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Chandralekha Singh - One of the best experts on this subject based on the ideXlab platform.
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Validation and Administration of a Conceptual Survey on the Formalism and Postulates of Quantum Mechanics
Physical Review Physics Education Research, 2019Co-Authors: Emily Marshman, Chandralekha SinghAbstract:We developed and validated a conceptual survey that focuses on the formalism and postulates of quantum mechanics covered in upper-level undergraduate quantum mechanics courses. The concepts included in the Quantum Mechanics Formalism and Postulate Survey (QMFPS) focus on Dirac Notation, the Hilbert space, state vectors, physical observables and their corresponding Hermitian operators, compatible and incompatible observables, quantum measurement, time-dependence of quantum states and expectation values, and spin angular momenta. Here we describe the validation and administration of the survey, which has been administered to over 400 upper-level undergraduate and graduate students from six institutions. The QMFPS is valid and reliable for use as a low-stakes test to measure the effectiveness of instruction in an undergraduate quantum mechanics course that covers relevant content. The survey can also be used by instructors to identify student understanding of the formalism and postulates of quantum mechanics at the beginning and end of a graduate quantum mechanics course since graduate students are expected to have taken an undergraduate quantum mechanics course that covers the content included in the survey. We found that undergraduate students who engaged with research-validated learning tools performed better than students who did not on the QMFPS after the first semester of a junior/senior level quantum mechanics course. In addition, the performance of graduate students on QMFPS after instruction in the first semester of a core graduate-level quantum mechanics course was significantly better than the performance of undergraduate students at the end of the first semester of an undergraduate quantum mechanics course. A comparison with the base line data on the validated QMFPS presented here can aid instructors in assessing the effectiveness of their instructional approaches.
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investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics
European Journal of Physics, 2017Co-Authors: Emily Marshman, Chandralekha SinghAbstract:A solid grasp of the probability distributions for measuring physical observables is central to connecting the quantum formalism to measurements. However, students often struggle with the probability distributions of measurement outcomes for an observable and have difficulty expressing this concept in different representations. Here we first describe the difficulties that upper-level undergraduate and PhD students have with the probability distributions for measuring physical observables in quantum mechanics. We then discuss how student difficulties found in written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of the probability distributions of measurement outcomes for physical observables. The QuILT strives to help students become proficient in expressing the probability distributions for the measurement of physical observables in Dirac Notation and in the position representation and be able to convert from Dirac Notation to position representation and vice versa. We describe the development and evaluation of the QuILT and findings about the effectiveness of the QuILT from in-class evaluations.
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Student difficulties with representations of quantum operators corresponding to observables
2016 Physics Education Research Conference Proceedings, 2016Co-Authors: Emily Marshman, Chandralekha SinghAbstract:Dirac Notation is used commonly in quantum mechanics. However, many upper-level undergraduate and graduate students in physics have difficulties with representations of quantum operators corresponding to observables especially when using Dirac Notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students in advanced quantum mechanics courses. We discuss the analysis of data on the common difficulties found.
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Student difficulties with determining expectation values in quantum mechanics
2016 Physics Education Research Conference Proceedings, 2016Co-Authors: Chandralekha Singh, Emily MarshmanAbstract:The expectation value of an observable is an important concept in quantum mechanics. However, upper-level undergraduate and graduate students in physics have both conceptual and procedural difficulties when determining the expectation value of physical observables, especially when using Dirac Notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students. Here, we discuss the analysis of data on student difficulties when determining the expectation value.
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Student difficulties with quantum states while translating state vectors in Dirac Notation to wave functions in position and momentum representations
2015 Physics Education Research Conference Proceedings, 2015Co-Authors: Emily Marshman, Chandralekha SinghAbstract:We administered written free-response and multiple-choice questions and conducted individual interviews to investigate the difficulties that upper-level undergraduate and graduate students have with quantum states while translating state vectors in Dirac Notation to wave functions in position and momentum representations. We find that students share common difficulties with translating a state vector written in Dirac Notation to the wave function in position or momentum representation.
Anne Hillebrand - One of the best experts on this subject based on the ideXlab platform.
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This work is licensed under the Creative Commons Attribution License. Superdense Coding with GHZ and Quantum Key Distribution with W in the ZX-calculus
2016Co-Authors: Bart Jacobs, Peter Selinger, Bas Spitters, Anne HillebrandAbstract:Quantum entanglement is a key resource in many quantum protocols, such as quantum teleportation and quantum cryptography. Yet entanglement makes protocols presented in Dirac Notation difficult to verify. This is why Coecke and Duncan have introduced a diagrammatic language for quantum protocols, called the ZX-calculus [11]. This diagrammatic Notation is both intuitive and formally rigorous. It is a simple, graphical, high level language that emphasises the composition of systems and naturally captures the essentials of quantum mechanics. In the author’s MSc thesis [18] it has been shown for over 25 quantum protocols that the ZX-calculus provides a relatively easy and more intuitive presentation. Moreover, the author embarked on the task to apply categorical quantum mechanics on quantum security; earlier works did not touch anything but Bennett and Brassard’s quantum key distribution protocol, BB84. Two of the protocols in [18], namely superdense coding with the Greenberger-Horne-Zeilinger state and quantum key distribution with the W-state, will be presented in this paper.
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QPL - Superdense Coding with GHZ and Quantum Key Distribution with W in the ZX-calculus
Electronic Proceedings in Theoretical Computer Science, 2012Co-Authors: Anne HillebrandAbstract:Quantum entanglement is a key resource in many quantum protocols, such as quantum teleportation and quantum cryptography. Yet entanglement makes protocols presented in Dirac Notation difficult to verify. This is why Coecke and Duncan have introduced a diagrammatic language for quantum protocols, called the ZX-calculus. This diagrammatic Notation is both intuitive and formally rigorous. It is a simple, graphical, high level language that emphasises the composition of systems and naturally captures the essentials of quantum mechanics. In the author's MSc thesis it has been shown for over 25 quantum protocols that the ZX-calculus provides a relatively easy and more intuitive presentation. Moreover, the author embarked on the task to apply categorical quantum mechanics on quantum security; earlier works did not touch anything but Bennett and Brassard's quantum key distribution protocol, BB84. Superdense coding with the Greenberger-Horne-Zeilinger state and quantum key distribution with the W-state are presented in the ZX-calculus in this paper.
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Quantum Protocols involving Multiparticle Entanglement and their Representations in the zx-calculus.
2011Co-Authors: Anne HillebrandAbstract:Quantum entanglement, described by Einstein as “spooky action at a distance”, is a key resource in many quantum protocols, like quantum teleportation and quantum cryptography. Yet entanglement makes protocols presented in Dirac Notation difficult to follow and check. This is why Coecke nad Duncan have introduced a diagrammatic language for multi-qubit systems, called the red/green calculus or the zx-calculus [23]. This diagrammatic Notation is both intuitive and formally rigorous. It is a simple, graphical, high level language that emphasises the composition of systems and naturally captures the essentials of quantum mechanics. One crucial feature that will be exploited here is the encoding of complementary observables and corresponding phase shifts. Reasoning is done by rewriting diagrams, i.e. locally replacing some part of a diagram. Diagrams are defined by their topology only; the number of inputs and outputs and the way they are connected. This exemplifies the ‘flow’ of information. For protocols involving multipartite entangled states, such as the GreenbergerHorne-Zeilinger and W -state, it will be shown that the zx-calculus provides a relatively easy and more intuitive presentation. Moreover, in this representation it is easier to check that protocols are correct. Protocols that will be discussed in detail are quantum teleportation, quantum cryptography, leader election, superdense coding and quantum direct communication with multipartite entangled states.
James Freericks - One of the best experts on this subject based on the ideXlab platform.
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Calculating spherical harmonics without derivatives
Condensed Matter Physics, 2018Co-Authors: M. Weitzman, James FreericksAbstract:The derivation of spherical harmonics is the same in nearly every quantum mechanics textbook and classroom. It is found to be difficult to follow, hard to understand, and challenging to reproduce by most students. In this work, we show how one can determine spherical harmonics in a more natural way based on operators and a powerful identity called the exponential disentangling operator identity (known in quantum optics, but little used elsewhere). This new strategy follows naturally after one has introduced Dirac Notation, computed the angular momentum algebra, and determined the action of the angular momentum raising and lowering operators on the simultaneous angular momentum eigenstates (under $\hat L^2$ and $\hat L_z$).
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Incorporating the Stern-Gerlach delayed-choice quantum eraser into the undergraduate quantum mechanics curriculum
arXiv: Physics Education, 2017Co-Authors: William F. Courtney, Lucas B. Vieira, Paul S. Julienne, James FreericksAbstract:As "Stern-Gerlach first" becomes the new paradigm within the undergraduate quantum mechanics curriculum, we show how one can extend the treatment found in conventional textbooks to cover some of the exciting new developments within the quantum field. Namely, we illustrate how one can employ Dirac Notation and conventional quantum rules to describe a delayed choice variant of the quantum eraser which is realized within the Stern-Gerlach framework. Covering this material, allows the instructor to reinforce notions of changes of basis functions, quantum superpositions, quantum measurement, and the complementarity principle as expressed in whether we know "which-way" information or not. It also allows the instructor to dispel common misconceptions of when a measurement occurs and when a system is in a superposition of states. We comment at the end how a similar methodology can be employed when the more conventional two-slit experiment is treated.
Freericks J. K. - One of the best experts on this subject based on the ideXlab platform.
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Calculating spherical harmonics without derivatives
'Institute for Condensed Matter Physics', 2018Co-Authors: Weitzman M., Freericks J. K.Abstract:The derivation of spherical harmonics is the same in nearly every quantum mechanics textbook and classroom. It is found to be difficult to follow, hard to understand, and challenging to reproduce by most students. In this work, we show how one can determine spherical harmonics in a more natural way based on operators and a powerful identity called the exponential disentangling operator identity (known in quantum optics, but little used elsewhere). This new strategy follows naturally after one has introduced Dirac Notation, computed the angular momentum algebra, and determined the action of the angular momentum raising and lowering operators on the simultaneous angular momentum eigenstates (under $\hat L^2$ and $\hat L_z$).Comment: 12 pages, 1 figur
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Incorporating the Stern-Gerlach delayed-choice quantum eraser into the undergraduate quantum mechanics curriculum
2017Co-Authors: Courtney W. F., Vieira L. B., Julienne P. S., Freericks J. K.Abstract:As "Stern-Gerlach first" becomes the new paradigm within the undergraduate quantum mechanics curriculum, we show how one can extend the treatment found in conventional textbooks to cover some of the exciting new developments within the quantum field. Namely, we illustrate how one can employ Dirac Notation and conventional quantum rules to describe a delayed choice variant of the quantum eraser which is realized within the Stern-Gerlach framework. Covering this material, allows the instructor to reinforce notions of changes of basis functions, quantum superpositions, quantum measurement, and the complementarity principle as expressed in whether we know "which-way" information or not. It also allows the instructor to dispel common misconceptions of when a measurement occurs and when a system is in a superposition of states. We comment at the end how a similar methodology can be employed when the more conventional two-slit experiment is treated.Comment: (20 pages, 8 figures
Emily Marshman - One of the best experts on this subject based on the ideXlab platform.
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Validation and Administration of a Conceptual Survey on the Formalism and Postulates of Quantum Mechanics
Physical Review Physics Education Research, 2019Co-Authors: Emily Marshman, Chandralekha SinghAbstract:We developed and validated a conceptual survey that focuses on the formalism and postulates of quantum mechanics covered in upper-level undergraduate quantum mechanics courses. The concepts included in the Quantum Mechanics Formalism and Postulate Survey (QMFPS) focus on Dirac Notation, the Hilbert space, state vectors, physical observables and their corresponding Hermitian operators, compatible and incompatible observables, quantum measurement, time-dependence of quantum states and expectation values, and spin angular momenta. Here we describe the validation and administration of the survey, which has been administered to over 400 upper-level undergraduate and graduate students from six institutions. The QMFPS is valid and reliable for use as a low-stakes test to measure the effectiveness of instruction in an undergraduate quantum mechanics course that covers relevant content. The survey can also be used by instructors to identify student understanding of the formalism and postulates of quantum mechanics at the beginning and end of a graduate quantum mechanics course since graduate students are expected to have taken an undergraduate quantum mechanics course that covers the content included in the survey. We found that undergraduate students who engaged with research-validated learning tools performed better than students who did not on the QMFPS after the first semester of a junior/senior level quantum mechanics course. In addition, the performance of graduate students on QMFPS after instruction in the first semester of a core graduate-level quantum mechanics course was significantly better than the performance of undergraduate students at the end of the first semester of an undergraduate quantum mechanics course. A comparison with the base line data on the validated QMFPS presented here can aid instructors in assessing the effectiveness of their instructional approaches.
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investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics
European Journal of Physics, 2017Co-Authors: Emily Marshman, Chandralekha SinghAbstract:A solid grasp of the probability distributions for measuring physical observables is central to connecting the quantum formalism to measurements. However, students often struggle with the probability distributions of measurement outcomes for an observable and have difficulty expressing this concept in different representations. Here we first describe the difficulties that upper-level undergraduate and PhD students have with the probability distributions for measuring physical observables in quantum mechanics. We then discuss how student difficulties found in written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of the probability distributions of measurement outcomes for physical observables. The QuILT strives to help students become proficient in expressing the probability distributions for the measurement of physical observables in Dirac Notation and in the position representation and be able to convert from Dirac Notation to position representation and vice versa. We describe the development and evaluation of the QuILT and findings about the effectiveness of the QuILT from in-class evaluations.
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Student difficulties with representations of quantum operators corresponding to observables
2016 Physics Education Research Conference Proceedings, 2016Co-Authors: Emily Marshman, Chandralekha SinghAbstract:Dirac Notation is used commonly in quantum mechanics. However, many upper-level undergraduate and graduate students in physics have difficulties with representations of quantum operators corresponding to observables especially when using Dirac Notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students in advanced quantum mechanics courses. We discuss the analysis of data on the common difficulties found.
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Student difficulties with determining expectation values in quantum mechanics
2016 Physics Education Research Conference Proceedings, 2016Co-Authors: Chandralekha Singh, Emily MarshmanAbstract:The expectation value of an observable is an important concept in quantum mechanics. However, upper-level undergraduate and graduate students in physics have both conceptual and procedural difficulties when determining the expectation value of physical observables, especially when using Dirac Notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students. Here, we discuss the analysis of data on student difficulties when determining the expectation value.
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Student difficulties with quantum states while translating state vectors in Dirac Notation to wave functions in position and momentum representations
2015 Physics Education Research Conference Proceedings, 2015Co-Authors: Emily Marshman, Chandralekha SinghAbstract:We administered written free-response and multiple-choice questions and conducted individual interviews to investigate the difficulties that upper-level undergraduate and graduate students have with quantum states while translating state vectors in Dirac Notation to wave functions in position and momentum representations. We find that students share common difficulties with translating a state vector written in Dirac Notation to the wave function in position or momentum representation.