density matrices from measurement data (quantum state tomography) is the most comprehensive method for assessing the accuracy and performance of quantum devices. Existing methods to reconstruct two-photon density matrices require the detection of both photons unless a priori information is available. Based on the concept of quantum-induced coherence by path identity, we present an approach to quantum state tomography that circumvents the requirement of detecting both photons. We show that an arbitrary two-qubit density matrix, which can contain up to fifteen free parameters, can be fully reconstructed from single-photon measurement data without any postselection and a priori information. In addition to advancing an alternative approach to quantum state measurement problems, our results also have notable practical implications. A practical challenge in quantum state measurement arises from the fact that effective single-photon detectors are not readily accessible for a wide spectral range. Our method, which eliminates the need for coincidence measurements, enables quantum state tomography in the case where one of the two photons is challenging or impossible to detect. It therefore opens the door to measuring quantum states hitherto inaccessible.

DOI
10.48550/arxiv.2503.07999

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The reconstruction of density matrices from measurement data (quantum state tomography) is the most comprehensive method for assessing the accuracy and performance of quantum devices. Existing methods to reconstruct two-photon density matrices require the detection of both photons unless a priori information is available. Based on the concept of quantum-induced coherence by path identity, we present an approach to quantum state tomography that circumvents the requirement of detecting both photons. We show that an arbitrary two-qubit density matrix, which can contain up to fifteen free parameters, can be fully reconstructed from single-photon measurement data without any postselection and a priori information. In addition to advancing an alternative approach to quantum state measurement problems, our results also have notable practical implications. A practical challenge in quantum state measurement arises from the fact that effective single-photon detectors are not readily accessible for a wide spectral range. Our method, which eliminates the need for coincidence measurements, enables quantum state tomography in the case where one of the two photons is challenging or impossible to detect. It therefore opens the door to measuring quantum states hitherto inaccessible.
Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possible paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.
Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possibles paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.
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Two-photon entangled quantum states are a fundamental tool for quantum information and quantum cryptography. A complete description of a generic quantum state is provided by its density matrix: the technique allowing experimental reconstruction of the density matrix is called quantum state tomography. Entangled states density matrix reconstruction requires a large number of measurements on many identical copies of the quantum state. An alternative way of certifying the amount of entanglement in two-photon states is represented by the estimation of specific parameters, e.g., negativity and concurrence. If we have a priori partial knowledge of our state, it's possible to develop several estimators for these parameters that require lower amount of measurements with respect to full density matrix reconstruction. The aim of this work is to introduce and test different estimators for negativity and concurrence for a specific class of two-photon states.
Quantum State Tomography (QST) of optical states is typically performed in the photon number degree of freedom, a procedure which is well understood and has been experimentally demonstrated. However, optical states have other degrees of freedom than just photon number, such as the spatial and temporal/spectral ones. Full characterization of photonic states requires state reconstruction in these additional degrees of freedom. In this paper we present a technique for performing QST of single photon states in the spectral degree of freedom. This is of importance, for example, in quantum information processing applications, which typically impose strict requirements on the purity and distinguishability of independently produced single photons. The described technique allows for full reconstruction of the spectral density matrix, allowing the purity and distinguishability of different sources to be readily calculated.
One of the fundamental problems of experimental quantum physics is the determination of the state of a system, which provides its accurate description and contains all the available information about it. The standard solution is quantum state tomography, a technique that employs a large number of measurements of complementary observables to reconstruct a general density operator. Recently, new protocols have been proposed which allow to obtain the matrix elements one by one with fewer and less complicated observations by exploiting so-called weak measurements, that perturb the system less than ideal projections at the cost of being less precise. This thesis presents an evolution of these schemes that eschews the weakness of the measurement, thus gaining in the accuracy of the results and in practical feasibility. We realized an experiment that uses these methods to reconstruct the density operator of the polarization state of light in single photons regime.