This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.
We give a communication problem between two players, Alice and Bob, that can be solved by Alice sending a quantum message to Bob, for which any classical interactive protocol requires exponentially more communication.
We show that singlets composed of multiple multi-level quantum systems can naturally arise as the ground state of a physically-motivated Hamiltonian. The Hamiltonian needs to be one which simply exchanges the states of nearest neighbours in any graph of interacting d-level quantum systems (qudits) as long as the graph also has d sites. We point out that local measurements on some of these qudits, with the freedom of choosing a distinct measurement basis at each qudit randomly from an infinite set of bases, project the remainder onto a singlet state.
We propose an extended quantum theory, in which the number of degrees of freedom K behaves as FOURTH power the number N of distinguishable states. As the simplex of classical N--point probability distributions can be embedded inside a higher dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in N dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality.
If a large quantum computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a conventional computer? In this talk, I argue that a QC could solve some relevant physical "questions" more efficiently. First, I will focus on the quantum simulation of quantum systems satisfying different particle statistics (e.g., anyons), using a QC made of two-level physical systems or qubits.
Kolmogorov complexity is a measure of the information contained in a binary string. We investigate the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity.
Although entanglement constitutes one of the most remarkable differences between classical and quantum mechanics, and entanglement does have directly observable consequences, entanglement is not a regular observable like momentum or energy. It is rather a non-linear functional of a typically large set of such observables.
We explore the role of rotational symmetry of quantum key distribution
(QKD) protocols in their security. Specifically, in the first part of the
talk, we consider a generalized QKD protocol with discrete rotational
symmetry. Note that, before our work, each QKD protocol seems to have a
different security proof. Given that the techniques of those proofs are
similar, it will be interesting to have a unified proof for QKD protocols
with symmetry (e.g., the BB84 protocol and the SARG04 protocol). This is
Most modern discussions of Bell's theorem take microscopic causality (the arrow of time) for granted, and raise serious doubts concerning realism and/or relativity. Alternatively, one may allow a weak form of backwards-in-time causation, by considering "causes" to have not only "effects" at later times but also "influences" at earlier times. These "influences" generate the correlations of quantum entanglement, but do not enable information to be transmitted to the past. Can one realize this scenario in a mathematical model?