基于量子相干性的四体贝尔不等式构建

贝尔不等式在定域性和实在性的双重假设下,对于被分隔的粒子同时被测量时其结果的可能关联程度建立了一个严格的限制,违反贝尔不等式确保量子态存在纠缠.本文利用量子相干性的l1和相对熵测度构建了四体量子贝尔不等式,发现一般实系数Greenberger-Horne-Zeilinger纯态和簇纯态总是违反四体相对熵相干性测度贝尔不等式,因此违反四体相对熵相干性测度贝尔不等式的这些态是纠缠态.     

基于最少中继节点约束的量子VoIP路由优化策略

量子信息的传输过程中,由于拥塞、链路故障等原因,导致数据分组在路由器排队,产生时延、丢包.为了保证量子Vo IP系统的性能,本文提出了基于最少中继节点约束的路由优化策略.采用基于纠缠交换的中继技术,通过优先选择最少中继节点的量子信道,实现多用户量子Vo IP通信.理论分析和仿真结果表明,当链路出现故障和拥塞时,基于M/M/m型排队系统,采用本策略,当设定量子比特的误码率为0.2,共用信道数目从4增加到8时,量子网络的呼损率由0.25下降到0.024,量子网络的最大吞吐量由64 kbps增加到132 kbps.当设定共用信道数目为4,控制量子比特的误码率从0.3到0.1时,可使量子网络最大吞吐量从41 kbps增加到140 kbps.由此可见,本策略能够极大地提高量子Vo IP网络的性能.     

Dynamics of a qubit as a classical stochastic process with time-correlated noise: minimal measurement invasiveness

So far it has been shown that the quantum dynamics cannot be described as a classical Markov process unless the number of classical states is uncountably infinite. In this Letter, we present a stochastic model with time-correlated noise that exactly reproduces any unitary evolution of a qubit and requires just four classical states. The invasive updating of only 1 bit during a measurement accounts for the quantum violation of the Leggett-Garg inequalities. Unlike in a pilot-wave theory, the stochastic forces governing the jumps among the four states do not depend on the quantum state but only on the unitary evolution. This model is used to derive a local hidden variable model, augmented by 1 bit of classical communication, for simulating entangled Bell states.     

A Measure of Quantum Correlation Based on von Neumann Entropy and Positive Operator-Valued Measurement

Quantum correlations in composite quantum systems are at the origin of the most peculiar features of quantum mechanics such as the violation of Bells inequalities and non-locality. In quantum information theory, they are viewed as quantum resources used by quantum algorithms and communication protocols to outperform their classical analogs. In this paper, we define a new measure of quantum correlation based on von Neumann entropy and positive operator-valued measurement,which has clear physical meaning and we can prove that it satisfying many good property for a measure of quantumness.     

Advantage of Quantum Theory over Nonclassical Models of Communication

Quantum correlations provide dramatic advantage over the corresponding classical resources in several communication tasks. However, a broad class of probabilistic theories exists that attributes greater success than quantum theory in many of these tasks by allowing supra-quantum correlations in “space-like” and/or “time-like” paradigms. In this letter, a communication task involving three spatially separated parties is proposed where one party (verifier) aims to verify whether the bit strings possessed by the other two parties (terminals) are equal or not. This task is called authentication with limited communication, the restrictions on communication being: i) the terminals cannot communicate with each other, but (ii) each of them can communicate with the verifier through single use of channels with limited capacity. Manifestly, classical resources are not sufficient for perfect success of this task. Moreover, it is also not possible to perform this task with certainty in several nonclassical theories although they might possess stronger “space-like” and/or “time-like” correlations. Surprisingly, quantum resources can achieve the perfect winning strategy. The proposed task thus stands apart from all previously known communication tasks as it exhibits quantum advantage over other nonclassical strategies.     

Bell inequalities with no quantum violation and unextendable product bases

The strength of classical correlations is subject to certain constraints, commonly known as Bell inequalities. Violation of these inequalities is the manifestation of nonlocality-displayed, in particular, by quantum mechanics, meaning that quantum mechanics can outperform classical physics at tasks associated with such Bell inequalities. Interestingly, however, there exist situations in which this is not the case. We associate an intriguing class of bound entangled states, constructed from unextendable product bases with a wide family of tasks, for which (i) quantum correlations do not outperform the classical ones but (ii) there exist supraquantum nonsignaling correlations that do provide an advantage.     

Inequalities for nonnegative numbers and information properties of qudit tomograms

We discuss some inequalities for N nonnegative numbers. We use these inequalities to obtain known inequalities for probability distributions and new entropic and information inequalities for quantum tomograms of qudit states. The inequalities characterize the degree of quantum correlations in addition to noncontextuality and quantum discord. We use the subadditivity and strong subadditivity conditions for qudit tomographic-probability distributions depending on the unitary-group parameters in order to derive new inequalities for Shannon, Rényi, and Tsallis entropies of spin states.     

Structure of reversible computation determines the self-duality of quantum theory

Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory, however, both notions are in some sense identical: outcome probabilities are given by the overlap between two state vectors--quantum theory is self-dual. In this Letter, we show that this notion of self-duality can be understood from a dynamical point of view. We prove that self-duality follows from a computational primitive called bit symmetry: every logical bit can be mapped to any other logical bit by a reversible transformation. Specifically, we consider probabilistic theories more general than quantum theory, and prove that every bit-symmetric theory must necessarily be self-dual. We also show that bit symmetry yields stronger restrictions on the set of allowed bipartite states than the no-signalling principle alone, suggesting reversible time evolution as a possible reason for limitations of nonlocality.     

Bell's inequalities between independent particles

The prospect of inducing quantum correlations between two particles that have never interacted is discussed. It is shown that a quantum mechanical state can be formed that predicts violations of Bell's inequalities of the Clauser-Horne-Shimony-Holt type between two particles which have been at space-like separations for all times. It is also shown that these are the strongest inequalities derivable from a general local realistic theory using the same strong locality assumptions as in the Bell inequalities.     

On Bell's inequalities and algebraic invariants

Some algebraic invariants associated with Bell's inequalities are defined for inclusions of von Neumann algebras and studied within the context of general algebraic quantum theory. More special results are proven for quantum field theory which establish that these invariants take infinitely many values. Sharp short-distance bounds on the Bell correlations are also demonstrated in the context of relativistic quantum field theory.     

Information Invariance and Quantum Probabilities

We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The requirement of invariance of the information under a continuous change of the set of mutually complementary measurements uniquely singles out a measure of information, which is quadratic in probabilities. The assumption which gives the same scaling of the number of degrees of freedom with the dimension as in quantum theory follows essentially from the assumption that all physical states of a higher dimensional system are those and only those from which one can post-select physical states of two-dimensional systems. The requirement that no more than one bit of information (as quantified by the quadratic measure) is contained in all possible post-selected two-dimensional systems is equivalent to the positivity of density operator in quantum theory. This article is dedicated to Pekka Lahti on the occasion of his 60th birthday.     

Quantum Correlations,Nuclearity, and Spacetime Curvature

It is proved for a Haag–Araki–Kastler quantum field theory, that gravitation reduces the correlations in the vacuum state. Secondly, we prove Bell's inequalities by nuclearity assumptions. The so-called -content of certain compact mappings restricts the size of the set of measurements which violate Bell's inequalities.     

Distinguishability and Disturbance in the Quantum Key Distribution Protocol Using the Mean Multi-Kings’ Problem

We introduce a quantum key distribution protocol using mean multi-kings’ problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users’ information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users’ systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper’s extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.     

Generic Bell inequalities for multipartite arbitrary dimensional systems

We present generic Bell inequalities for multipartite arbitrary dimensional systems. The inequalities that any local realistic theory must obey are violated by quantum mechanics for even dimensional systems. A large set of variants are shown to naturally emerge from the generic Bell inequalities. We discuss particular variants of Bell inequalities that are violated for all the systems including odd dimensional systems.     

Strong Constraints on Models that Explain the Violation of Bell Inequalities with Hidden Superluminal Influences

We discuss models that attempt to provide an explanation for the violation of Bell inequalities at a distance in terms of hidden influences. These models reproduce the quantum correlations in most situations, but are restricted to produce local correlations in some configurations. The argument presented in (Bancal et al. Nat Phys 8:867, 2012) applies to all of these models, which can thus be proved to allow for faster-than-light communication. In other words, the signalling character of these models cannot remain hidden.     

Operational quantification of continuous-variable correlations

We quantify correlations (quantum and/or classical) between two continuous-variable modes as the maximal number of correlated bits extracted via local quadrature measurements. On Gaussian states, such "bit quadrature correlations" majorize entanglement, reducing to an entanglement monotone for pure states. For non-Gaussian states, such as photonic Bell states, photon-subtracted states, and mixtures of Gaussian states, the bit correlations are shown to be a monotonic function of the negativity. This quantification yields a feasible, operational way to measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without a complete state tomography.     

Observable measure of bipartite quantum correlations

We introduce a measure Q of bipartite quantum correlations for arbitrary two-qubit states, expressed as a state-independent function of the density matrix elements. The amount of quantum correlations can be quantified experimentally by measuring the expectation value of a small set of observables on up to four copies of the state, without the need for a full tomography. We extend the measure to 2×d systems, providing its explicit form in terms of observables and applying it to the relevant class of multiqubit states employed in the deterministic quantum computation with one quantum bit model. The number of required measurements to determine Q in our scheme does not increase with d. Our results provide an experimentally friendly framework to estimate quantitatively the degree of general quantum correlations in composite systems.     

Quantifying interference in multipartite quantum systems

The characterization of quantum correlations is crucial to the development of new quantum technologies and to understand how dramatically quantum theory departs from classical physics. Here we systematically study single- and multiparticle interference patterns produced by general two- and three-qubit systems. From this we establish on phenomenological grounds a new type of quantum correlation for these systems, which we name quantum interference, deriving some quantifiers that are given explicitly in terms of the density matrix elements of the complete system. By using these quantifiers, we show that, contrary to our expectations, entanglement is not a required property for a composite quantum system to manifest multiparticle interference.     

Photon Flux and Distance from the Source: Consequences for Quantum Communication

The paper explores the fundamental physical principles of quantum mechanics (in fact, quantum field theory) that limit the bit rate for long distances and examines the assumption used in this exploration that losses can be ignored. Propagation of photons in optical fibers is modelled using methods of quantum electrodynamics. We define the “photon duration” as the standard deviation of the photon arrival time; we find its asymptotics for long distances and then obtain the main result of the paper: the linear dependence of photon duration on the distance when losses can be ignored. This effect puts the limit to joint increasing of the photon flux and the distance from the source and it has consequences for quantum communication. Once quantum communication develops into a real technology (including essential decrease of losses in optical fibres), it would be appealing to engineers to increase both the photon flux and the distance. And here our “photon flux/distance effect” has to be taken into account. This effect also may set an additional constraint to the performance of a loophole free test of Bell’s type—to close jointly the detection and locality loopholes.     

Asymptotic violation of Bell inequalities and distillability

A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the Clauser-Horne-Shimony-Holt inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In the multipartite case we consider the complete set of full-correlation Bell inequalities with two dichotomic observables per site. We show that asymptotic violation of any of these inequalities by a multipartite state implies that pure-state entanglement can be distilled from it, although the corresponding distillation protocol may require that some of the parties join into several groups. We also obtain the extreme points of the set of distributions generated by measuring N quantum systems with two dichotomic observables per site.