Publications & Presentations

## LVC Mathematical Physics Research Group

### Publications

David W. Lyons, Nathaniel P. Gibbons, Mark A. Peters, Daniel J. Upchurch,
Scott N. Walck, and Ezekiel W. Wertz.
Local Pauli stabilizers of symmetric hypergraph states.
2016.
*(under review)*.
[ arXiv |
e-print ]

David W. Lyons, Daniel J. Upchurch, Scott N. Walck, and Chase D. Yetter.
Local unitary symmetries of hypergraph states.
*Journal of Physics A: Mathematical and Theoretical*,
48(9):095301, February 2015.
arXiv:1410.3904.
[ journal |
e-print ]

Scott N. Walck.
Learn Physics by Programming in Haskell.
In James Caldwell, Philip Hölzenspies, and Peter Achten, editors,
*Proceedings 3rd International Workshop on Trends in Functional
Programming in Education, Soesterberg, The Netherlands, 25th May 2014*,
volume 170 of *Electronic Proceedings in Theoretical Computer Science*,
pages 67--77. Open Publishing Association, May 2014.
[ DOI |
e-print ]

Curt D. Cenci, David W. Lyons, and Scott N. Walck.
Local unitary group stabilizers and entanglement for multiqubit
symmetric states.
In Dave Bacon, Miguel Martin-Delgado, and Martin Roetteler, editors,
*Theory of Quantum Computation, Communication, and Cryptography*, volume
6745 of *Lecture Notes in Computer Science*, pages 198--207. Springer,
March 2014.
arXiv:1011.5229v1.
[ e-print ]

David W. Lyons and Scott N. Walck.
Entanglement verification using local unitary stabilizers.
*Phys. Rev. A*, 87:062321, Jun 2013.
arXiv:1303.6497 [quant-ph].
[ DOI |
journal |
e-print ]

David W. Lyons, Abigail M. Skelton, and Scott N. Walck.
Werner state structure and entanglement classification.
*Advances in Mathematical Physics*, 2012:463610, 2012.
arXiv:1109.6063v2 [quant-ph].
[ DOI |
journal |
e-print ]

David W. Lyons and Scott N. Walck.
Entanglement classes of symmetric Werner states.
*Phys. Rev. A*, 84:042316, October 2011.
arXiv:1106.4220v2 [quant-ph].
[ DOI |
journal |
e-print ]

David W. Lyons and Scott N. Walck.
Symmetric mixed states of *n* qubits: Local unitary stabilizers and
entanglement classes.
*Phys. Rev. A*, 84:042340, October 2011.
arXiv:1107.1372v1 [quant-ph].
[ DOI |
journal |
e-print ]

Curt D. Cenci, David W. Lyons, Laura M. Snyder, and Scott N. Walck.
Symmetric states: local unitary equivalence via stabilizers.
*Quantum Information and Computation*, 10:1029--1041, November
2010.
arXiv:1007.3920v1 [quant-ph].
[ journal |
e-print ]

Scott N. Walck and David W. Lyons.
Only *n*-qubit Greenberger-Horne-Zeilinger states contain
*n*-partite information.
*Phys. Rev. A*, 79:032326, March 2009.
arXiv:0808.0859v1 [quant-ph].
[ DOI |
journal |
e-print ]

David W. Lyons and Scott N. Walck.
Multiparty quantum states stabilized by the diagonal subgroup of the
local unitary group.
*Phys. Rev. A*, 78:042314, October 2008.
arXiv:0808.2989v2 [quant-ph].
[ DOI |
journal |
e-print ]

David W. Lyons. Survey of Hopf fibrations and rotation conventions in mathematics and physics. arXiv:0808.3089v2 [math-ph], September 2008. [ e-print ]

David W. Lyons, Scott N. Walck, and Stephanie A. Blanda.
Classification of nonproduct states with maximum stabilizer
dimension.
*Phys. Rev. A*, 77:022309, 2008.
arXiv:0709.1105 [quant-ph].

Scott N. Walck and David W. Lyons.
Only n-qubit Greenberger-Horne-Zeilinger states are
undetermined by their reduced density matrices.
*Phys. Rev. Lett.*, 100:050501, 2008.
arXiv:0707.4428 [quant-ph].

Scott N. Walck and David W. Lyons.
Maximum stabilizer dimension for nonproduct states.
*Phys. Rev. A*, 76:022303, 2007.
arXiv:0706.1785 [quant-ph].

David W. Lyons and Scott N. Walck.
Classification of *n*-qubit states with minimum orbit dimension.
*J. Phys. A: Math. Gen.*, 39:2443--2456, 2006.
arXiv:quant-ph/0506241.

David W. Lyons and Scott N. Walck.
Minimum orbit dimension for local unitary action on *n*-qubit pure
states.
*J. Math. Phys.*, 46:102106, 2005.
arXiv:quant-ph/0503052.

Scott N. Walck, James K. Glasbrenner, Matthew H. Lochman, and Shawn A. Hilbert.
Topology of the three-qubit space of entanglement types.
*Phys. Rev. A*, 72:052324, 2005.
arXiv:quant-ph/0507208v2.
[ DOI |
journal |
e-print ]

David W. Lyons.
An elementary introduction to the Hopf fibration.
*Mathematics Magazine*, 76(2):87--98, 2003.
[ journal |
e-print ]

S. N. Walck and N. C. Hansell.
Characterization and visualization of the state and entanglement of
two spins.
*Eur. J. Phys.*, 22:343--350, 2001.
[ DOI |
journal ]

### Presentations

David W. Lyons. Permutation subgroup invariant states: entanglement and applications. Seefeld QI Workshop, Seefeld, Austria, June 2016.

Scott N. Walck. Learn Quantum Mechanics with Haskell. 5th International Workshop on Trends in Functional Programming in Education, College Park, Maryland, June 2016.

Scott N. Walck. Qubits and Entanglement. Physics Colloquium, Franklin and Marshall College, April 2016.

David W. Lyons. Discrete symmetries of hypergraph states. Tetrahedral Geometry and Topology Seminar, Hempfield, PA, April 2016.

Mark A. Peters. Local unitary stabilizers of symmetric hypergraph states. Moravian College Student Mathematics Conference, Moravian College, February 2016.

Nathaniel P. Gibbons. Pauli stabilizers of symmetric hypergraph states. Moravian College Student Mathematics Conference, Moravian College, February 2016.

Daniel J. Upchurch. Symmetric hypergraph state reconstruction. Moravian College Student Mathematics Conference, Moravian College, February 2016.

Chase D. Yetter. Discrete Symmetries of Symmetric Hypergraph States. Inquiry 2015 Student Research Symposium, Lebanon Valley College, April 2015.

David W. Lyons. Adventure in the Quantum World. Pi Mu Epsilon (Mathematics Honor Society), Elizabethtown College, PA, April 2015.

David W. Lyons. Entanglement properties of hypergraph states. British Mathematics Colloquium, University of Cambridge, UK, March 2015.

David W. Lyons. A Few of My Favorite Things. Sabbatical Talk, Lebanon Valley College, PA, March 2015.

Scott N. Walck. Learn Physics by Programming in Haskell. Annual Meeting of the Mid-Atlantic Section of the American Physical Society, Pennsylvania State University, October 2014.

Chase D. Yetter. Discrete Symmetries of Symmetric Hypergraph States. Annual Meeting of the Mid-Atlantic Section of the American Physical Society, Pennsylvania State University, October 2014.

Dan J. Upchurch. Partial Trace of Hypergraph States. Annual Meeting of the Mid-Atlantic Section of the American Physical Society, Pennsylvania State University, October 2014.

David W. Lyons. Graphs and Hypergraphs, Symmetry and Entanglement. Tetrahedral Geometry and Topology Seminar, Hempfield, PA, September 2014.

David W. Lyons. Undergraduate research in quantum information science. MathFest, Portland, OR, August 2014.

David W. Lyons. Local Unitary Symmetries of Hypergraph States. Quantum Information Workshop, Seefeld, Austria, July 2014.

Scott N. Walck. Learn Physics by Programming in Haskell. 3rd International Workshop on Trends in Functional Programming in Education, Soesterberg, Netherlands, May 2014.

David W. Lyons. Local Unitary Symmetries of Hypergraph States. University of Cambridge, May 2014.

David W. Lyons. Local Unitary Symmetries of Hypergraph States. University of Bristol, May 2014.

David W. Lyons. Local Unitary Symmetries of Hypergraph States. Télécom Paris Tech, May 2014.

Sarah M. Black. Mixed Werner Basis Conjecture: Ongoing Work. Inquiry 2014 Student Research Symposium, Lebanon Valley College, April 2014.

Ian Finley. Functions for Determining Nonlocality. Inquiry 2014 Student Research Symposium, Lebanon Valley College, April 2014.

Anthony Hoover. Verification of Quantum Processes using Functional Programming. Inquiry 2014 Student Research Symposium, Lebanon Valley College, April 2014.

Adam Rosier. Searching for Quantum Contextual Models. Inquiry 2014 Student Research Symposium, Lebanon Valley College, April 2014.

David W. Lyons. Entanglement and local unitary stabilizer subgroups. Quantum Information Seminar, Institute for Quantum Optics and Quantum Information, Innsbruck, Austria, March 2014.

Anthony Hoover. Verification of Quantum Processes using Functional Programming. American Physical Society National Meeting, March 2014.

Adam Rosier. Searching for Quantum Contextual Models. American Physical Society National Meeting, March 2014.

David W. Lyons. Entanglement verification using local unitary stabilizers. Central European Quantum Information Processing Workshop, Valtice, Czech Republic, June 2013.

Ian H. Bond. Programming Grover's Search Algorithm and Quantum Counting. Inquiry 2013 Student Research Symposium, Lebanon Valley College, April 2013.

Anthony R. Hoover. Procedure Verification in a Functional Quantum Programing Language. Inquiry 2013 Student Research Symposium, Lebanon Valley College, April 2013.

Oliver D. Lyons. Determining the Accuracy of a Quantum Testing Protocol for Werner States. Inquiry 2013 Student Research Symposium, Lebanon Valley College, April 2013.

Kelsey A. Moore. Investigation of a Werner State basis. Mathematical Association of America Undergraduate Poster Session, Joint Meetings of the American Mathematical Association and the Mathematical Association of America, San Diego, January 2013.

Ian H. Bond. Programming Grover's Search Algorithm and Quantum Counting. Mathematical Association of America Undergraduate Poster Session, Joint Meetings of the American Mathematical Association and the Mathematical Association of America, San Diego, January 2013.

Anthony R. Hoover. Procedure Verification in a Functional Quantum Programing Language. Mathematical Association of America Undergraduate Poster Session, Joint Meetings of the American Mathematical Association and the Mathematical Association of America, San Diego, January 2013.

Oliver D. Lyons. Determining the Accuracy of a Quantum Testing Protocol for Werner States. Mathematical Association of America Undergraduate Poster Session, Joint Meetings of the American Mathematical Association and the Mathematical Association of America, San Diego, January 2013.

David W. Lyons. Quantum information: An ongoing research program with undergraduate students. The MD-DC-VA Section meeting of the Mathematical Association of America, Virginia Military Institute, Lexington, VA, October 2012.

Scott N. Walck. Multi-particle entanglement classification. University of Glasgow, August 2012.

David W. Lyons. Linear basis for decoherence-free subspace for collective decoherence. Quantum Information Workshop, Seefeld, Austria, July 2012.

Scott N. Walck. Two examples of entanglement classification. Anacapa Society Meeting, Hamline University, St. Paul, Minnesota, May 2012.

David W. Lyons. Local unitary stabilizers, symmetric states, and Werner states. Télécom Paris Tech, March 2012.

Abigail M. Skelton.
Structure of *n*-qubit Werner States.
Mathematical Association of America Undergraduate Poster Session,
Joint Meetings of the American Mathematical Association and the Mathematical
Association of America, Boston, January 2012.

David W. Lyons, Abigail M. Skelton, and Scott N. Walck. Local Unitary Classes of Symmetric Mixed States and Ongoing Work on Werner States. Quantum Information Processing (QIP) 2012, Montréal, December 2011.

David W. Lyons.
Classifying entanglement for symmetric states of *n* quantum bits.
Tetrahedral Geometry and Topology Seminar, Elizabethtown College, PA,
September 2011.

David W. Lyons. Local unitary group stabilizers and entanglement for multiqubit symmetric states. Theory of Quantum Computation, Communication and Cryptography (TQC) 2011, Madrid, May 2011.

Laura M. Snyder. Stabilizer formalism and symmetric states. Research Poster Session, Celebration of Student Learning, Lebanon Valley College, April 2011.

Adam B. Hansell. Quantum states determined by their 2-qubit reduced density matrices. Research Presentation Session, Celebration of Student Learning, Lebanon Valley College, April 2011.

Ian M. Younker. Quantum states and their subsystems. Research Poster Session, Celebration of Student Learning, Lebanon Valley College, April 2011.

Nathan L. Kearney. Decomposing states of multiple quantum bits. Moravian College Student Mathematics Conference, Moravian College, February 2011.

Curt D. Cenci. Classification of symmetric states under local unitary action. Joint Meetings of the American Mathematical Association and the Mathematical Association of America, New Orleans, January 2011.

Curt D. Cenci. Quantum information: Classification of symmetric states under local unitary action. Mathematical Association of America Undergraduate Poster Session, Joint Meetings of the American Mathematical Association and the Mathematical Association of America, New Orleans, January 2011.

Laura M. Snyder. Stabilizer formalism and symmetric states. Mathematical Association of America Undergraduate Poster Session, Joint Meetings of the American Mathematical Association and the Mathematical Association of America, New Orleans, January 2011.

Edward C. Ulicny. Preconcurrence for two-qubit states. Mathematical Association of America Undergraduate Poster Session, Joint Meetings of the American Mathematical Association and the Mathematical Association of America, New Orleans, January 2011.

David W. Lyons. Some questions about local unitary stabilizers. Theory of Quantum Computation, Communication and Cryptography (TQC) 2010, Leeds, UK, April 2010.

Adam B. Hansell. One dimensional stabilizers for 2-, 3-, and 4-qubit states. Eastern Pennsylvania and Delaware Section of the Mathematical Association of America, Elizabethtown College, April 2010.

Laura M. Snyder. Classifying two-qubit states by their subsystems. American Association of Physics Teachers Central Pennsylvania Section Meeting, LaSalle University, March 2010.

Curt D. Cenci. Classification of entanglement types in quantum information. Moravian College Student Mathematics Conference, Moravian College, February 2010.

Curt D. Cenci. Quantum Information and 1-dimensional Stabilizers in Multiparty States. Mathematical Association of America Undergraduate Poster Session, Joint Meetings of the American Mathematical Society and the Mathematical Association of America, San Francisco, CA, January 2010.

Scott N. Walck. Local unitary stabilizers and multipartite entanglement. Plenary Lecture at the Symposium on Optical Interactions and Quantum Systems, University of Rochester, October 2009.

Scott N. Walck.
Only *n*-qubit Greenberger-Horne-Zeilinger states contain
*n*-partite information.
40th Annual Meeting of the APS Division of Atomic, Molecular and
Optical Physics, Charlottesville, Virginia, May 2009.

David W. Lyons. Quantum entanglement: When the whole is more than the sum of the parts. Lebanon Valley College Faculty Colloquium, Annville, PA, March 2009.

Stephanie A. Blanda. Classifying States With Near Maximum Entanglement. Moravian College Student Mathematics Conference, Moravian College, February 2009.

Stephanie A. Blanda. Multiparty Quantum States with Nearly Maximal Stabilizer. AMS Session on Quantum Theory and Fluid Mechanics, Joint Meetings of the American Mathematical Society and the Mathematical Association of America, Washington, DC, January 2009.

David W. Lyons. Classification of Multi-party Quantum Entanglement: Continuing Work. Tetrahedral Geometry and Topology Seminar, Hempfield, PA, October 2008.

David W. Lyons. An Application of Combinatorics in Quantum Information. Virginia Commonwealth University Discrete Mathematics Seminar, Richmond, VA, October 2008.

David W. Lyons. Quantum Information and Entanglement. Virginia Commonwealth University Mathematical Expositions Talk, Richmond, VA, October 2008.

Stephanie A. Blanda. Multiparty Quantum States with Nearly Maximal Stabilizer. Disappearing Boundaries Symposium Poster Session, Lebanon Valley College, October 2008.

David W. Lyons. Entanglement Classification Using Stabilizer Subalgebras. Susquehanna University Research Experience for Undergraduates in Quantum Information Theory, Selinsgrove, PA, July 2008.

David W. Lyons. Maximum Stabilizer Dimension for Multiparty States. University of Bristol Quantum Computation and Information Seminar, Bristol, UK, February 2008.

David W. Lyons. Maximum Stabilizer Dimension for Multiparty States. University of York Quantum Information Seminar, York, UK, January 2008.

Stephanie A. Blanda. Quantum Information and 4-Qubit States. EPaDel Section of the Mathematical Association of America, Drexel University, November 2007.

Stephanie A. Blanda. Quantum Information and 4-Qubit States. Disappearing Boundaries Symposium Poster Session, Lebanon Valley College, October 2007.

David W. Lyons. Hamilton, Hopf and Bloch. Joint Math Colloquium of Franklin and Marshall College and Millersville University, Millersville, PA, April 2007.

Daniel A. Pitonyak.
Quantum Computation, Quantum Information, and Irreducible
*n*-qubit Entanglement.
Moravian College Student Mathematics Conference, Moravian College,
February 2007.

Robert Schaeffer. Computations of Quantum Entanglement. Shenandoah Undergraduate Mathematics and Statistics Conference, James Madison University, October 2006.

Daniel A. Pitonyak.
Irreducible *n*-qubit Entanglement.
Disappearing Boundaries Symposium Poster Session, Lebanon Valley
College, September 2006.

Robert Schaeffer. Quantum Entanglement Computations. Disappearing Boundaries Symposium Poster Session, Lebanon Valley College, September 2006.

Scott N. Walck. Classifying Quantum Entanglement Using the Local Unitary Group Action. Tetrahedral Geometry and Topology Seminar, Hempfield, PA, September 2006.

David W. Lyons. Classification of Multiparticle Entanglement Types with Minimum Orbit Dimension. Joint Meetings of the American Mathematical Society and the Mathematical Association of America, San Antonio, TX, January 2006.

Scott N. Walck. Classifying Quantum Entanglement Using the Local Unitary Group Action. University of Pennsylvania, Spring 2006.

David W. Lyons. Minimum Orbit for the Local Unitary Group Action on State Space for a System of Qubits. Joint Meetings of the American Mathematical Society and the Mathematical Association of America, Atlanta, GA, January 2005.

James K. Glasbrenner. Types of Three-Qubit Entanglement. Lebanon Valley College Science Colloquium Poster Session, Fall 2005.

David W. Lyons. Rotations, Quaternions and the Hopf Map. Joint Math Colloquium of Franklin and Marshall College and Millersville University, Lancaster, PA, April 2004.

David W. Lyons. Problems in Quantum Entanglement. Tetrahedral Geometry and Topology Seminar, Hempfield, PA, October 2003.

David W. Lyons. Quantum Information. Lebanon Valley College Faculty Colloquium, Annville, PA, April 2003.

Nicholas Hamblet. Computer Animation of the Hopf Fibration. Joint Meetings of the American Mathematical Society and the Mathematical Association of America Student Poster Session, Baltimore, January 2003.

Jonathan Pitt. Stationary 2-qubit Quantum States. Joint Meetings of the American Mathematical Society and the Mathematical Association of America Student Poster Session, Baltimore, January 2003.

Scott N. Walck. Bloch-Sphere-Based Visualization of Quantum Systems. Gordon Conference on Physics Research and Education in Quantum Mechanics Poster Session, Mount Holyoke College, South Hadley, MA, 2002.

Scott N. Walck. Topological Decomposition of Composite Quantum State Spaces. International Conference on Quantum Information, University of Rochester, Rochester, NY, 2001.

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