基于两步测量方法及其最少观测次数的任意量子纯态估计

量子状态层析所需要的完备观测次数d~2(d=2~n)随着状态的量子位数n的增加呈指数增长,这使得对高维量子态的层析变得十分困难.本文提出一种基于两步测量的量子态估计方法,可以对任意量子纯态的估计提供最少的观测次数.本文证明:当选择泡利观测算符,采用本文所提出的量子态估计方法对d=2n维希尔伯特空间中的任意n量子位纯态进行重构时,如果为本征态,那么所需最少观测次数memin仅为memin=n;对于包含l(2 6 l 6 d)个非零本征值的叠加态,重构所需最少观测次数msmin满足msmin=d+2l..3,此数目远小于压缩传感理论给出的量子态重构所需测量配置数目O(rd log d),以及目前已发表论文给出的纯态唯一确定所需最少观测次数4d..5.同时给出最少观测次数对应的最优观测算符集的构建方案,并通过仿真实验对本文所提出的量子态估计方法进行验证,实验中重构保真度均达到97%以上.     

Generalized teleportation by quantum walks

We develop a generalized teleportation scheme based on quantum walks with two coins. For an unknown qubit state, we use two-step quantum walks on the line and quantum walks on the cycle with four vertices for teleportation. For any d-dimensional states, quantum walks on complete graphs and quantum walks on d-regular graphs can be used for implementing teleportation. Compared with existing d-dimensional states teleportation, prior entangled state is not required and the necessary maximal entanglement resource is generated by the first step of quantum walk. Moreover, two projective measurements with d elements are needed by quantum walks on the complete graph, rather than one joint measurement with \(d^2\) basis states. Quantum walks have many applications in quantum computation and quantum simulations. This is the first scheme of realizing communicating protocol with quantum walks, thus opening wider applications.     

On Ideal Measurements and Their Corresponding Instruments on von Neumann Algebras

We study some features of quantum measurement in the framework of the theory of instruments — a mathematical model for measurement theory. This investigation is carried in an algebraic formalism in which the observables are represented by elements of a von Neumann algebra and the states are linear normal positive functionals on this algebra. We give a characterization of ideal instruments and study their connections with weakly and strongly repeatable instruments under the assumption that the associated observables are projection-valued measures. We also show that the observables of ideal weakly repeatable instruments must be projection-valued measures.     

Biology and the measurement problem

Present-day molecular biology, despite its name, is almost entirely committed to a macroscopic, classical picture of the organism; one in which quantum aspects play no role, except as a source of noise. Particularly is this true when dealing with informational aspects; especially "genetic information". The pervading metaphor here is an identification of "genetic information" with DNA sequence, and thence with program or software. We take a quite different view herein. If we presume, to the contrary, that microphysical processes play a role in primary genetic processes, then the "information" they can convey consists of observables evaluated on states. It is then natural to analogize a complex, consisting of (observed system + observer) with the biological partition between genome (observed system) and phenotype (observer). Such a picture immediately raises the deep issues surrounding "the measurement problem" in quantum mechanics. In our brief consideration of such matters, we suggest that standard quantum mechanics is too narrow to deal with the biological pictures, because it is inexorably tied to quantifications of classical, conservative systems; there is no such for an organism. Rather, we are led to consider subsystems we call "sites", for which there is in principle no Hamiltonian. We then query the extent to which such "genetic information" is already subsumed in traditional observables a physicist would measure in vitro in a laboratory. We suggest there is no reason to believe that "genetic information", manifested in bioactivities, is reducible to these. Finally, we contrast this view of "genetic information" with more traditional ideas of program and computability. We argue that computability (algorithms) are entirely classical concepts, in a physical sense, and quite inadequate for a biology (or even a physics) in which quantum measurement processes are important.     

A cloned qutrit and its utility in information processing tasks

We analyze the efficacy of an output as a resource from a universal quantum cloning machine in information processing tasks such as teleportation and dense coding. For this, we have considered the $3 \otimes 3$ dimensional systems. The output states are found to be NPT states for a certain range of machine parameters. Using the output state as an entangled resource, we also study the optimal fidelities of teleportation and capacities of dense coding protocols with respect to the machine parameters and make some interesting observations. Our work is motivated from the fact that the cloning output can be used as a resource in quantum information processing and adds a valuable dimension to the applications of cloning machines.     

Quantum Set Theory Extending the Standard Probabilistic Interpretation of Quantum Theory

The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of equality between two arbitrary observables, since the Born formula gives the probability distribution only for a commuting family of observables. In this paper, quantum set theory developed by Takeuti and the present author is used to systematically extend the standard probabilistic interpretation of quantum theory to define the probability of equality between two arbitrary observables in an arbitrary state. We apply this new interpretation to quantum measurement theory, and establish a logical basis for the difference between simultaneous measurability and simultaneous determinateness.     

Localization of two-particle quantum walk on glued-tree and its application in generating Bell states

Studies on two-particle quantum walks show that the spatial interaction between walkers will dynamically generate complex entanglement. However, those entanglement states are usually on a large state space and their evolutions are complex. It makes the entanglement states generated by quantum walk difficult to be applied directly in many applications of quantum information, such as quantum teleportation and quantum cryptography. In this paper, we firstly analyse a localization phenomena of two-particle quantum walk and then introduce how to use it to generate a Bell state. We will show that one special superposition component of the walkers’ state is localized on the root vertex if a certain interaction exists between walkers. This localization is interesting because it is contrary to our knowledge that quantum walk spreads faster than its classical counterpart. More interestingly, the localized component is a Bell state in the coin space of two walkers. By this method, we can obtain a Bell state easily from the quantum walk with spatial interaction by a local measurement, which is required in many applications. Through simulations, we verify that this method is able to generate the Bell state \(\frac{1}{\sqrt{2}}(|A \rangle _1|A\rangle _2 \pm |B\rangle _1|B\rangle _2)\) in the coin space of two walkers with fidelity greater than \(99.99999\,\%\) in theory, and we have at least a \(50\,\%\) probability to obtain the expected Bell state after a proper local measurement.     

Controlling quantum memory-assisted entropic uncertainty in non-Markovian environments

Quantum memory-assisted entropic uncertainty relation (QMA EUR) addresses that the lower bound of Maassen and Uffink’s entropic uncertainty relation (without quantum memory) can be broken. In this paper, we investigated the dynamical features of QMA EUR in the Markovian and non-Markovian dissipative environments. It is found that dynamical process of QMA EUR is oscillation in non-Markovian environment, and the strong interaction is favorable for suppressing the amount of entropic uncertainty. Furthermore, we presented two schemes by means of prior weak measurement and posterior weak measurement reversal to control the amount of entropic uncertainty of Pauli observables in dissipative environments. The numerical results show that the prior weak measurement can effectively reduce the wave peak values of the QMA-EUA dynamic process in non-Markovian environment for long periods of time, but it is ineffectual on the wave minima of dynamic process. However, the posterior weak measurement reversal has an opposite effects on the dynamic process. Moreover, the success probability entirely depends on the quantum measurement strength. We hope that our proposal could be verified experimentally and might possibly have future applications in quantum information processing.     

Quantum probabilistically cloning and computation

In this article we make a review on the usefulness of probabilistically cloning and present examples of quantum computation tasks for which quantum cloning offers an advantage which cannot be matched by any approach that does not resort to it. In these quantum computations, one needs to distribute quantum information contained in states about which we have some partial information. To perform quantum computations, one uses state-dependent probabilistic quantum cloning procedure to distribute quantum information in the middle of a quantum computation. And we discuss the achievable efficiencies and the efficient quantum logic network for probabilistic cloning the quantum states used in implementing quantum computation tasks for which cloning provides enhancement in performance.     

Continuous-variable quantum network coding for coherent states

As far as the spectral characteristic of quantum information is concerned, the existing quantum network coding schemes can be looked on as the discrete-variable quantum network coding schemes. Considering the practical advantage of continuous variables, in this paper, we explore two feasible continuous-variable quantum network coding (CVQNC) schemes. Basic operations and CVQNC schemes are both provided. The first scheme is based on Gaussian cloning and ADD/SUB operators and can transmit two coherent states across with a fidelity of 1/2, while the second scheme utilizes continuous-variable quantum teleportation and can transmit two coherent states perfectly. By encoding classical information on quantum states, quantum network coding schemes can be utilized to transmit classical information. Scheme analysis shows that compared with the discrete-variable paradigms, the proposed CVQNC schemes provide better network throughput from the viewpoint of classical information transmission. By modulating the amplitude and phase quadratures of coherent states with classical characters, the first scheme and the second scheme can transmit \(4{\log _2}N\) and \(2{\log _2}N\) bits of information by a single network use, respectively.     

Wigner–Yanase skew information and entanglement generation in quantum measurement

The first step of quantum measurement procedure is known as premeasurement, during which correlation is established between the system and the measurement apparatus. Such correlation may be classical or nonclassical in nature. One compelling nonclassical correlation is entanglement, a useful resource for various quantum information theoretic protocols. Quantifying the amount of entanglement, generated during quantum measurement, therefore, seeks importance from practical ground, and this is the central issue of the present paper. Interestingly, for a two-level quantum system, we obtain that the amount of entanglement, measured in term of negativity, generated in premeasurement process can be quantified by two factors: skew information, which quantifies the uncertainty in the measurement of an observable not commuting with some conserved quantity of the system, and mixedness parameter of the system’s initial state.     

Cyclic joint remote state preparation in noisy environment

We propose a scheme of cyclic joint remote state preparation for three sides, which takes advantage of three GHZ states to compose product state as quantum channel. Suppose there are six legitimate participants, says Alice, Bob, Charlie, David, Emma and Fred in the scheme. It can be shown that Alice and David can remotely prepare a single-qubit state on Bob’s side; meanwhile, Bob and Emma can remotely prepare a desired quantum state on Charlie’s side, and Charlie and Fred can also remotely prepare a single-qubit state on Alice’s side at the same time. Further, it can be achieved in the opposite direction of the cycle by changing the quantum channel. Based on it, we generalize this protocol to \(N (N\ge 3)\) sides utilizing three multi-qubit GHZ-type states as quantum channel. Therefore, the scheme can achieve cyclic joint remote state preparation, which remotely prepares N states in quantum network with N-party, simultaneously. In addition, we consider that the effect of amplitude-damping noise of the initial states is prepared in four different laboratory. Clearly, we use fidelity to describe how much information has been lost in the cyclic process. Our investigation about the effect of noise shows that the preparing of the initial state in different laboratories will affect the loss of information.     

Probing entropic uncertainty relations under a two-atom system coupled with structured bosonic reservoirs

The uncertainty principle imposes constraints on an observer’s ability to make precision measurements for two incompatible observables; thus, uncertainty relations play a key role in quantum precision measurement in the field of quantum information science. Here, our aim is to examine non-Markovian effects on quantum-memory-assisted entropic uncertainty relations in a system consisting of two atoms coupled with structured bosonic reservoirs. Explicitly, we explore the dynamics of the uncertainty relations via entropic measures in non-Markovian regimes when two atomic qubits independently interact with their own infinite degree-of-freedom bosonic reservoir. We show that measurement uncertainty vibrates with periodically increasing amplitude with growing non-Markovianity of the observed system and ultimately saturates toward a fixed value at a long time limit. It is worth noting that there are several appealing conclusions raised by us: First, the uncertainty’s lower bound does not entirely depend on the quantum correlations within the two-qubit system, being affected by an interplay between the quantum discord and the minimal von Neumann conditional entropy \(\mathcal{S}_\mathrm{ce}\). Second, the dynamic characteristic of the measurement uncertainty is considerably distinctive with regard to Markovian and non-Markovian regimes, respectively. Third, the measurement uncertainty is closely correlated with the Bell non-locality \({\mathcal{B}}\). Moreover, we claim that the entropic uncertainty relation could be a promising tool with which to probe entanglement in current architecture.     

Controlled quantum secure direct communication by entanglement distillation or generalized measurement

We propose two controlled quantum secure communication schemes by entanglement distillation or generalized measurement. The sender Alice, the receiver Bob and the controllers David and Cliff take part in the whole schemes. The supervisors David and Cliff can control the information transmitted from Alice to Bob by adjusting the local measurement angles \(\theta _4\) and \(\theta _3\). Bob can verify his secret information by classical one-way function after communication. The average amount of information is analyzed and compared for these two methods by MATLAB. The generalized measurement is a better scheme. Our schemes are secure against some well-known attacks because classical encryption and decoy states are used to ensure the security of the classical channel and the quantum channel.     

Quantum Subspace Measurements

Fundamental studies of quantum measurements and their capacity to acquire information are typically based on scenarios in which the full Hilbert space of the measured quantum system is open to measurement interactions. In this work, we consider a class of incomplete quantum measurements – quantum subspace measurements (QSM’s) – for which all measurement interactions are restricted to an arbitrary but specified subspace of the measured system Hilbert space. We define QSM’s formally through a condition on the measurement Hamiltonian, obtain forms for the post-measurement states and positive operators (POVM elements) associated with QSM’s acting in a specified subspace, and upper bound the accessible information for such measurements. Characteristic features of QSM’s are identified and discussed.     

Beyond complete positivity

We provide a general and consistent formulation for linear subsystem quantum dynamical maps, developed from a minimal set of postulates, primary among which is a relaxation of the usual, restrictive assumption of uncorrelated initial system-bath states. We describe the space of possibilities admitted by this formulation, namely that, far from being limited to only completely positive (CP) maps, essentially any \({\mathbb {C}}\)-linear, Hermiticity-preserving, trace-preserving map can arise as a legitimate subsystem dynamical map from a joint unitary evolution of a system coupled to a bath. The price paid for this added generality is a trade-off between the set of admissible initial states and the allowed set of joint system-bath unitary evolutions. As an application, we present a simple example of a non-CP map constructed as a subsystem dynamical map that violates some fundamental inequalities in quantum information theory, such as the quantum data processing inequality.     

基于团簇态的量子秘密共享方案

提出了一个基于团簇态的量子秘密共享方案,发送者通过Pauli操作将经典秘密信息编码在团簇态上进行分发,接收者通过联合测量实现秘密共享。协议插入EPR对作为诱骗态以防止窃听,通过安全性分析证明本协议是安全的,可以抵抗截获-测量、截获-重发和纠缠-测量攻击。此外,协议传输一个四粒子团簇态可以共享四个经典比特信息,量子比特效率达到100%。     

Performance of quantum cloning and deleting machines over coherence

Coherence, being at the heart of interference phenomena, is found to be an useful resource in quantum information theory. Here we want to understand quantum coherence under the combination of two fundamentally dual processes, viz., cloning and deleting. We found the role of quantum cloning and deletion machines with the consumption and generation of quantum coherence. We establish cloning as a cohering process and deletion as a decohering process. Fidelity of the process will be shown to have connection with coherence generation and consumption of the processes.     

Exploring the joint measurability using an information-theoretic approach

We explore the legal purity parameters for the joint measurements. Instead of direct unsharpening the measurements, we perform the quantum cloning before the sharp measurements. The necessary fuzziness in the unsharp measurements is equivalently introduced in the imperfect cloning process. Based on the information causality and the consequent noisy nonlocal computation, one can derive the information-theoretic quadratic inequalities that must be satisfied by any physical theory. On the other hand, to guarantee the classicality, the linear Bell-type inequalities deduced by these quadratic ones must be obeyed. As for the joint measurability, the purity parameters must be chosen to obey both types of inequalities. Finally, the quadratic inequalities for purity parameters in the joint measurability region are derived.