| I have recently changed the focus of my research efforts to the immensely exciting field of quantum information, which is closely related to quantum computation, as well as to foundational questions concerning our understanding of quantum mechanics. I work closely with the quantum information group at Carnegie-Mellon University, an institution at which I also hold an ongoing appointment as Visiting Professor.
Many of the problems of interest to me involve entanglement – a rather strange kind of purely quantum correlations possibly existing across widely separated locations – and how to use entanglement to perform tasks that are impossible to accomplish without it. Such questions often also involve a restriction by the separated parties to acting locally on their subsystems (global measurements on the overall system are not allowed) and communicating classical messages (perhaps via a telephone) amongst themselves. This restriction is termed LOCC, or local operations and classical communication.
The problems I've been studying include:
• Local quantum state discrimination, whereby the parties attempt to distinguish which of a set of orthogonal states their overall system is in, by using LOCC;
• Implementation of non-local operations by LOCC using entanglement as resource;
• Dense coding, which involves sending classical messages encoded in a quantum system; by using entanglement more information can be sent than would otherwise be possible.
Some recent results, most of which are described in the papers listed below, include using a new diagrammatic approach to these problems, which provides deep insights into why entanglement is useful as a resource; seminal work on preserving entanglement in the process of state discrimination; a partial explanation of the shape and location of boundaries in dense coding (these boundaries delineate regions within which it is possible to transmit different numbers of classical messages); and a very recent result showing that even with a relatively small number of randomly chosen orthogonal states, the resulting set of states will almost never be distinguishable by LOCC.
As quantum information is a relatively new field, it offers numerous opportunities for innovation, as well as many fascinating problems for advanced undergraduates to sink their teeth into. Interested students are encouraged to contact me about possible research involvement.
1. S.M. Cohen , Almost every set of N = d+1 orthogonal states on d Ä n is locally indistinguishable , preprint available at http://xxx.lanl.gov/abs/0801.3993.
2. S.M. Cohen , Visualizing Teleportation , preprint available at http://xxx.lanl.gov/abs/0704.0051.
3. S.M. Cohen , Understanding Entanglement as Resource: Locally Distinguishing Unextendible Product Bases , Physical Review A 77 , 012304, 1 – 19 (2008).
4.
S.M. Cohen , Local Distinguishability with Preservation of Entanglement , Physical Review A 75 , 052313, 1 – 19 (2007) .
5. R. B. Griffiths, S. Wu, L. Yu, and S.M. Cohen , Atemporal Diagrams for Quantum Circuits , Physical Review A 73 , 052309, 1 – 17 (2006) .
6. S. Wu, S.M. Cohen , Y. Sun, and R. B. Griffiths, Unambiguous and Deterministic Dense Coding , Physical Review A 73 , 042311, 1 – 12 (2006) .
Phone: 412.396.6353
E-mail: cohensm@duq.edu |
Dr.
Scott Cohen
