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Journal of Physics A: Mathematical and Theoretical - latest papers

Latest articles for Journal of Physics A: Mathematical and Theoretical

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  • Control power in quantum teleportation and dense coding via three-particle pure states
    Ensuring information security in quantum communication often requires a supervisory mechanism to regulate and authenticate information transmission. In this study, we investigate controlled quantum teleportation (CQT) and controlled dense coding (CDC) using parameterized three-particle pure states as quantum channels. We assess the authority of the controlling party through two key metrics: uncontrolled fidelity and minimal control power. Our analysis reveals that for single-parameter three-particle pure states, when no controlling party is involved, the average uncontrolled fidelity exceeds the classical fidelity threshold, rendering them unsuitable as arbitrary single-particle CQT channels. For multi-parameter three-particle pure states, we derive explicit parameter conditions under which non-trivial control power emerges and provide analytical expressions for several representative cases. Additionally, in the context of CDC, we quantify the minimal control power required when employing single-parameter three-particle states as quantum channels. Our findings establish rigorous criteria for controller authority in parameterized quantum communication, offering both theoretical guarantees and practical insights for secure quantum networks. This work lays the foundation for adaptive quantum protocols where control power and fidelity can be dynamically optimized to enhance security and performance in real-world implementations.

  • Corrigendum: First exit times of harmonically trapped particles: a didactic review (2015 J. Phys. A: Math. Theor. 48 013001)
  • Unitary-invariant method for witnessing nonstabilizerness in quantum processors
    Nonstabilizerness, also known as ‘magic’, is a crucial resource for quantum computation. The growth in complexity of quantum processing units (QPUs) demands robust and scalable techniques for characterizing this resource. We introduce the basis-independent notion of set magic: a set of states has this property if at least one state in the set is a magic state. We show that certain two-state overlap inequalities, recently introduced as witnesses of basis-independent coherence, are also witnesses of set magic. Finally, we show that using such witnesses one can robustly certify nonstabilizerness in a network of QPUs without having to entangle the different devices and with reduced demands compared to the individual certification of each QPU.

  • Dependence of scalar matter vacuum energy, induced by a magnetic topological defect, on the coupling to space-time curvature
    We considered the vacuum polarization of a quantized charged scalar matter field in the background of a topological defect modeled by a finite-thickness tube with magnetic flux inside. The tube is impenetrable for quantum matter, and a generalized boundary condition of the Robin type is imposed at its surface. We have shown that in the flat space-time, the total induced vacuum energy does not depend on the coupling (ξ) of the scalar field’s interaction with the space-time curvature, only for the partial cases of the Dirichlet and Neumann boundary conditions on the tube’s edge. However, for generalized Robin boundary conditions, the total induced energy depends on the coupling ξ in flat space-time, at least for negative values of the boundary condition parameter .

  • Exact Bethe quantum numbers of the massive XXZ chain in the two down-spin sector
    Every solution of the Bethe ansatz equations (BAEs) is characterized by a set of quantum numbers called the Bethe quantum numbers, which are fundamental for evaluating each Bethe root numerically. We rigorously derive the Bethe quantum numbers for the real solutions of the spin-1/2 massive XXZ spin chain in the two down-spin sector, assuming the existence of solutions to some form of BAE. In the sector the quantum numbers J1 and J2 were derived for complex solutions, but not for real solutions. We show the exact results in the sector as follows. (i) When two Bethe quantum numbers are different, i.e. for , we introduce a graphical method, which we call a contour method, for deriving the solution of BAE to a given set of Bethe quantum numbers. By the method, we can readily show the existence and the uniqueness of the solution. (ii) When two Bethe quantum numbers are equal, i.e. for , we derive the criteria for the collapse of two-strings and the emergence of an extra two-string by an analytic method. (iii) We obtain the number of real solutions, which depends on the site number N and the XXZ anisotropy parameter ζ. (iv) We derive all infinite-valued solutions of BAE for the XXX spin chain in the two down-spin sector through the XXX limit. (v) We explicitly show the completeness of the Bethe ansatz in terms of the Bethe quantum numbers.