Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1910.09574 · Journal of Optics

Quantum coherence of spatial photonic qudits: experimental measurement and path-marker analysis

Paula Machado, Sebastião Pádua

Published Mar 27, 2020• 5 citations
arXivHTMLPDF

Abstract

Abstract Discussions about quantum interference, indistinguishability, and superposition between quantum states go back to the beginning of quantum mechanics. However, the theoretical problem, concerning quantitative measures for quantum coherence, was only recently solved by Baumgratz et al (2014 Phys. Rev. Lett. 113 140401). Since then, many works have explored one of the possible coherence measures: the l 1 norm, which has not yet been obtained experimentally for spatial photonic states in high dimensions. In this article, we study the measurement of spatial qudits quantum coherence. We treat the optical measure-operators as path-markers and show in which condition an interference pattern can be used for measure l 1 norm. We analyze the validity of a l 1 norm measurement method, proposed by Paul and Qureshi (2017 Phys. Rev. A 95 042110), implementing it experimentally in qutrit states, and propose an alternative method for qudits states in which one of their assumptions does not apply.

DOI
10.1088/2040-8986/ab8451

Related papers

Interferometric visibility and coherence

Tanmoy Biswas, María García Díaz, Andreas Winter

Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. ( Phys. Rev. Lett. 113 , 140401. (doi:10.1103/PhysRevLett.113.140401)), following Åberg ( http://arxiv.org/abs/quant-ph/0612146 ), have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here, we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here is to consider an idealized multi-path interferometer, with a suitable detector, in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state. We present a general framework of deriving coherence measures from visibility, and demonstrate it by analysing several concrete visibility parameters, recovering some known coherence measures and obtaining some new ones.

arXiv:1701.05051•Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Jul 1, 2017•78 citations

Fidelity and trace-norm distances for quantifying coherence

Lian-He Shao, Zhengjun Xi, Heng Fan +1 more

We investigate the coherence measures induced by fidelity and trace norm, based on the coherence quantification recently proposed by Baumgratz et al. [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. We show that the fidelity of coherence does not in general satisfy the monotonicity requirement as a measure of coherence under the subselection of the measurement condition. We find that the trace norm of coherence can act as a measure of coherence for qubits and some special class of qutrits with some restrictions on the incoherent operators, while the general case needs to be explored further.

arXiv:1410.8327•Physical Review A•Apr 15, 2015•272 citations

Experimental test of the relation between coherence and path information

Jun Gao, Zhi‐Qiang Jiao, Cheng-Qiu Hu +7 more

Abstract Quantum coherence stemming from the superposition behaviour of a particle beyond the classical realm, serves as one of the most fundamental features in quantum mechanics. The wave-particle duality phenomenon, which shares the same origin, has a strong relationship with quantum coherence. Recently, an elegant relation between quantum coherence and path information has been theoretically derived. Here, we experimentally test such new duality by l1-norm measure and the minimum-error state discrimination. We prepare three classes of two-photon states encoded in polarisation degree of freedom, with one photon serving as the target and the other photon as the detector. We observe that wave-particle-like complementarity and Bagan’s equality, defined by the duality relation between coherence and path information, is well satisfied. Our results may shed new light on the original nature of wave-particle duality and on the applications of quantum coherence as a fundamental resource in quantum technologies.

arXiv:1703.08026•Communications Physics•Nov 23, 2018•18 citations

Nonlocal quantum state interferography

P. Dhilipan, G. Raghavan

Quantum state interferography has recently been proposed as an interference-based technique for the measurement of the general qubit and pure qudit states [Phys. Rev. Lett. 125, 123601 (2020)]. This interferometric method exploits the relationship between the off-diagonal elements of the density matrix and the expectation values of non-Hermitian spin ladder operators. The extension of this method to a composite system is however nontrivial, as it involves the measurement of both single-photon and nonlocal multiphoton interferences. In this work, we present the theoretical analysis of the two-photon quantum state interferography of an arbitrary quantum state. We show that complete state information could in principle be obtained with two measurement settings and by recording six interferograms, using a single-photon sensitive imaging device. We then experimentally demonstrate two-photon nonlocal quantum state interferography of polarization-entangled photon pairs generated with type-I spontaneous parametric down conversion. Quantum state interferography of all four Bell states is performed. An upper bound on the separability of the bipartite states is established in terms of the visibility, phase average intensity, and phase shift of the interference patterns related to the antidiagonal elements of the matrix. Each of the four Bell states can be distinguished by the violation of these bounds uniquely.

Physical Review A•Jun 24, 2022•1 citation

Coherence measures with respect to general quantum measurements

Jianwei Xu, Lian-He Shao, Shao-Ming Fei

Quantum coherence with respect to orthonormal bases has been studied extensively in the past few years. Recently, Bischof, Kampermann, and Bru\ss{} [Phys. Rev. Lett. 123, 110402 (2019)] generalized it to the case of general positive operator-valued measure (POVM) measurements. Such POVM-based coherence, including the block coherence as a special case, have significant operational interpretations in quantifying the advantage of quantum states in quantum information processing. In this work we first establish an alternative framework for quantifying the block coherence and provide several block coherence measures. We then present several coherence measures with respect to POVM measurements, and prove a conjecture on the ${l}_{1}$-norm related POVM coherence measure.

arXiv:2007.09587•Physical Review A•Jul 16, 2020•41 citations

Directly Measuring the Degree of Quantum Coherence using Interference Fringes

Yi‐Tao Wang, Jian‐Shun Tang, Zhi-Yuan Wei +5 more

Quantum coherence is the most distinguished feature of quantum mechanics. It lies at the heart of the quantum-information technologies as the fundamental resource and is also related to other quantum resources, including entanglement. It plays a critical role in various fields, even in biology. Nevertheless, the rigorous and systematic resource-theoretic framework of coherence has just been developed recently, and several coherence measures are proposed. Experimentally, the usual method to measure coherence is to perform state tomography and use mathematical expressions. Here, we alternatively develop a method to measure coherence directly using its most essential behavior-the interference fringes. The ancilla states are mixed into the target state with various ratios, and the minimal ratio that makes the interference fringes of the "mixed state" vanish is taken as the quantity of coherence. We also use the witness observable to witness coherence, and the optimal witness constitutes another direct method to measure coherence. For comparison, we perform tomography and calculate l_{1} norm of coherence, which coincides with the results of the other two methods in our situation. Our methods are explicit and robust, providing a nice alternative to the tomographic technique.

Physical Review Letters•Jan 12, 2017•92 citations
Abstract Discussions about quantum interference, indistinguishability, and superposition between quantum states go back to the beginning of quantum mechanics. However, the theoretical problem, concerning quantitative measures for quantum coherence, was only recently solved by Baumgratz et al (2014 Phys. Rev. Lett. 113 140401). Since then, many works have explored one of the possible coherence measures: the l 1 norm, which has not yet been obtained experimentally for spatial photonic states in high dimensions. In this article, we study the measurement of spatial qudits quantum coherence. We treat the optical measure-operators as path-markers and show in which condition an interference pattern can be used for measure l 1 norm. We analyze the validity of a l 1 norm measurement method, proposed by Paul and Qureshi (2017 Phys. Rev. A 95 042110), implementing it experimentally in qutrit states, and propose an alternative method for qudits states in which one of their assumptions does not apply.
Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. ( Phys. Rev. Lett. 113 , 140401. (doi:10.1103/PhysRevLett.113.140401)), following Åberg ( http://arxiv.org/abs/quant-ph/0612146 ), have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here, we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here is to consider an idealized multi-path interferometer, with a suitable detector, in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state. We present a general framework of deriving coherence measures from visibility, and demonstrate it by analysing several concrete visibility parameters, recovering some known coherence measures and obtaining some new ones.
We investigate the coherence measures induced by fidelity and trace norm, based on the coherence quantification recently proposed by Baumgratz et al. [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. We show that the fidelity of coherence does not in general satisfy the monotonicity requirement as a measure of coherence under the subselection of the measurement condition. We find that the trace norm of coherence can act as a measure of coherence for qubits and some special class of qutrits with some restrictions on the incoherent operators, while the general case needs to be explored further.
Abstract Quantum coherence stemming from the superposition behaviour of a particle beyond the classical realm, serves as one of the most fundamental features in quantum mechanics. The wave-particle duality phenomenon, which shares the same origin, has a strong relationship with quantum coherence. Recently, an elegant relation between quantum coherence and path information has been theoretically derived. Here, we experimentally test such new duality by l1-norm measure and the minimum-error state discrimination. We prepare three classes of two-photon states encoded in polarisation degree of freedom, with one photon serving as the target and the other photon as the detector. We observe that wave-particle-like complementarity and Bagan’s equality, defined by the duality relation between coherence and path information, is well satisfied. Our results may shed new light on the original nature of wave-particle duality and on the applications of quantum coherence as a fundamental resource in quantum technologies.
Quantum state interferography has recently been proposed as an interference-based technique for the measurement of the general qubit and pure qudit states [Phys. Rev. Lett. 125, 123601 (2020)]. This interferometric method exploits the relationship between the off-diagonal elements of the density matrix and the expectation values of non-Hermitian spin ladder operators. The extension of this method to a composite system is however nontrivial, as it involves the measurement of both single-photon and nonlocal multiphoton interferences. In this work, we present the theoretical analysis of the two-photon quantum state interferography of an arbitrary quantum state. We show that complete state information could in principle be obtained with two measurement settings and by recording six interferograms, using a single-photon sensitive imaging device. We then experimentally demonstrate two-photon nonlocal quantum state interferography of polarization-entangled photon pairs generated with type-I spontaneous parametric down conversion. Quantum state interferography of all four Bell states is performed. An upper bound on the separability of the bipartite states is established in terms of the visibility, phase average intensity, and phase shift of the interference patterns related to the antidiagonal elements of the matrix. Each of the four Bell states can be distinguished by the violation of these bounds uniquely.
Quantum coherence with respect to orthonormal bases has been studied extensively in the past few years. Recently, Bischof, Kampermann, and Bru\ss{} [Phys. Rev. Lett. 123, 110402 (2019)] generalized it to the case of general positive operator-valued measure (POVM) measurements. Such POVM-based coherence, including the block coherence as a special case, have significant operational interpretations in quantifying the advantage of quantum states in quantum information processing. In this work we first establish an alternative framework for quantifying the block coherence and provide several block coherence measures. We then present several coherence measures with respect to POVM measurements, and prove a conjecture on the l1{l}_{1}l1​-norm related POVM coherence measure.
Quantum coherence is the most distinguished feature of quantum mechanics. It lies at the heart of the quantum-information technologies as the fundamental resource and is also related to other quantum resources, including entanglement. It plays a critical role in various fields, even in biology. Nevertheless, the rigorous and systematic resource-theoretic framework of coherence has just been developed recently, and several coherence measures are proposed. Experimentally, the usual method to measure coherence is to perform state tomography and use mathematical expressions. Here, we alternatively develop a method to measure coherence directly using its most essential behavior-the interference fringes. The ancilla states are mixed into the target state with various ratios, and the minimal ratio that makes the interference fringes of the "mixed state" vanish is taken as the quantity of coherence. We also use the witness observable to witness coherence, and the optimal witness constitutes another direct method to measure coherence. For comparison, we perform tomography and calculate l_{1} norm of coherence, which coincides with the results of the other two methods in our situation. Our methods are explicit and robust, providing a nice alternative to the tomographic technique.