Some Characterizations of EPR Steering

Einstein-Podolsky-Rosen(EPR) steering is one of important quantum correlations of a composite quantum system, which was observed firstly by Schrödinger in the context of the famous EPR paradox and has been discussed recently. In this paper, we give some characterizations of EPR steerability of bipartite states by proving some necessary and sufficient conditions for a state to be unsteerable with a measurement assemblage of Alice. Based on one of the obtained characterizations, we derive an EPR steering inequality, which serves to check EPR steerability of the maximally entangled states.     

Activating the Violation of Steering Inequality for Two‐Qubit X States

The phenomenon of superactivation of quantum steering, that is, the fact that by combining several copies of the unsteerable quantum state one can get a steerable quantum state, has recently attracted much attention. This property is currently only known for isotropic states, and whether there exists an example other than isotropic states is so far an open question. It is of great importance to learn the activation property of non‐isotropic states. In this paper, it is shown that the violation of the local uncertainty relations (LUR) steering inequality can be activated for two‐qubit X type entangled mixed states. Although the activation phenomenon proven in this paper cannot guarantee the superactivation of steering for two‐qubit X states, it does provide clues for this goal. In addition, previous results indicate that two copies are enough for the superactivation of steering, while the price to pay is a high local dimension, and it is unclear whether superactivation is possible with few copies in low‐dimensional systems such as two‐qubit systems. By providing examples of activation of LUR steering inequality with two copies in a two‐qubit system, the work may open a potential way to the solution of this question.     

Spooky action-at-a-distance in general probabilistic theories

We call a probabilistic theory “complete” if it cannot be further refined by no-signaling hidden-variable models, and name a theory “spooky” if every equivalent hidden-variable model violates Shimony?s Outcome Independence. We prove that a complete theory is spooky if and only if it admits a pure steering state in the sense of Schrödinger. Finally we show that steering of complementary states leads to a Schrödinger?s-cat-like paradox.     

Neural network representations of quantum many-body states

Machine learning is currently the most active interdisciplinary field having numerous applications;additionally,machine-learning techniques are used to research quantum many-body problems.In this study,we first propose neural network quantum states(NNQSs)with general input observables and explore a few related properties,such as the tensor product and local unitary operation.Second,we determine the necessary and sufficient conditions for the representability of a general graph state using normalized NNQS.Finally,to quantify the approximation degree of a given pure state,we define the best approximation degree using normalized NNQSs.Furthermore,we observe that some 7V-qubit states can be represented by a normalized NNQS,such as separable pure states,Bell states and GHZ states.     

Local Channels Preserving Maximal Entanglement or Schmidt Number

It is well know that entanglement is invariant under local unitary operations. In this paper we show that a local channel preserves maximal entanglement state (MES) or preserves pure states with Schmidt number r (r is an arbitrarily fixed integer) if and only if it is a local unitary operation. That is, the only local channel that leaves entanglement invariant is the local unitary operation.     

Bayes' rule and hidden variables

We show that a quantum system admits hidden variables if and only if there is a rich set of states which satisfy a Bayesian rule. The result is proved using a relationship between Bayesian type states and dispersion-free states. Various examples are presented. In particular, it is shown that for classical systems every state is Bayesian and for traditional Hilbert space quantum systems no state is Bayesian.     

Some Measurement-Based Characterizations of Separability of Bipartite States

Importance of quantum entanglement has been demonstrated in various applications. Usually, separability of a bipartite state is defined by its algebraic structure, i.e. a convex combination of product states. But it seems to be hard to check separability (equivalently, entanglement) of a state from its algebraic structure. In this note, we give some characterizations of separability of bipartite states based on POVM measurements. For bipartite pure states, we prove the separability, Bell locality, unsteerability and classical correlation are the same. As a consequence, every entangled pure bipartite state is always Bell nonlocal, steerable and quantum correlated.

     

纠缠相干态的纠缠浓缩

利用线性光学元器件对光场量子态进行操纵,可以实现远程的量子纠缠调控和量子通讯.通过分析光学分束器对相干态光场的作用,发现当初始光场态是两个两部分纠缠态的直乘时,让其中的两模通过光学分束器作用后再对其进行光子计数,另外两模将会塌缩到新的纠缠态.基于这个特点,提出了一个实现部分纠缠相干态纠缠浓缩的方案.在这个方案中,两个部分纠缠相干态被用来作为量子信道,通过光学分束器作用后对光场进行光子数探测时,如果测量到光场的两模分别处于奇光子数态和零光子数态,则光场另外的两模将塌缩到最大纠缠态,从而完成纠缠浓缩的过程.计算结果表明,对于纠缠相干态,无论其初始的纠缠是多么微弱,利用这种方法总有一定的几率可以从中提纯出最大纠缠态.     

Stability of quantum states of finite macroscopic systems against classical noises,perturbations from environments,and local measurements

We study the stability of quantum states of macroscopic systems of finite volume V. By using both the locality and huge degrees of freedom, we show the following: (i) If square fluctuation of every additive operator is O(V) or less for a pure state, then it is not fragile for any weak classical noises or weak perturbations from environments. (ii) If square fluctuation of some additive operator is O(V2) for a pure state, then it is fragile for some of these. (iii) If a state, pure or mixed, has the "cluster property," then it is stable against local measurements, and vice versa. Among many applications, we discuss the mechanism of symmetry-breaking in finite systems.     

Bose-Hubbard模型中系统初态对量子关联的影响

量子关联是量子信息、量子计算与量子计量领域的重要资源, 在量子纠缠和贝尔非局域性中, 两子系统起着同等关键的作用, Einstein-Podolsky-Rosen (EPR)量子引导关联的强度介于量子纠缠和贝尔非局域性之间, 对单向EPR量子引导关联而言两子系统的作用不对等. 本文研究了双模Bose-Hubbard模型中模间量子关联的动态特性, 揭示了EPR量子引导关联的取向对系统初态模间交换对称性的依赖关系. 根据Hillery-Zubairy纠缠判据以及基于最大平均量子Fisher信息的纠缠判据考察了系统初态对模间量子纠缠演化规律的影响. 如果模间耦合强度远大于同一势阱内粒子间的相互作用, 初始处于SU(2)相干态的系统在具有确定的两子系统交换对称性的条件下, 其量子关联呈现简单的周期性演化规律; 当这种对称性破缺时, 模间量子关联的演化呈现较复杂的崩塌与回复现象.     

Description of physical systems

A general “logical” scheme, containing both classical and quantum mechanics, is developed on the basis of plausible axioms. We introduce the division of states and yes-no measurements into sharp and diffuse ones, and prove that sharp states possess their carriers. Owing to this result, the existence of lattice joins and meets is proved for a wide class of elements of the logic. This “semi-lattice” structure gives the familiar lattice picture for special cases of classical and quantum mechanics. The notion of quantum superposition is introduced in this general scheme. It is proved that if in a theory appear nontrivial quantum superpositions, then this theory is “undeterministic” and vise versa. Further analysis of the pure state space leads to the construction of the canonical embedding of the general logic into an orthomodular complete ortho-lattice. After defining the probability of transition between pure states, the pure state space appears to be a generalization of Mielnik's “probability space” of quantum mechanics.     

Quantum State Discrimination with Prior Knowledge in Noisy Quantum Channels

Discrimination between two states of a qubit is investigated, which is performed under the influence of noisy quantum channels. When prior knowledge about on the quantum states is available, the detection probability of quantum measurement is compared with that of pure guessing during the irreversible time evolution. In the case of a Markovian channel, the superiority of quantum measurement to pure guessing is lost at finite time which is determined by the prior probability and the fidelity of the quantum states. For a non-Markovian channel, however, it is possible to recover the superiority of quantum measurement even if it is lost. The effect of a system-environment initial correlation on the quantum state discrimination is also investigated.     

Quantum logic properties of hypergraphs

In quantum logics, the notions of strong and full order determination and unitality for states on orthomodular posets are well known. These notions are defined for hypergraphs and their state spaces in a consistent manner and the relations between them and to the notions defined for orthomodular posets are discussed. The state space of a hypergraph is a polytope. This polytope is a simplex if and only if every superposition of pure states is a mixture of these same pure states. Isomorphic hypergraphs have convexly isomorphic state spaces. A class of hypergraphs is given whose group of automorphisms is group-isomorphic to the group of convex automorphisms of their state spaces.Work supported by the Swiss National Science Foundation.     

Quantum Gibbs Samplers: The Commuting Case

We analyze the problem of preparing quantum Gibbs states of lattice spin Hamiltonians with local and commuting terms on a quantum computer and in nature. Our central result is an equivalence between the behavior of correlations in the Gibbs state and the mixing time of the semigroup which drives the system to thermal equilibrium (the Gibbs sampler). We introduce a framework for analyzing the correlation and mixing properties of quantum Gibbs states and quantum Gibbs samplers, which is rooted in the theory of non-commutative \({\mathbb{L}_p}\) spaces. We consider two distinct classes of Gibbs samplers, one of them being the well-studied Davies generator modelling the dynamics of a system due to weak-coupling with a large Markovian environment. We show that their spectral gap is independent of system size if, and only if, a certain strong form of clustering of correlations holds in the Gibbs state. Therefore every Gibbs state of a commuting Hamiltonian that satisfies clustering of correlations in this strong sense can be prepared efficiently on a quantum computer. As concrete applications of our formalism, we show that for every one-dimensional lattice system, or for systems in lattices of any dimension at temperatures above a certain threshold, the Gibbs samplers of commuting Hamiltonians are always gapped, giving an efficient way of preparing the associated Gibbs states on a quantum computer.     

Digraph states and their neural network representations

With the rapid development of machine learning, artificial neural networks provide a powerful tool to represent or approximate many-body quantum states. It was proved that every graph state can be generated by a neural network. Here, we introduce digraph states and explore their neural network representations (NNRs). Based on some discussions about digraph states and neural network quantum states (NNQSs), we construct explicitly an NNR for any digraph state, implying every digraph state is an NNQS. The obtained results will provide a theoretical foundation for solving the quantum many-body problem with machine learning method whenever the wave-function is known as an unknown digraph state or it can be approximated by digraph states.     

The parts determine the whole in a generic pure quantum state

We show that almost every pure state of multiparty quantum systems (each of whose local Hilbert space has the same dimension) is completely determined by the state's reduced density matrices of a fraction of the parties; this fraction is less than about two-thirds of the parties for states of large numbers of parties. In other words, once the reduced states of this fraction of the parties have been specified, there is no further freedom in the state.     

Reconstruction of Superoperators from Incomplete Measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[ρ_j] that originate from a set of four linearly independent “test” states ρ_j (j = 1,2,3,4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator ρ = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.We have originally dedicated this paper to Asher Peres on the occasion of his 70th birthday. Unfortunately, since the submission of the paper for publication Asher Peres passed away so we dedicate this paper to his memory.     

Einstein-Podolsky-Rosen Steering for Mixed Entangled Coherent States

By using the Born Markovian master equation, we study the relationship among the Einstein–Podolsky–Rosen (EPR) steering, Bell nonlocality, and quantum entanglement of entangled coherent states (ECSs) under decoherence. We illustrate the dynamical behavior of the three types of correlations for various optical field strength regimes. In general, we find that correlation measurements begin at their maximum and decline over time. We find that quantum steering and nonlocality behave similarly in terms of photon number during dynamics. Furthermore, we discover that ECSs with steerability can violate the Bell inequality, and that not every ECS with Bell nonlocality is steerable. In the current work, without the memory stored in the environment, some of the initial states with maximal values of quantum steering, Bell nonlocality, and entanglement can provide a delayed loss of that value during temporal evolution, which is of interest to the current study.     

Quantum entanglement swapping of two arbitrary biqubit pure states

In this paper, the issue of swapping quantum entanglements in two arbitrary biqubit pure states via a local bipartite entangledstate projective measure in the middle node is studied in depth, especially with regard to quantitative aspects. Attention is mainly focused on the relation between the measure and the final entanglement obtained via swapping. During the study, the entanglement of formation (EoF) is employed as a quantifier to characterize and quantify the entanglements present in all involved states. All concerned EoFs are expressed analytically; thus, the relation between the final entanglement and the measuring state is established. Through concrete analyses, the measure demands for getting a certain amount of a final entanglement are revealed. It is found that a maximally entangled final state can be obtained from any two given initial entangled states via swapping with a certain probability; however, a peculiar measure should be performed. Moreover, some distinct properties are revealed and analyzed. Such a study will be useful in quantum information processes.     

对称噪声信道下利用多纠缠态实现量子密钥分配

研究了对称噪声信道下的量子密钥分配(Quantum Key Distribution,QKD)过程，并得到了其误码率和信道保真度的关系式。基于量子态的局域区分原理，我们提出了使用“多纠缠态”进行噪声信道下的密钥分配的新方案。应用这个新方案，我们可以获得和在理想无噪声信道下使用最大纠缠态(四个Bell态之一)进行QKD一样好的结果。