The classicality and quantumness of a quantum ensemble

In this Letter, we investigate the classicality and quantumness of a quantum ensemble. We define a quantity called ensemble classicality based on classical cloning strategy (ECCC) to characterize how classical a quantum ensemble is. An ensemble of commuting states has a unit ECCC, while a general ensemble can have a ECCC less than 1. We also study how quantum an ensemble is by defining a related quantity called quantumness. We find that the classicality of an ensemble is closely related to how perfectly the ensemble can be cloned, and that the quantumness of the ensemble used in a quantum key distribution (QKD) protocol is exactly the attainable lower bound of the error rate in the sifted key.     

A New Quantum Proxy Signature Model Based on a Series of Genuine Entangled States

Quantum proxy signature(QPS) is one of the most important topics in quantum signature. In this paper, we propose a new and general model of QPS based on genuine entangled N_j-qubit (3 ≤ N_j ≤ 6,N_j ∈ N^∗,j = 1,2,3,4.) states. In our model, only the teleportation of multiparty entangled states and quantum one-time pad(QOTP) encryption algorithm have been applied to ensure the security. We hope our results will be helpful to the research of quantum signature in future.

     

Relativistic chemical shielding: formally exact solutions for one—electron atoms of maximum total angular momentum for any principal quantum number

Analytical solutions have been derived for the chemical shieding of one-electron atoms in states of maximum total angular momentum (j = n -1/2). The variation of terms connecting states of different angular momentum is discussed as a function of the quantum numbers, k(= n), j and m the magnetic quantum number, and of Z, the atomic number.     

Correlation properties of entangled multiphoton states and Bernstein’s paradox

A normally ordered characteristic function (NOCF) of Bose operators is calculated for a number of discrete-variable entangled states (Greenberger-Horne-Zeilinger (GHZ) and Werner (W) qubit states and a cluster state). It is shown that such NOCFs contain visual information on two types of correlations: pseudoclassical and quantum correlations. The latter manifest themselves in the interference terms of the NOCFs and lead to quantum paradoxes, whereas the pseudoclassical correlations of photons and their cumulants satisfy the relations for classical random variables. Three- and four-qubit states are analyzed in detail. An implementation of an analog of Bernstein’s paradox on discrete quantum variables is discussed. A measure of quantumness of an entangled state is introduced that is not related to the entropy approach. It is established that the maximum of the degree of quantumness substantiates the numerical values of the coefficients in multiqubit vector states derived from intuitive considerations.     

Optimal Estimate of a Pure Qubit State from Uhlmann–Josza Fidelity

In the framework of collective measurements, efforts have been made to reconstruct one-qubit states. Such schemes find an obstacle in the no-cloning theorem, which prevents full reconstruction of a quantum state. Quantum Mechanics thus restricts us to obtaining estimates of the reconstruction of a pure qubit. We discuss the optimal estimate on the basis of the Uhlmann–Josza fidelity, respecting the limitations imposed by the no-cloning theorem. We derive a realistic optimal expression for the average fidelity. Our formalism also introduces an optimization parameter L. Values close to zero imply full reconstruction of the qubit (i.?e., the classical limit), while larger L’s represent good quantum optimization of the qubit estimate. The parameter L is interpreted as the degree of quantumness of the average fidelity associated with the reconstruction.     

Maximal entanglement of bipartite spin states in the context of quantum algebra

In the framework of the U _q (su(2)) quantum algebra, we investigate the entanglement properties of two-spin systems, of arbitrary spins j ₁ and j ₂, defined in an entanglement of deformed spin coherent states of each of the spins. We derive the amount of entanglement and we give conditions under which bipartite entangled states become maximally entangled. Using these conditions, we construct a large class of Bell states for any choices of the parameters that specify the spin coherent states.     

Non-zero total correlation means non-zero quantum correlation

We investigated the super quantum discord based on weak measurements. The super quantum discord is an extension of the standard quantum discord defined by projective measurements and also describes the quantumness of correlations. We provide some equivalent conditions for zero super quantum discord by using quantum discord, classical correlation and mutual information. In particular, we find that the super quantum discord is zero only for product states, which have zero mutual information. This result suggests that non-zero correlations can always be detected using the quantum correlation with weak measurements. As an example, we present the assisted state-discrimination method.     

Classical-Noise-Free Sensing Based on Quantum Correlation Measurement

Quantum sensing,using quantum properties of sensors,can enhance resolution,precision,and sensitivity of imaging,spectroscopy,and detection.An intriguing question is:Can the quantum nature(quantumness)of sensors and targets be exploited to enable schemes that are not possible for classical probes or classical targets?Here we show that measurement of the quantum correlations of a quantum target indeed allows for sensing schemes that have no classical counterparts.As a concrete example,in the case that the second-order classical correlation of a quantum target could be totally concealed by non-stationary classical noise,the higher-order quantum correlations can single out a quantum target from the classical noise background,regardless of the spectrum,statistics,or intensity of the noise.Hence a classical-noise-free sensing scheme is proposed.This finding suggests that the quantumness of sensors and targets is still to be explored to realize the full potential of quantum sensing.New opportunities include sensitivity beyond classical approaches,non-classical correlations as a new approach to quantum many-body physics,loophole-free tests of the quantum foundation,et cetera.     

No-local-broadcasting theorem for multipartite quantum correlations

We prove that the correlations present in a multipartite quantum state have an operational quantum character even if the state is unentangled, as long as it does not simply encode a multipartite classical probability distribution. Said quantumness is revealed by the new task of local broadcasting, i.e., of locally sharing preestablished correlations, which is feasible if and only if correlations are stricly classical. Our operational approach leads to natural definitions of measures for quantumness of correlations. It also reproduces the standard no-broadcasting theorem as a special case.     

Superadditivity of Wigner-Yanase-Dyson Information Revisited

The Wigner-Yanase-Dyson information is an important variant of quantum Fisher information. Two fundamental requirements concerning this notion of information content originally postulated by Wigner and Yanase are convexity and superadditivity. The former was fully established by Lieb in 1973, and led to the first proof of the strong subadditivity of quantum entropy. The latter, although widely believed to be true, was quite recently disproved by Hansen. Nevertheless, superadditivity has also been established in two extreme cases, i.e., when the states are pure or classical. In this paper, we first review a scheme to classify bipartite states into a hierarchy of classical, semi-quantum, and quantum states, which are arranged in the order of increasing quantumness. We then prove the superadditivity of the Wigner-Yanase-Dyson information for all semi-quantum states. The convexity of the Wigner-Yanase-Dyson information plays a crucial role here.     

Behavior of quantum correlations under local noise

We characterize the behavior of quantum correlations under the influence of local noisy channels. Intuition suggests that such noise should be detrimental for quantumness. When considering qubit systems, we show for which channels this is indeed the case: The amount of quantum correlations can only decrease under the action of unital channels. However, nonunital channels (e.g., such as dissipation) can create quantum correlations for some initially classical states. Furthermore, for higher-dimensional systems even unital channels may increase the amount of quantum correlations. Thus, counterintuitively, local decoherence can generate quantum correlations.     

Correspondence between classical and quantummechanical Boltzmann equations

To compare quantummechanical and classical Boltzmann equations for molecular gases, a correspondence is proposed for functions of angular momentum. Equivalence between irreducible tensors of both kinds is prescribed in a unique way by demanding that trace-averages of binary operator products be equal to solid-angle averages of products of the classical equivalents. Application to the linearized Waldmann-Snider equation for rigid linear molecules leads to an equivalent system for a set of functions φ_j(r, υ, ω, t), j = 0, 1, 2,…. If the quantum number j is approximated by a continuous variable, the system goes over into a single classical equation.     

Computing spin networks

We expand a set of notions recently introduced providing the general setting for a universal representation of the quantum structure on which quantum information stands. The dynamical evolution process associated with generic quantum information manipulation is based on the (re)coupling theory of SU (2) angular momenta. Such scheme automatically incorporates all the essential features that make quantum information encoding much more efficient than classical: it is fully discrete; it deals with inherently entangled states, naturally endowed with a tensor product structure; it allows for generic encoding patterns. The model proposed can be thought of as the non-Boolean generalization of the quantum circuit model, with unitary gates expressed in terms of 3nj coefficients connecting inequivalent binary coupling schemes of n + 1 angular momentum variables, as well as Wigner rotations in the eigenspace of the total angular momentum. A crucial role is played by elementary j-gates (6j symbols) which satisfy algebraic identities that make the structure of the model similar to “state sum models” employed in discretizing topological quantum field theories and quantum gravity. The spin network simulator can thus be viewed also as a Combinatorial QFT model for computation. The semiclassical limit (large j) is discussed.     

Semirigid vibrating rotor target calculation for reaction O(<Superscript>3</Superscript>P)+CH<Subscript>4</Subscript>→CH<Subscript>3</Subscript>+OH

The time-dependent quantum dynamics calculation for reaction O(³P)+CH₄ →CH₃+OH is made, using of the semirigid vibrating rotor target (SVRT) model and the time-dependent wave packet (TDWP) method. The corresponding reaction probabilities of different initial states are provided. From the calculation of initial rovibrational statej=0,v=0, 1, we can see that the excitation of the H-CH₃ stretching vibration gives significant enhancement of reaction probability and the reaction threshold decreases dramatically with the enhancement of the vibrating excitation, which indicates that the vibrating energy of reagent molecules contributes a lot to the molecular collision. As for the calculation of reaction probability of statev=0,j=0,1,2,3, the results show that the reaction probability rises significantly with the enhancement of rotational quantum numberj while the reaction threshold has no changes. The spatial steric effect of the title reaction is studied and analyzed too after the calculation of reaction probability of statesj=5,k=0–2,n=0 andj=5,k=2,n=0–2 is made.     

Interacting Quantum and Classical Continuous Systems I. The Piecewise Deterministic Dynamics

A mathematical construction of a Markov–Feller process associated with a completely positive coupling between classical and quantum systems is proposed. The example of the free classical particle on the Lobatchevski space Q interacting with the quantum system characterized by coherent states on Q is considered.     

On Quantum No-Broadcasting

We address the issue of one-side local broadcasting for correlations in a quantum bipartite state, and conjecture that the correlations can be broadcast if and only if they are classical–quantum, or equivalently, the quantum discord, as defined by Ollivier and Zurek (Phys Rev Lett 88:017901, 2002), vanishes. We prove this conjecture when the reduced state is maximally mixed and further provide various plausible arguments supporting this conjecture. Moreover, we demonstrate that the conjecture implies the following two elegant and fundamental no-broadcasting theorems: (1) The original no-broadcasting theorem by Barnum et al. (Phys Rev Lett 76:2818, 1996), which states that a family of quantum states can be broadcast if and only if the quantum states commute. (2) The no-local-broadcasting theorem for quantum correlations by Piani et al. (Phys Rev Lett 100:090502, 2008), which states that the correlations in a single bipartite state can be locally broadcast if and only if they are classical. The results provide an informational interpretation for classical–quantum states from an operational perspective and shed new lights on the intrinsic relation between non-commutativity and quantumness.