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Register a new userViolating the no-signaling principle with classical inseparable beams in an optical parity-time symmetric system
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We show that the no-signaling principle can be violated with classical inseparable beams in the presence of a parity-time (PT) symmetric subsystem. Thus, the problems associated to PT-symmetric quantum theories recently discovered by Lee et al. [Phys. Rev. Lett. 112, 130404 (2014)] are not exclusive to quantum mechanics, but already exist in the classical case. The possibility to implement local optical PT-symmetric subsystems via light-matter interactions enables the experimental exploration of local PT symmetry and subtle quantum concepts via classical analogues.
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In this work, we propose a PT-symmetric coupler whose arms are birefringent waveguides as a realistic physical model which leads to a so-called quadrimer i.e., a four complex field setting. We seek stationary solutions of the resulting linear and nonlinear model, identifying its linear point of PT symmetry breaking and examining the corresponding nonlinear solutions that persist up to this point, as well as, so-called, ghost states that bifurcate from them. We obtain the relevant symmetry breaking bifurcations and numerically follow the associated dynamics which give rise to growth/decay even within the PT-symmetric phase. Our obtained stationary nonlinear solutions are found to terminate in saddle-center bifurcations which are analogous to the linear PT-phase transition.
Classical open systems with balanced gain and loss, i.e. parity-time ($mathcal{PT}$) symmetric systems, have attracted tremendous attention over the past decade. Their exotic properties arise from exceptional point (EP) degeneracies of non-Hermitian Hamiltonians that govern their dynamics. In recent years, increasingly sophisticated models of $mathcal{PT}$-symmetric systems with time-periodic (Floquet) driving, time-periodic gain and loss, and time-delayed coupling have been investigated, and such systems have been realized across numerous platforms comprising optics, acoustics, mechanical oscillators, optomechanics, and electrical circuits. Here, we introduce a $mathcal{PT}$-symmetric (balanced gain and loss) system with memory, and investigate its dynamics analytically and numerically. Our model consists of two coupled $LC$ oscillators with positive and negative resistance, respectively. We introduce memory by replacing either the resistor with a memristor, or the coupling inductor with a meminductor, and investigate the circuit energy dynamics as characterized by $mathcal{PT}$-symmetric or $mathcal{PT}$-symmetry broken phases. Due to the resulting nonlinearity, we find that energy dynamics depend on the sign and strength of initial voltages and currents, as well as the distribution of initial circuit energy across its different components. Surprisingly, at strong inputs, the system exhibits self-organized Floquet dynamics, including $mathcal{PT}$-symmetry broken phase at vanishingly small dissipation strength. Our results indicate that $mathcal{PT}$-symmetric systems with memory show a rich landscape.
Non-Hermitian systems with parity-time ($mathcal{PT}$) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the classical domain, where second or higher order EPs have been proposed or realized. In contrast, quantum information studies of $mathcal{PT}$-symmetric systems have been confined to systems with a two-dimensional Hilbert space. Here by using a single-photon interferometry setup, we simulate quantum dynamics of a four-dimensional $mathcal{PT}$-symmetric system across a fourth-order exceptional point. By tracking the coherent, non-unitary evolution of the density matrix of the system in $mathcal{PT}$-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire system, and the gain and loss subsystems. Our setup is scalable to the higher-dimensional $mathcal{PT}$-symmetric systems, and our results point towards the rich dynamics and critical properties.
The perturbation of the free rigid rotator by the trigonometric Scarf potential is shown to conserve its energy excitation patterns and change only the wave functions towards spherical harmonics rescaled by a function of an unspecified parity, or mixtures of such rescaled harmonics of equal magnetic quantum numbers and different angular momenta. In effect, no parity can be assigned to the states of the rotational bands emerging in this exotic way, and the electric dipole operator is allowed to acquire non-vanishing expectation values.
Pure states are very important in any theory since they represent states of maximal information about the system within the theory. Here, we show that no non-trivial (not local realistic) extremal states (boxes) of general no-signaling theories can be realized within quantum theory. We then explore three interesting consequences of this fact. Firstly, since the pure states are uncorrelated from the environment, the statement forms a no-go result against the most straightforward device-independent protocol for randomness or secure key generation against general no-signaling adversaries. It also leads to the interesting question whether all non-extremal boxes allow for non-local correlations with the adversary. Secondly, in addition to the fact that new information-theoretic principles (designed to pick out the set of quantum correlations from among all non signaling ones) can in consequence be tested on arbitrary non-local vertices to check their validity, it also allows the possibility of excluding from the quantum set any box of no-signaling correlations that can be distilled to a non-local vertex. Finally, it also forms a sufficient condition to identify non-local games with no quantum winning strategy, when one can show that the game has a single unique non-signaling winning strategy. We illustrate each of these consequences with the example of generalized Popescu-Rohrlich boxes.
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