This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
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.
Throughout the development of quantum mechanics, the striking refusal of nature to obey classical reasoning and intuition has driven both curiosity and confusion. From the apparent inescapably probabilistic nature of the theory, to more subtle issues such as entanglement, nonlocality, and contextuality, it has always been the `nonclassical’ features that present the most interesting puzzle. More recently, it has become apparent that these features are also the primary resource for quantum information processing.
We investigate the quantum trajectories of jointly monitored transmon qubits, tracking measurement-induced entanglement creation as a continuous process. The quantum trajectories naturally split into low and high entanglement classes corresponding to partial parity collapse. We theoretically calculate the distribution of concurrence at any given time and show good agreement with the constructed histogram of measured concurrence trajectories. The distribution exhibits a sharp cut-off in the high concurrence limit, defining a maximal concurrence boundary.
In the device-independent paradigm, the labeling of parties/inputs/outputs has no physical meaning and thus the behavior of the system should be studied up to symmetry. We conduct the first formal study of relabelings appearing in Bell scenarios. The talk includes a review of previous works, a definition of Bell relabeling groups illustrated by examples, and applications, including the classification of Bell inequalities, the generalization of binary correlators to d outcomes and the computation of exact bounds using the NPA hierarchy.