This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
A single classical system is characterized by its manifold of states; and to combine several systems, we take the product of manifolds. A single quantum system is characterized by its Hilbert space of states; and to combine several systems, we take the tensor product of Hilbert spaces. But what if we choose to combine an infinite number of systems? A naive attempt to describe such combinations fails, for there is apparently no natural notion of an infinite product of manifolds; nor of an infinite tensor product of Hilbert spaces.
We prove that all non-conspiratorial/retro-causal hidden variable theories has to be measurement ordering contextual, i.e. there exists
*commuting* operator pair (A,B) and a hidden state \\\\lambda such that the outcome of A depends on whether we measure B before or after.
Interestingly this rules out a recent proposal for a psi-epistemic due to Barrett, Hardy, and Spekkens. We also show that the model was in fact partly discovered already by vanFraassen 1973; the only thing missing was giving a probability distribution on the space of ontic states (the hidden variables).
The purpose of this talk is to describe bosonic fields and their Lagrangians in the causal set context. Spin-0 fields are defined to be real-valued functions on a causal set. Gauge fields are viewed as SU(n)-valued functions on the set of pairs of elements of a causal set, and gravity is viewed as the causal relation itself.
Mutually unbiased bases (MUBs) have attracted a lot of attention the last years. These bases are interesting for their potential use within quantum information processing and when trying to understand quantum state space. A central question is if there exists complete sets of N+1 MUBs in N-dimensional Hilbert space, as these are desired for quantum state tomography. Despite a lot of effort they are only known in prime power dimensions.
Bell\\\'s theorem is commonly understood to show that EPR correlations are not explainable via a local hidden variable theory.
In any attempt to construct a Quantum Theory of Gravity, one has to deal with the fact that Time in Quantum Mechanics appears to be very different from Time in General Relativity. This is the famous (or actually
We derive a set of Bell inequalities using correlated random variables. Our inequalities are necessary conditions for the existence of a local realistic description of projective measurements on qubits. We analyze our inequalities for the case of two qubits and find that they are equivalent to the well known CHSH inequalities. We also discuss the sufficiency of our inequalities as well as their applicability to more than two qubits.
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation.
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The distinguishing feature of the proposed equilibrium state is that the corresponding density of states is a continuous function of the energy, and hence thermodynamic functions are well defined for finite quantum systems. The density of states, however, is not in general an analytic function.
What if the second law of thermodynamics, in the hierarchy of physical laws, were at the same level as the fundamental laws of mechanics, such as the great conservation principles? What if entropy were an intrinsic property of matter at the same level as energy is universally understood to be? What if irreversibility were an intrinsic feature of the microscopic dynamical law of all physical objects, including an individual qubit or qudit?