Measurement and quantum indeterminateness

Albert and Loewer^[1] have recently clarified their earlier objection to the interactive interpretation presented in Healey^[2]. They now charge that this interpretation fails to solve a problem of which the measurement problem is but a special case. The general problem is to reconcile quantum mechanics with theprima facie determinateness of such dynamical properties as the positions of macroscopic objects. In response I defend both the preeminent significance of determinate measurement outcomes and the claim that the models of Healey^[3] go a long way toward securing their determinateness.1. They note ironically that the proponent of this interpretation must argue that since a natural measure of the set of states whose biorthonormal expansion has equal amplitudes is zero these states should be neglected. In fact these states werenot neglected in Healey^[2] (see pp. 98-100) where I argued that even though the resulting indeterminateness in any such states would be real, it would be rapidly removed by subsequent environmental interactions.     

On the physical impossibility of ideal quantum measurements

Albert and Loewer have argued in this journal [4] that modal interpretations of quantum mechanics are ruled out if the abstract structure of Hilbert space is taken realistically. Their argument contains a dubious inference from a measure-zero set of non-ideal interactions. I look at possible ways to make this inference valid and I conclude that the evidence against the modal interpretation cannot be found in the Hilbert space alone. Instead an analysis of specific cases is required.I want to thank the audience at the 1995 Florence IUHPS Conference, and Harvey Brown, Nancy Cartwright, Jim Cushing, Marco Del Seta, Arthur Fine, Margaret Morrison, Fred Müller and Pieter Vermaas for comments and suggestions.     

Protective measurement and quantum reality

It is shown that from the expectation values of obervables, which can be measured for a single system using protective measurements, the linear structure, inner product, and observables in the Hilbert space can be reconstructed. A universal method of measuring the wave function of a single particle using its gravitational field is given. Protective measurement is generalized to the measurement of a degenerate state and to many particle systems. The question of whether the wave function is real is examined, and an argument of Einstein in favor of the ensemble interpretation of quantum theory is refuted.     

Maximum confidence measurements via probabilistic quantum cloning

Probabilistic quantum cloning(PQC) cannot copy a set of linearly dependent quantum states.In this paper,we show that if incorrect copies are allowed to be produced,linearly dependent quantum states may also be cloned by the PQC.By exploiting this kind of PQC to clone a special set of three linearly dependent quantum states,we derive the upper bound of the maximum confidence measure of a set.An explicit transformation of the maximum confidence measure is presented.     

基于部分测量增强量子隐形传态过程的量子Fisher信息

量子Fisher信息(QFI)是量子度量学中的一个重要物理量,可给出预估参数精度的最优值.本文研究如何引入弱测量和测量反转操作,来提高有限温环境下以Greenberger-Horne-Zeilinger态作为量子通道的隐形传态过程中的QFI.依据隐形传态过程中量子比特的传输情形,考虑了三种不同方案相应的QFI.首先,通过构造每种量子隐形传态方案的量子线路图,分析了QFI与推广振幅衰减噪声参数的变化关系.随后对各种方案中的受噪声粒子施加弱测量和测量反转操作,并对相应的部分测量参数进行优化,着重探讨了施加最优部分测量操作后QFI的改进量.结果表明,经过优化后的部分测量操作能有效提高有限温环境下量子隐形传态过程输出态的QFI;而且量子系统所处的环境温度越低,QFI的提高效果可越显著.     

Non-ideal measurements

We have previously objected to modal interpretations of quantum theory by showing that these interpretations do not assign outcomes to non-ideal measurements. Bub and Healey replied (in this journal) by offering alternative accounts of non-ideal measurements. In this paper we argue, first, that our account of non-ideal measurements is correct and, second, even if it is not correct, it is overwhelmingly likely that interactions satisfying our characterization of non-ideal measurements actually occur and that such interactions possess outcomes. A successful defense of the modal interpretation must assign outcomes to these interactions or show that they do not have outcomes or show that in fact they never occur. Bub and Healey show none of this.1. Modal interpretations are those which assign values to observables even when the quantum state is not an eigenstate of the observable,and in accord with some rule which involves the quantum state or the Hamiltonian that governs the evolution of the state. Healey rejects the name modal interpretation for his account preferring interactive interpretation. In previous papers we cited a number of problems with modal interpretations including the difficulty of adding to them a dynamics for their hidden variables and their failure to assign outcomes to nonideal measurements. It is the latter objection which is at issue in these papers. This objection applies to Kochen's, Dieks', and Healey's interpretations, which all use the polar decomposition theorem to determine which observables possess values, and to Van Fraassen's interpretation, which characterizes the observables that possess values in terms of the Hamiltonian governing the interaction. It does not apply to Bub's interpretation, which doesn't rely on this theorem.2. The analysis is slightly more complicated for disturbing measurements. Healey seems to consider it a defect that in our original discussion we restricted our discussion to non-disturbing measurements, but he would surely admit that the added complication is irrelevant to the issues at hand.3. There are only two honest ways of responding to the measurement problem. One is to break the eigenstate-eigenvalue link. This is the approach taken by modal interpretations, hiddenvariable theories like Bohm's, and our many-minds interpretation. The other is to modify the laws of evolution of state. This is what is done by orthodox quantum theory, which exempts measurements from the linear laws of state evolution and, more plausibly, by recent collapse theories like GRW, which modify the laws of state evoultion so that macroscopic interactions result in states which are close to being eigenstates of familiar observables.4. When the amplitudes are exactly equal (as in the usual EPR state), there is not a unique bi-orthonormal form. An advocate of the modal interpretation must argue that, since the measure of the set of such states is 0, it is very unlikely that they are actually encountered.5. For any observableA*, there is an initial state that the Hamiltonian evolves into, a state in whichA* is well defined. We mentioned this in Albert and Loewer (1991) and owe the point to Yakir Aharonhov.6. In (1990) and (1991) we showed how the many-minds interpretation and CRW handle inaccurate measurements (viz. interactions that conform to (2)). The analysis of these interactions within Bohm's theory is straightforward.7. The irony here will not be lost on the reader who recalls, from Note 4, that Healey must argue that, since the measure of the set of states whose bi-orthonormal form has equal amplitudes is 0, one can neglect such states.8. The Copenhagen interpretation is sometimes so understood; see for example Van Fraassen's (1992) discussion.     

Direct measurement for general quantum states using parametric quantum circuits

In the field of quantum information,the acquisition of information for unknown quantum states is very important.When we only need to obtain specific elements of a state density matrix,the traditional quantum state tomography will become very complicated,because it requires a global quantum state reconstruction.Direct measurement of the quantum state allows us to obtain arbitrary specific matrix elements of the quantum state without state reconstruction,so direct measurement schemes have obtained...     

Number-resolved master equation approach to quantum measurement and quantum transport

In addition to the well-known Landauer–Büttiker scattering theory and the nonequilibrium Green’s function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number (n)-resolved master equation (n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.     

Improved quantum state transfer via quantum partially collapsing measurements

In this work, we present a general scheme to improve quantum state transfer (QST) by taking advantage of quantum partially collapsing measurements. The scheme consists of a weak measurement performed at the initial time on the qubit encoding the state of concern and a subsequent quantum reversal measurement at a desired time on the destined qubit. We determine the strength q_r$q_r$ of the post quantum reversal measurement as a function of the strength p$p$ of the prior weak measurement and the evolution time t$t$ so that near-perfect QST can be achieved by choosing p$p$ close enough to 1, with a finite success probability, regardless of the evolution time and the distance over which the QST takes place. The merit of our scheme is twofold: it not only improves QST, but also suppresses the energy dissipation, if any.     

Model apparatus for quantum measurements

We present a model system that behaves as a measurement apparatus for quantum systems should. The device is macroscopic, it interacts with the microscopic system to be measured, and the results of that interaction affect the macroscopic device in a macroscopic, irreversible way. Everything is treated quantum mechanically: the apparatus is defined in terms of its (many) coordinates, the Hamiltonian is given, and time evolution follows Schrödinger's equation. It is proposed that this model be itself used as a laboratory for testing ideas on the measurement process.     

Copenhagen quantum mechanics

In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists’ laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr’s quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.     

基于量子存储的长距离测量设备无关量子密钥分配研究

针对量子中继器短时间内难以应用于长距离量子密钥分配系统的问题, 提出了基于量子存储的长距离测量设备无关量子密钥分配协议, 分析了其密钥生成率与存储效率、信道传输效率和安全传输距离等参数间的关系, 研究了该协议中量子存储单元的退相干效应对最终密钥生成率的影响, 比较了经典测量设备无关量子密钥分配协议和基于量子存储的测量设备无关量子密钥分配协议的密钥生成率与安全传输距离的关系. 仿真结果表明, 添加量子存储单元后, 协议的安全传输距离由无量子存储的216 km增加至500 km, 且量子存储退相干效应带来的误码对最终的密钥生成率影响较小. 实验中可以采取调节信号光强度的方式提高测量设备无关量子密钥分配系统的密钥生成率, 为实用量子密钥分配实验提供了重要的理论参数.     

Amplifying and freezing of quantum coherence using weak measurement and quantum measurement reversal

We analyze universal conditions where the l_1 norm and relative entropy of coherence are amplified and frozen under identical bit-flip channels;that is,using pre-measurements(quantum weak measurements or quantum measurement reversals) on the systems before undergoing local bit-flip channels.With the option of quantum weak measurements or quantum measurement reversals,the measurement strength and the success probability are all determined by the initial state of the quantum system.     

Dynamics of quantum zeno and anti-zeno efects in an open system

We provide a general dynamical approach for the quantum Zeno and anti-Zeno efects in an open quantum system under repeated non-demolition measurements.In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation.Based on that model,we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements,and derive the measurement-modified decay rates of the excited state.In the cases with frequent ideal measurements at zero-temperature,we re-obtain the same decay rate as that from the wave function collapse postulation(Nature,2000,405:546).The correction to the ideal decay rate is also obtained under the non-ideal measurements.Especially,we find that the quantum Zeno and anti-Zeno efects are possibly enhanced by the non-ideal natures of measurements.For the open system under measurements with arbitrary period,we generally derive the rate equation for the long-time evolution for the cases with arbitrary temperature and noise spectrum,and show that in the long-time evolution the noise spectrum is efectively tuned by the repeated measurements.Our approach is also able to describe the quantum Zeno and anti-Zeno efects given by the phase modulation pulses,as well as the relevant quantum control schemes.     

Measurement-device-independent quantum dialogue

Recently, measurement-device-independent quantum secure direct communication schemes were proposed by Niu et al. [Sci. Bull. 63 1345(2018)] and Zhou et al. [Sci. China-Phys. Mech. Astron. 63 230362(2020)]. Inspired by their ideas,in this paper, a measurement-device-independent quantum dialogue protocol based on entanglement is designed and proven to be secure. The advantage of this scheme is that it can not only allow two communicators to transmit secret messages between each other, making the application scenarios more extensive, but can also eliminate all the security loopholes related to the measurement device and information leakage. In terms of experimental implementation, the scheme mainly involves the preparation of entangled states, the preparation of single photons, quantum storage, Bell measurement and other technologies, all of which are mature at present, therefore, the scheme is feasible by using current technologies.     

基于非对称量子通道受控QOT量子投票协议

提出一种量子投票协议, 协议基于非对称量子通道受控量子局域幺正操作隐形传输(quantum operation teleportation, QOT). 由公正机构CA提供的零知识证明的量子身份认证, 保证选民身份认证的匿名性. 计票机构Bob制造高维Greenberger-Horne-Zeilinger 纠缠态建立一个高维量子通信信道. 选民对低维的量子选票进行局域幺正操作的量子投票, 是通过非对称基的测量和监票机构Charlie的辅助测量隐形传输的. Bob在Charlie帮助下可以通过幺正操作结果得到投票结果. 与其他一般的QOT量子投票协议相比, 该协议利用量子信息与传输的量子信道不同维, 使单粒子信息不能被窃取、防止伪造.选举过程由于有Charlie的监督, 使得投票公正和不可抵赖.由于量子局域幺正操作隐形传输的成功概率是1, 使量子投票的可靠性得以保证. 关键词： 量子投票 高维GHZ纠缠态 非对称基测量 量子操作隐形传输     

Limiting distribution of periodic position measurements of a quantum harmonic oscillator

We consider a particle in harmonic oscillator potential, whose position is periodically measured with an instrument of finite precision. We show that the distribution of the measured positions tends to a limiting distribution when the number of measurements tends to infinity. We derive the expression for the limiting position distribution and validate it with numerical simulation.     

Controlled quantum state transfer via parity measurement

In this work, a scheme for controlled quantum state transfer is proposed using parity measurement in a cavity-waveguide system. As two special cases, two schemes of controlled quantum state transfer for one qubit and two qubits are investigated in detail. An important advantage is that controlled quantum state transfer can be completed by single-qubit rotations and the measurement of parity. Therefore, the present scheme might be realized in the scope of current experimental technology.