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UCLQ Miniworkshop: Operators, quantum information processing, and communication
February 11, 2015 @ 2:00 pm - 5:00 pm
The venue is Bedford Way LG04:
Speaker: Vern Paulsen (University of Houston)
Title: Quantum Chromatic Numbers
Speaker: Giannicola Scarpa (Autonomous University of Barcelona)
Title: Multi-party zero-error classical channel coding with entanglement
Abstract: We study the effects of quantum entanglement on the performance of two classical zero-error communication tasks among multiple parties. Both tasks are generalizations of the two-party zero-error channel-coding problem, where a sender and a receiver want to perfectly communicate messages through a one-way classical noisy channel. If the two parties are allowed to share entanglement, there are several positive results that show the existence of channels for which they can communicate strictly more than what they could do with classical resources. In the first task, one sender wants to communicate a common message to multiple receivers. We show that if the number of receivers is greater than a certain threshold then entanglement does not allow for an improvement in the communication for any finite number of uses of the channel. On the other hand, when the number of receivers is fixed, we exhibit a class of channels for which entanglement gives an advantage. The second problem we consider features multiple collaborating senders and one receiver. Classically, cooperation among the senders might allow them to communicate on average more messages than the sum of their individual possibilities. We show that whenever a channel allows single-sender entanglement-assisted advantage, then the gain extends also to the multi-sender case. Furthermore, we show that entanglement allows for a peculiar amplification of information which cannot happen classically, for a fixed number of uses of a channel with multiple senders.
Time: 16:00, Wednesday 11th February
Speaker: Alex Monras (Autonomous University of Barcelona)
Title: Quantum learning of classical stochastic processes: The Completely-Positive Realization Problem
Abstract: Among several tasks in Machine Learning, a specially important one is that of inferring the latent variables of a system and their causal relations with the observed behavior. Learning a Hidden Markov Model of given stochastic process is a textbook example, known as the positive realization problem (PRP). The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and positive systems theory. We consider the scenario where the latent variables are quantum states, and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument â€“if anyâ€“ yields the process at hand by iterative application. We take as starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the Hidden Markov Model, or the iterated quantum instrument, is nevertheless devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The Completely-Positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, yielding possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and dynamical processes with quantum memory.
Note: Alex Monras, Andreas Winter, Ivan Todorov, Vern Paulsen, and Giannicola Scarpa will visit UCL from Monday 9th February to Saturday 14th February.