Experimental Test of Tracking the King Problem

In quantum theory, the retrodiction problem is not as clear as its classical counterpart because of the uncertainty principle of quantum mechanics. In classical physics, the measurement outcomes of the present state can be used directly for predicting the future events and inferring the past events which is known as retrodiction. However, as a probabilistic theory, quantum-mechanical retrodiction is a nontrivial problem that has been investigated for a long time, of which the Mean King Problem is one of the most extensively studied issues. Here, we present the first experimental test of a variant of the Mean King Problem, which has a more stringent regulation and is termed "Tracking the King". We demonstrate that Alice, by harnessing the shared entanglement and controlled-not gate, can successfully retrodict the choice of King's measurement without knowing any measurement outcome. Our results also provide a counterintuitive quantum communication to deliver information hidden in the choice of measurement.Comment: 16 pages, 5 figures, 2 table

Remarks on Hawking radiation as tunneling from the BTZ black holes

Hawking radiation viewed as a semiclassical tunneling process from the event horizon of the (2 + 1)-dimensional rotating BTZ black hole is carefully reexamined by taking into account not only the energy conservation but also the conservation of angular momentum when the effect of the emitted particle's self-gravitation is incorporated. In contrast to previous analysis of this issue in the literature, our result obtained here fits well to the Kraus-Parikh-Wilczek's universal conclusion without any modification to the Bekenstein-Hawking area-entropy formulae of the BTZ black hole.Comment: 12pages, no figure, use JHEP3.cls. Version better than published one in JHE

Entanglement Creation and Storage in Two Qubits Coupling to an Anisotropic Heisenberg Spin Chain

The time evolution of the entanglement of a pair of two spin qubits is investigated when the two qubits simultaneously couple to an environment of an anisotropic Heisenberg XXZ spin chain. The entanglement of the two spin qubits can be created and is a periodic function of the time if the magnetic field is greater than a critical value. If the two spin qubits are in the Bell state, the entanglement can be stored with relatively large value even when the magnetic field is large.Comment: 4figures

State-Compensation-Linearization-Based Stability Margin Analysis for a Class of Nonlinear Systems: A Data-Driven Method

The classical stability margin analysis based on the linearized model is widely used in practice even in nonlinear systems. Although linear analysis techniques are relatively standard and have simple implementation structures, they are prone to misbehavior and failure when the system is performing an off-nominal operation. To avoid the drawbacks and exploit the advantages of linear analysis methods and frequency-domain stability margin analysis while tackling system nonlinearity, a state-compensation-linearization-based stability margin analysis method is studied in the paper. Based on the state-compensation-linearization-based stabilizing control, the definition and measurement of the stability margin are given. The l2 gain margin and l2 time-delay margin for the closed-loop nonlinear system with state-compensation-linearization-based stabilizing control are defined and derived approximatively by the small-gain theorem in theory. The stability margin measurement can be carried out by the frequency-sweep method in practice. The proposed method is a data-driven method for obtaining the stability margin of nonlinear systems, which is practical and can be applied to practical systems directly. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method