Quantum Foundations

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. Notably, in superconducting circuit QED implementations, the choice between which type of stochastic rotation occurs may be made long after the qubit and measurement field interact.

The Aharonov-Casher Effect, interactions between charges and fluxes; Dynamical nonlocal exchange of modular momentum.

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. We also obtain an entanglement classification of four qubits, where we find 27 fundamental sets of classes.

 

Nonrelativistic quantum mechanics in absolute time, the Heisenberg representation on a lattice with nonlocal jumps (teleportation), discretizing the position in order to obtain simple Heisenberg equations of motion; Intuition from this strictly nonrelativistic picture will still be useful in the general case; The importance of the right story and intuition, arguments against Many-Worlds;  More on the paradox of a superposed flux shielded by a superconductor.

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. We derive the systematic error of maximum likelihood estimation in general to the first order approximation of a small deviation in the probability distribution, and compare the systematic error of standard weak measurement and postselected weak measurements, which shows that the systematic error of a postselected weak measurement with a large weak value can be significantly lower than that of a standard weak measurement when the probe undergoes decoherence.

Commutations Relations for Modular Variables, Connection to Action-Angle Variables; Periodic Potentials with the Aharonov-Bohm Effect; Paradox of a superposed flux shielded by a superconductor.

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. This work is collaborated with Hirokazu Kobayashi (Kochi University of Technology).

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.  In this case established scaling bounds on the quantum Fisher information can be broken, and the quantum control is needed to do it.  A simple spin example will be given to illustrate the general results.

The Aharonov-Bohm Effect with an infinite grating with solenoids between each slit, Modular Momentum; Nonlocal exchange of Modular Momentum and Modular Energy; Scattering with both local and nonlocal interactions.