Quantum phases with differing computational power

Abstract

The observation that concepts from quantum information has generated many alternative indicators of quantum phase transitions hints that quantum phase transitions possess operational significance with respect to the processing of quantum information. Yet, studies on whether such transitions lead to quantum phases that differ in their capacity to process information remain limited. Here We show that there exist quantum phase transitions that cause a distinct qualitative change in our ability to simulate certain quantum systems under perturbation of an external field by local operations and classical communication. In particular, we show that in certain quantum phases of the XY model, adiabatic perturbations of the external magnetic field can be simulated by local spin operations, whereas the resulting effect within other phases results in coherent non-local interactions. We discuss the potential implications to adiabatic quantum computation, where a computational advantage exists only when adiabatic perturbation results in coherent multi-body interactions.

7 pages, 4 figures, with published title "Quantum phases with differing computational power"

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• Coherence susceptibility as a probe of quantum phase transitions
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• Exploring multipartite quantum correlations with the square of quantum discord
• Extracting quantum coherence via steering
• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
• Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
• Entanglement Rényi $\alpha$-entropy
• General monogamy property of global quantum discord and the application
• Characterization of an operational quantum resource in a critical many-body system
• Local characterization of 1d topologically ordered states
• Local convertibility and the quantum simulation of edge states in many-body systems
• Local response of topological order to an external perturbation
• Characterizing Genuine Multisite Entanglement in Isotropic Spin Lattices
• Entanglement convertibility by sweeping through the quantum phases of the alternating bonds $XXZ$ chain
• Quantum network teleportation for quantum information distribution and concentration
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Global quantum discord and quantum phase transition in XY model
• Local convertibility of the ground state of the perturbed Toric code
• Entanglement rates for Renyi, Tsallis and other entropies
• One-way deficit and quantum phase transitions in $XY$ model and extended Ising model
• Non universality of entanglement convertibility
• Monogamy relations and upper bounds for the generalized $W$-class states using Rényi-$\alpha$ entropy
• Local softening of information geometric indicators of chaos in statistical modeling in the presence of quantum-like considerations
• Cumulative quantum work-deficit versus entanglement in the dynamics of an infinite spin chain
• Lower and upper bounds for entanglement of Rényi-$\alpha$ entropy
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• Quantum coherence and correlations in quantum system
• Role of weak measurements on states ordering and monogamy of quantum correlation
• Investigating disordered many-body system with entanglement in momentum space
• Condition on the Rényi Entanglement Entropy under Stochastic Local Manipulation
• Probing Planckian physics in de Sitter space with quantum correlations
• Entanglement and measurement-induced nonlocality of mixed maximally entangled states in multipartite dynamics
• Majorization relation in quantum critical systems
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Entanglement-fluctuation relation for bipartite pure states
• Classification of no-signaling correlations and the guess your neighbor's input game
• Phase diagram of quantum critical system via local convertibility of ground state
• Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model
• Diagonal entropy in many-body systems: Volume effect and quantum phase transitions
• One-way deficit and quantum phase transitions in $XX$ Model
• Exclusive quantum channels in quantum networks
• Resource complexity of Symmetry Protected Topological phases
• Tighter monogamy and polygamy relations using Rényi-$\alpha$ entropy