This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction.
Most physicists take it for granted that the experimental violation of Bell's inequality provides evidence that it is not possible to completely describe the state of a physical system in terms of purely local information when this system is entangled with some other system. We disagree. Provided we redefine appropriately what is the information-theoretic state of a quantum system, it becomes possible to recover the whole from the description of its parts.
For a spin 1/2 (a qubit), Hamiltonian evolution is equivalent to an elliptic rotation of the (Bloch) spin vector in 3D space. In contrast, measurement alters the state norm, so may not be described as such a rotation. Nevertheless, extending the 3D spin vector to a 4D "spacetime" representation allows weak measurements to be interpreted as hyperbolic (boost) rotations. The combined Hamiltonian and measurement dynamics in continuous weak measurement trajectories are then equivalent to (stochastic) Lorentz transformations.
Considering a conformally coupled massless scalar field with arbitrary sign of kinetic energy and show that the conformal fluctuations in flatspace will increase without bounds if the mass of the scalar field is greater than a critical value.
We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the invariants and sets of equivalent classes of entangled states. The new method works for an arbitrary finite number of finite-dimensional state subspaces. As an application of the method, we considered a large selection of cases of three subspaces of various dimensions.
Among QM's (in)famous oddities, perhaps the most intriguing is the capability of an event that did not occur, only could have, to exert a causal effect. How can a non-event leave a trace as concrete as a detector's click? I discuss this question and a novel insight into it offered by Cohen and Elitzur's "Quantum Oblivion" (20014).
Decoherence in quantum metrology may deviate the estimate of a parameter from the real value of the parameter. In this talk, we show how to suppress the systematic error of weak-measurement-based quantum metrology under decoherence.
When we estimate a quantum state, we normally use the quantum state tomography. However, this needs the post-information processing. Here, we propose a new idea on visualizing technique of the quantum state. Under the specific configuration, in which the optical vortex beam is used, we experimentally demonstrate the visualization of the specific two-dimensional quantum state; the polarized state of light by the weak measurement initiated by Yakir Aharonov and his colleagues. The entangled state can be also visualized via the concurrence as the extension of this idea.
I will give an overview of two ways to estimate parameters with a quantum system when the dynamics is nontrivial. In the first case, the parameter is changing in an irregular way, and we use consider the use of continuous measurement to track it in time. Tracking speed is of the essence for feedback purposes, and I will present our new and improved way to speed up the estimation algorithm. In the second case, I will consider the use of Hamiltonian control to estimate a fixed parameter, but of a time-dependent Hamiltonian.