We review concepts and methods associated with quantum discord and related topics. We also describe their possible connections with other aspects of quantum information and beyond, including quantum ...communication, quantum computation, many-body physics, and open quantum dynamics. Quantum discord in the multiparty regime and its applications are also discussed.
•Bipartite and multipartite entanglement in the quantum spin-1/2 XXZ ladder ground state are analyzed.•Phase diagram in the model discernible by using bipartite and multipartite entanglement.•Using ...moderate-sized system is sufficient.
Phase transition in quantum many-body systems inevitably causes changes in certain physical properties which then serve as potential indicators of critical phenomena. Besides the traditional order parameters, characterization of quantum entanglement has proven to be a computationally efficient and successful method for detection of phase boundaries, especially in one-dimensional models. Here we determine the rich phase diagram of the ground states of a quantum spin-1/2 XXZ ladder by analyzing the variation of bipartite and multipartite entanglements. Our study characterizes the different ground state phases and notes the correspondence with known results, while highlighting the finer details that emerge from the behavior of ground state entanglement. Analysis of entanglement in the ground state provides a clearer picture of the complex ground state phase diagram of the system using only a moderate-size model.
We investigate the action of global noise and local channels, namely, amplitude-damping, phase-damping, and depolarizing channels, on monogamy of quantum correlations, such as negativity and quantum ...discord, in three-qubit systems. We discuss the monotonic and non-monotonic variation, and robustness of the monogamy scores. By using monogamy scores, we propose a two-step protocol to conclusively identify the noise applied to the quantum system, by using generalized Greenberger–Horne–Zeilinger and generalized W states as resource states. We discuss a possible generalization of the results to higher number of parties.
•Monogamy score monotonically decays with noise for generalized GHZ state as input.•Non-monotonically decaying monogamy score with noise for generalized W state as input.•Characterizing the dynamics of monogamy score.•Dynamics terminal quantifying robustness of monogamy score against noise.•Conclusively identifying the type of noise using monogamy score.
•Short-range RVB states can be recursively generated from smaller configurations.•For undoped two-legs ladders such recursion follows the fabled Fibonacci sequence.•Generalized sequences for ...multi-legged doped and undoped spin-ladders can be obtained.•The sequences allow estimation of many relevant physical quantities.
An interesting aspect of antiferromagnetic quantum spin ladders, with complete dimer coverings, is that the wave function can be recursively generated by estimating the number of coverings in the valence bond basis, which follow the fabled Fibonacci sequence. In this work, we derive generalized forms of this sequence for multi-legged and doped quantum spin ladders, which allow the corresponding dimer-covered state to be recursively generated. We show that these sequences allow for estimation of physically and information-theoretically relevant quantities in large spin lattices without resorting to complex numerical methods. We apply the formalism to calculate the valence bond entanglement entropy, which is an important figure of merit for studying cooperative phenomena in quantum spin systems with SU(2) symmetry. We show that introduction of doping may mitigate, within the quarters of entanglement entropy, the dichotomy between odd- and even- legged quantum spin ladders.
Benford's law is an empirical edict stating that the lower digits appear more often than higher ones as the first few significant digits in statistics of natural phenomena and mathematical tables. A ...marked proportion of such analyses is restricted to the first significant digit. We employ violation of Benford's law, up to the first four significant digits, for investigating magnetization and correlation data of paradigmatic quantum many-body systems to detect cooperative phenomena, focusing on the finite-size scaling exponents thereof. We find that for the transverse field quantum XY model, behavior of the very first significant digit of an observable, at an arbitrary point of the parameter space, is enough to capture the quantum phase transition in the model with a relatively high scaling exponent. A higher number of significant digits do not provide an appreciable further advantage, in particular, in terms of an increase in scaling exponents. Since the first significant digit of a physical quantity is relatively simple to obtain in experiments, the results have potential implications for laboratory observations in noisy environments.
•Benford's law states that lower digits appear more often than higher ones as first few significant digits.•First significant digit of observable enough to capture quantum phase transition with high finite-size scaling exponent.•Higher number of significant digits don't provide appreciable further advantage.•Results potentially important for observations in noisy environments.
PDF
