Heisenberg-Type Quantum Steering by Continuous Weak Measurement in Circuit QED *

Quantum steering has attracted great interest in the last decade, especially in the celebrated optomechanical, cold atom, and quantum optical systems. However, there is still a lack of studies on quantum steering in circuit quantum electrodynamics (QED), which provides a useful experimental platform for revealing novel quantum phenomena. In this work, we investigate the steering of qubit by continuous weak measurement in a circuit QED system and establish a set of multiplicative steering inequalities based on the Heisenberg uncertainty principle. Different from the widely studied systems mentioned above, multiplicative steering inequalities in the circuit QED system are in various forms. We find that only a portion of them can be used to show the detection dependence of the qubit state and we also analyze the reason. Furthermore, we discuss several conditions for the violation of a typical steering inequality, including the measurement strength and methods in detecting the cavity field as well as the quantum efficiency of the detector. This preliminary work could be helpful to quantum steering experiments in circuit QED systems.     

Intrinsic Relations of Bipartite Quantum Resources in Tripartite Systems

Quantum resources play crucial roles for displaying superiority in many quantum communication and computation tasks. To reveal the intrinsic relations hidden in these quantum resources, many efforts have been made in recent years. In this work, the correlations of the tripartite W‐type states based on bipartite quantum resources are investigated. The inter‐relations among the degree of coherence, concurrence, Bell nonlocality, and purity are presented. Considering Bell nonlocal and Bell local (satisfied the Clauser–Horne–Shimony–Holt inequality) states for the two‐qubit subsystems derived from the tripartite W‐type states, exact lower and upper boundaries of the degree of coherence versus concurrence are obtained. Interestingly, exact relation among the degree of coherence, concurrence, and purity is obtained. Moreover, coherence is also closely related to entanglement in two specific scenarios: the tripartite W‐type state under decoherence and a practical system for a renormalized spin‐1/2 Heisenberg model.     

Revealing hidden Einstein-Podolsky-Rosen nonlocality

Steering is a form of quantum nonlocality that is intimately related to the famous Einstein-Podolsky-Rosen (EPR) paradox that ignited the ongoing discussion of quantum correlations. Within the hierarchy of nonlocal correlations appearing in nature, EPR steering occupies an intermediate position between Bell nonlocality and entanglement. In continuous variable systems, EPR steering correlations have been observed by violation of Reid's EPR inequality, which is based on inferred variances of complementary observables. Here we propose and experimentally test a new criterion based on entropy functions, and show that it is more powerful than the variance inequality for identifying EPR steering. Using the entropic criterion our experimental results show EPR steering, while the variance criterion does not. Our results open up the possibility of observing this type of nonlocality in a wider variety of quantum states.     

Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox

The concept of steering was introduced by Schr?dinger in 1935 as a generalization of the Einstein-Podolsky-Rosen paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original Einstein-Podolsky-Rosen paradox.     

Improving Quantum Metrology via Purifying and Distilling Noisy Probe States

In quantum metrology, the precision of unknown parameter estimation is studied in the quantum regime, and the choice of the probe state plays an important role in determining the precision of the parameter to be estimated. The quality of quantum metrology will be reduced in the presence of quantum noise during the memory time of probe states after preparation. Meanwhile the noisy probe state can be manipulated by different protocols such as single‐qubit purification, entanglement purification, and entanglement distillation etc. In this paper, the effects of these manipulations on the usefulness, that is, quantum Fisher information (QFI), of the noisy probe state in quantum metrology are studied. The results show that joint operations in single‐qubit purification and entanglement purification processes play positive roles in enhancing the QFI of the probe states, and local measurements in entanglement purification and entanglement distillation processes play both positive and negative roles in enhancing the QFI of the probe states. In this sense, single‐qubit purification will always be helpful in parameter estimation by using single qubits as probe, and entanglement purification process maybe more suitable for improving the estimation precision when entangled‐state probe is adopted.     

通过纠缠交换实现N粒子任意态的概率传态

量子隐形传态的杰出安全特性使其在未来的通讯领域充满潜力.量子力学的不确定性原理和不可克隆定理禁止对量子态进行直接复制,因此,量子隐形传态将量子态划分为经典和量子两部分,信息分别经由经典和量子通道从发送者Alice传递给远方的接收者Bob,根据这两种信息,Bob实行相应操作就可以以一定的几率重建初始传送态.利用一般意义的隐形传态方案,提出一种简便的新方法实现了一个N粒子任意态的概率传态.方法采用N个非最大纠缠的三粒子GHZ态作为量子通道,避免了引入额外的辅助粒子.为了实现传态,Alice将所有粒子分成N份,对第i份的粒子对(i,x_i)实行Bell测量并将结果通过经典通道通知Bob,Bob对粒子(y_i,z_i)进行相应的操作就可以完成第i个粒子信息的传送.当完成N次相似的重复操作后,Bob就可以准确地重建初始传送态.文中以Bell态测量为基本手段,重复的操作同时也降低了实验难度,作为一个特例,文中给出了一个两粒子任意态的传态方案.     

Remote interactions on two distributed quantum systems： nonlocal unambiguous quantum-state discrimination

Remote quantum-state discrimination is a critical step for the implementation of quantum communication network and distributed quantum computation. We present a protocol for remotely implementing the unambiguous discrimination between nonorthogonal states using quantum entanglements, local operations, and classical communications. This protocol consists of a remote generalized measurement described by a positive operator valued measurement （POVM）. We explicitly construct the required remote POVM. The remote POVM can be realized by performing a nonlocal controlled-rotation operation on two spatially separated qubits, one is an ancillary qubit and the other is the qubit which is encoded by two nonorthogonal states to be distinguished, and a conventional local Von Neumann orthogonal measurement on the ancilla. The particular pair of states that can be remotely and unambiguously distinguished is specified by the state of the ancilla. The probability of successful discrimination is not optimal for all admissible pairs. However, for some subset it can be very close to an optimal value in an ordinary local POVM.     

Nonlocality and entanglement in a strange system

We show that the relation between nonlocality and entanglement is subtler than one naively expects. In order to do this we consider the neutral kaon system – which is oscillating in time (particle–anti-particle mixing) and decaying – and describe it as an open quantum system. We consider a Bell–CHSH inequality and show a novel violation for non-maximally entangled states. Considering the change of purity and entanglement in time we find that, despite the fact that only two degrees of freedom at a certain time can be measured, the neutral kaon system does not behave like a bipartite qubit system. PACS 03.65.Ud; 03.65.Yz     

Distribution and dynamics of entanglement in high-dimensional quantum systems using convex-roof extended negativity

Using convex-roof extended negativity, we generalize previous qubit results of entanglement distribution and entanglement dynamics into arbitrary-dimensional quantum systems for isotropic states and the depolarizing channel. We further investigate a relation between these two types of entanglement properties.     

Cloning the entanglement of a pair of d-dimensional quantum systems

We derive a quantum cloning machine that maximizes the entanglement of formation of the two copies of any maximally entangled input state, while preserving the separability of all unentangled input states. In addition, it is proven to optimally duplicate the entanglement of formation of all isotropic input states. For large d, the cloning machine behaves classically and outperforms a local entanglement cloner, studied for comparison. The text was submitted by the authors in English.     

Entanglement can completely defeat quantum noise

We describe two quantum channels that individually cannot send any classical information without some chance of decoding error. But together a single use of each channel can send quantum information perfectly reliably. This proves that the zero-error classical capacity exhibits superactivation, the extreme form of the superadditivity phenomenon in which entangled inputs allow communication over zero-capacity channels. But our result is stronger still, as it even allows zero-error quantum communication when the two channels are combined. Thus our result shows a new remarkable way in which entanglement across two systems can be used to resist noise, in this case perfectly. We also show a new form of superactivation by entanglement shared between sender and receiver.     

Quantum cobwebs: Universal entangling of quantum states

Entangling an unknown qubit with one type of reference state is generally impossible. However, entangling an unknown qubit with two types of reference states is possible. To achieve this, we introduce a new class of states called zero sum amplitude (ZSA) multipartite, pure entangled states for qubits and study their salient features. Using shared-ZSA states, local operations and classical communication, we give a protocol for creating multipartite entangled states of an unknown quantum state with two types of reference states at remote places. This provides a way of encoding an unknown pure qubit state into a multiqubit entangled state.     

概率性的量子态远程操作

提出一种理论方案,利用量子纠缠特性,实现对量子态的远程操作.采用两粒子非最大纠缠态作为资源,借助于辅助量子位,实现态算子的制备,并利用态算子特性,我们能够以一定的概率实现对量子态的远程操作.这种非局域的操作是量子世界特有的现象,这方面的研究有助于对量子力学基本问题的探讨.     

Qubits from tight knots, bent nano-bars and nano-tubes

We propose a novel mechanism for creating a qubit based on a tight trefoil knot, that is an electron nano-waveguide system so small as to be quantum coherent with respect to curvature-induced effects. To establish tight trefoil knots as legitimate candidates for qubits, we propose an effective curvature-induced potential that produces the two-level system and identify the tunnel coupling between the two local states. The proposed two-level system is geometrical in nature and is macroscopic of origin. It also represents new and peculiar property of the trefoil knot. We also propose a different realization of a qubit based on twisted nano-bars and nano-tubes.     

Generalized Steering Robustness of Bipartite Quantum States

EPR steering is a kind of quantum correlation that is intermediate between entanglement and Bell nonlocality. In this paper, by recalling the definitions of unsteerability and steerability, some properties of them are given, e.g, it is proved that a local quantum channel transforms every unsteerable state into an unsteerable state. Second, a way of quantifying quantum steering, which we called the generalized steering robustness (GSR), is introduced and some interesting properties are established, including: (1) GSR of a state vanishes if and only if the state is unsteerable; (2) a local quantum channel does not increase GSR of any state; (3) GSR is invariant under each local unitary operation; (4) as a function on the state space, GSR is convex and lower-semi continuous. Lastly, by using the majorization between the reduced states of two pure states, GSR of the two pure states are compared, and it is proved that every maximally entangled state has the maximal GSR.     

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.     

Non-Markovian random unitary qubit dynamics

We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator whereas it is in general not true for the latter one. A simple example of random unitary dynamics of a qubit shows the intricate difference between those approaches. Moreover, in this case both approaches are fully characterized in terms of local decoherence rates.     

Quantum uncertainty relations of two generalized quantum relative entropies of coherence

In this paper, we consider the quantum uncertainty relations of two generalized relative entropies of coherence based on two measurement bases. First, we give quantum uncertainty relations for pure states in a d-dimensional quantum system by making use of the majorization technique; these uncertainty relations are then generalized to mixed states. We find that the lower bounds are always nonnegative for pure states but may be negative for some mixed states. Second, the quantum uncertainty relations for single qubit states are obtained by the analytical method. We show that the lower bounds obtained by this technique are always positive for single qubit states. Third, the lower bounds obtained by the two methods described above are compared for single qubit states.     

Conversion of Knill–Laflamme–Milburn Entanglement to Greenberger–Horne–Zeilinger Entanglement

Schemes for converting photonic polarized‐entangled Knill–Laflamme–Milburn (KLM) states to Greenberger–Horne–Zeilinger (GHZ) states are proposed using weak cross‐Kerr nonlinearity and X‐quadrature homodyne measurement. Analyses show that the two‐qubit (Bell state) and three‐qubit conversion cases have very high fidelities and close‐to‐unity probabilities. The conversion processes are robust against photon loss. The schemes linking these two entangled states may be helpful to the study of quantum information processing based on them.     

Fidelity induced distance measures for quantum states

Fidelity plays an important role in quantum information theory. In this Letter, we introduce new metric of quantum states induced by fidelity, and connect it with the well-known trace metric, Sine metric and Bures metric for the qubit case. The metric character is also presented for the qudit (i.e., d-dimensional system) case. The CPT contractive property and joint convex property of the metric are also studied.