Notes on Joint Measurability of Quantum Observables

For sharp quantum observables the following facts hold: (i) if we have a collection of sharp observables and each pair of them is jointly measurable, then they are jointly measurable all together; (ii) if two sharp observables are jointly measurable, then their joint observable is unique and it gives the greatest lower bound for the effects corresponding to the observables; (iii) if we have two sharp observables and their every possible two outcome partitionings are jointly measurable, then the observables themselves are jointly measurable. We show that, in general, these properties do not hold. Also some possible candidates which would accompany joint measurability and generalize these apparently useful properties are discussed.     

Commutative POVMs and Fuzzy Observables

In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements. This article is dedicated to Pekka Lahti on the occasion of his 60th birthday.     

Retrocausality and Quantum Measurement

A retrocausal interpretation of quantum mechanics is examined and is applied to the problem of measuring an optical qubit before the qubit is actually created. Although the predictions of the retrocausal interpretation are the same as for the conventional causal picture, it provides a new perspective which should give a useful way of understanding some quantum mechanical processes.     

单质碘对水溶性CdTe量子点的荧光猝灭研究

合成了不同尺寸的、巯基丙酸和半胱氨酸修饰的水溶性CdTe量子点,并研究了I2与CdTe量子点的相互作用,实验发现I2能够明显猝灭CdTe量子点的荧光,且猝灭程度与量子点的修饰剂有关,没有表现出明显的尺寸依赖效应。     

On Quantum Spacetime and the horizon problem

In the special case of a spherically symmetric solution of Einstein equations coupled to a scalar massless field, we examine the consequences on the exact solution imposed by a semiclassical treatment of gravitational interaction when the scalar field is quantized. In agreement with Doplicher et al. (1995)  [2], imposing the principle of gravitational stability against localization of events, we find that the region where an event is localized, or where initial conditions can be assigned, has a minimal extension, of the order of the Planck length. This conclusion, though limited to the case of spherical symmetry, is more general than that of  [2] since it does not require the use of the notion of energy through the Heisenberg Principle, nor of any approximation as the linearized Einstein equations.We shall then describe the influence of this minimal length scale in a cosmological model, namely a simple universe filled with radiation, which is effectively described by a conformally coupled scalar field in a conformal KMS state. Solving the backreaction, a power law inflation scenario appears close to the initial singularity. Furthermore, the initial singularity becomes light like and thus the standard horizon problem is avoided in this simple model. This indication goes in the same direction as those drawn at a heuristic level from a full use of the principle of gravitational stability against localization of events, which point to a background dependence of the effective Planck length, through which a-causal effects may be transmitted.     

Stark效应对量子纠缠信息交换传递的影响

用多个“二能级原子与单模光场”组成的联合物理模型,考虑Stark效应后,推导了该系统的态矢演化式,得到光场纠缠度的数值计算结果.讨论了Stark效应和初始场强对量子纠缠信息交换传递的影响.结果发现,在一定条件下,原子纠缠态与光场纠缠态之间可以转化,实现了量子纠缠信息的交换传递,且Stark效应和初始场强对此过程有着显著的影响:光场的纠缠程度随着初始场强的增强而增大;在强场条件下,光场纠缠度出现崩塌-回复现象.Stark移位参量越大,光场纠缠度振荡越剧烈,说明Stark效应破坏了光场纠缠程度的稳定性.     

Quantum Cheshire cats and their elements of reality

Quantum Cheshire cats represent the violation of the product rule in terms of weak values being either 0 or 1. We explore the generalized fatter quantum Cheshire cats living in the larger Hilbert spaces. Specifically, two even-dimensional quantum systems are exploited. As for the physical implications, given that no disturbance is made in the weak measurements, quantum Cheshire cats reveal an alternative way of defying EPR elements of reality. In addition, we discuss the inconsistency between the Wigner's friend problem and quantum Cheshire cats.     

Quantum interference of charged identical particles

We present the results of a computer simulation study of charged-particle interferometry, combining features of both the Aharonov-Bohm and Hanbury Brown-Twiss experiment. In contrast to a previous theoretical analysis of this experiment, we find that the Aharonov-Bohm effect is also present in the cross-correlated two-particle intensity. A simple, time-independent scattering theory that leads to conclusions that are in concert with the simulation data is given.     

Tunneling in polymer quantization and the Quantum Zeno Effect

As an application of the polymer quantization scheme, in this work we investigate the one-dimensional quantum mechanical tunneling phenomenon from the perspective of polymer representation of a non-relativistic point particle and derive the transmission and reflection coefficients. Since any tunneling phenomenon inevitably evokes a tunneling time, we attempt an analytical calculation of tunneling times by defining an operator well suited in discrete spatial geometry. The results that we come up with hint at appearance of the Quantum Zeno Effect in polymer framework.     

On Classical and Quantum Objectivity

We propose a conceptual framework for understanding the relationship between observables and operators in mechanics. To do so, we introduce a postulate that establishes a correspondence between the objective properties permitting to identify physical states and the symmetry transformations that modify their gauge dependant properties. We show that the uncertainty principle results from a faithful—or equivariant—realization of this correspondence. It is a consequence of the proposed postulate that the quantum notion of objective physical states is not incomplete, but rather that the classical notion is overdetermined.     

Quantum correlation cost of the weak measurement

Quantum correlation cost (QCC) characterizing how much quantum correlation is used in a weak-measurement process is presented based on the trace norm. It is shown that the QCC is related to the trace-norm-based quantum discord (TQD) by only a factor that is determined by the strength of the weak measurement, so it only catches partial quantumness of a quantum system compared with the TQD. We also find that the residual quantumness can be ‘extracted’ not only by the further von Neumann measurement, but also by a sequence of infinitesimal weak measurements. As an example, we demonstrate our outcomes by the Bell-diagonal state.     

Quantum Information and Entropy

Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In view of this, we propose a new measure for the informational entropy of a quantum state that includes information in the pure states and the thermodynamic entropy. The origin of information is explained in terms of an interplay between unitary and non-unitary evolution. Such complementarity is also at the basis of the so-called interaction-free measurement.     

Phase transitions and relaxation characteristics of Quantum Magnets and Quantum Glasses

An overview is presented of the phase changes as well as certain relaxation characteristics of model quantum magnets, magnetic glasses and proton glasses. Although the systems considered are quite varied, they are connected by the common themes of tunneling, transverse Ising model, long-ranged interactions and above all, the occurrence of quantum phase transitions. Because the interactions are long-ranged, mean-field theory is eminently suitable for analyzing both the equilibrium and nonequilibrium properties. Wherever pertinent, detailed comparisons with experimental data have been presented.     

On the measurability of quantum correlation functions

The concept of correlation function is widely used in classical statistical mechanics to characterize how two or more variables depend on each other. In quantum mechanics, on the other hand, there are observables that cannot be measured at the same time; the so-called incompatible observables. This prospect imposes a limitation on the definition of a quantum analog for the correlation function in terms of a sequence of measurements. Here, based on the notion of sequential weak measurements, we circumvent this limitation by introducing a framework to measure general quantum correlation functions, in principle, independently of the state of the system and the operators involved. To illustrate, we propose an experimental configuration to obtain explicitly the quantum correlation function between two Pauli operators, in which the input state is an arbitrary mixed qubit state encoded on the polarization of photons.     

双原子Jaynes-Cummings模型下的量子失协和超量子失协

在量子信息的研究中,量子关联起着至关重要的作用,而弱测量对揭示量子关联有重要作用.在双原子Jaynes-Cummings(JC)模型下,分析了量子失协和超量子失协两种量子关联随时间演化过程中的差异性,以及测量强度参数、平均光子数在决定量子关联和影响其动态演化的一般作用.结果表明,弱测量可以更好地揭示量子关联,不仅可以更好地揭示量子关联的复活,还可以获得更大的关联最大值;平均光子数会有效影响两种关联的消失与复活,平均光子数越大,量子关联的消失与复活越快;平均光子数较大时,使用旋波近似得到的弱测量下的超量子失协比强测量下的量子失协与实际误差更小.     

基于相关光子的单光子探测器量子效率测量系统

为准确测量近红外波段单光子探测器量子效率,搭建了基于自发参量下转换效应的测量系统.系统利用中心波长为518nm的脉冲激光泵浦周期极化磷酸氧钛钾晶体,通过自发参量下转换过程产生相关光子对,分别测量了Si和InGaAs雪崩光电二极管单光子探测器在778nm和1 550nm波长点的量子效率,并对测量不确定度进行了分析.实验表明,该装置可以测量近红外单光子探测器量子效率参量,测量不确定度均优于1%.     

经典守恒定律的量子力学推导

从量子力学出发,推出了经典动量守恒定律和能量守恒定律,并讨论了在微观领域经典守恒定律适用的条件.     

基于cluster态任意单粒子态可控量子信息共享

基于cluster态具有较强的纠缠顽固性,提出两个利用四粒子cluster态传送任意单粒子态的量子信息共享方案.第一个方案中发送者Alice、控制者Charlie和接收者Bob共享一个四粒子纠缠态,首先Alice对自己拥有的粒子执行一个三粒子Von-Neumann联合测量,然后Charlie对其拥有粒子执行Z基测量,最后Bob根据发送者和控制者的测量结果,对所拥有的粒子做适当的幺正变换,就能重建共享的单粒子任意态.第二个方案利用一个辅助粒子,发送者Alice、控制者Charlie只需做Bell基测量,Bob通过比特位翻转和幺正变换即可得到Alice传送的量子态.与已有方案相比,两方案信息共享的成功概率为100%,且只需四粒子cluster态为载体,可在目前实验室技术条件下实现.     

单光子纠缠态的纠缠转移和量子隐形传态

使用光学分束器和单光子源,利用单光子态和真空态制备出了纠缠单光子态.利用光学分束器作用和单光子探测,实现了三个通讯伙伴之间的纠缠转移.提出了一个关于纠缠单光子态的量子隐形传态方案.在这个方案中,被传送的是一个未知的单光子纠缠态.通讯双方使用的量子信道是两个单光子纠缠态.通过使用分束器作用和对输出态进行光子测量以及在经典信息的帮助下,纠缠转移和量子隐形传态的过程被完成.