Quantum information theory broadly studies the different ways to store, process, and communicate information based on the principles of quantum mechanics. The specific interests of this research group involve studying the mathematical theories and practical applications of quantum channels, entanglement, and other non-classical phenomena. An over-arching objective is to understand different ways that quantum-correlated systems can enhance distant communication and improve security
Quantum communication and applications
There are many different tasks one may wish to accomplish when building a quantum network. The simplest involves sending classical messages (i.e. bits “101001…”) using quantum-encoded signals or quantum-enhanced transmission schemes, such as dense coding or entangled-
assisted communication. Using quantum strategies like these, it is possible to improve the communication rates for both point-to-point channels as well as multi-sender and multi-receiver networks. A more powerful communication task is transmitting the physical state of some quantum system from one laboratory to another, which is known as communicating quantum information (e.g. qubits, or “quantum bits”). This can be done by directly sending the physical system from one laboratory to another over some channel like a fiber optic cable, or it can be accomplished using more sophisticated entanglement-based protocols like quantum teleportation.
Our group develops protocols that support classical and quantum communication over noisy channels. We further explore strategies and limitations for distributing classical and quantum correlations across a network. A primary research focus is to understand how these correlations can certify certain features about a network such as its connectivity, the noise on its channels, the measurements at each node, and the entanglement being distributed.
Beyond communication, quantum networks can be used to realize other types of applications such as distributed computation or sensing. Our group has specific interests in studying protocols that are suitable for demonstration on near-term on quantum networks. This includes quantum position verification, multiparty computation, and secret sharing, all of which use basic features of quantum mechanics to achieve non-classical advantages. Our group works closely with experimentalists here at UIUC and elsewhere.
Quantum resource theories and foundations
A quantum resource theory is any model of restricted quantum information processing. The principles of quantum mechanics place certain limitations on what physical process are possible; for example the no-cloning theorem prohibits making copies of an unknown quantum source. However, in realistic scenarios, practical and non-fundamental constraints also limit what can be accomplished by a given quantum
system. For instance, separated quantum laboratories are limited by how well or how quickly they can exchange quantum information, whereas the exchange of classical information is relatively unrestricted. In this scenario, quantum entanglement is a resource for distributed quantum information processing, as it cannot be generated by classical communication alone. One can then study how the resource of quantum entanglement can be quantified and transformed from one form to another using the “free operations” or local quantum operations and classical communication (LOCC).
Our group focuses on different types of quantum resources that empower quantum information processing or that touch on the foundations of quantum mechanics. We are specifically interested in the resource-theoretic aspects of the following objects
- LOCC and entanglement
- Bell nonlocality and quantum steering
- Incompatibility and quantum measurements
- Secret key and private states
- Coherence and quantum thermodynamics
Typical questions we investigate are: what types of states or channels possess these resources, how can they be detected or quantified, what are the mathematical and physical relationships between these resources, and how does the convertibility of these resources depend on the type of operational restriction imposed? This line of research is interdisciplinary, bringing together ideas from physics, math, and information theory.
Work in the Chitambar group is supported by grants from the National Science Foundation and the Department of Energy.
