The LU-LC conjecture is false

The LU-LC conjecture is an important open problem concerning the structure of entanglement of states described in the stabilizer formalism. It states that two local unitary equivalent stabilizer states are also local Clifford equivalent. If this conjecture were true, the local equivalence of stabilizer states would be extremely easy to characterize. Unfortunately, however, based on the recent progress made by Gross and Van den Nest, we find that the conjecture is false.Comment: Added a new part explaining how the counterexamples are foun

Symmetric Extension of Two-Qubit States

Quantum key distribution uses public discussion protocols to establish shared secret keys. In the exploration of ultimate limits to such protocols, the property of symmetric extendibility of underlying bipartite states $\rho_{AB}$ plays an important role. A bipartite state $\rho_{AB}$ is symmetric extendible if there exits a tripartite state $\rho_{ABB'}$, such that the $AB$ marginal state is identical to the $AB'$ marginal state, i.e. $\rho_{AB'}=\rho_{AB}$. For a symmetric extendible state $\rho_{AB}$, the first task of the public discussion protocol is to break this symmetric extendibility. Therefore to characterize all bi-partite quantum states that possess symmetric extensions is of vital importance. We prove a simple analytical formula that a two-qubit state $\rho_{AB}$ admits a symmetric extension if and only if \tr(\rho_B^2)\geq \tr(\rho_{AB}^2)-4\sqrt{\det{\rho_{AB}}}. Given the intimate relationship between the symmetric extension problem and the quantum marginal problem, our result also provides the first analytical necessary and sufficient condition for the quantum marginal problem with overlapping marginals.Comment: 10 pages, no figure. comments are welcome. Version 2: introduction rewritte

Minimum Entangling Power is Close to Its Maximum

Given a quantum gate $U$ acting on a bipartite quantum system, its maximum (average, minimum) entangling power is the maximum (average, minimum) entanglement generation with respect to certain entanglement measure when the inputs are restricted to be product states. In this paper, we mainly focus on the 'weakest' one, i.e., the minimum entangling power, among all these entangling powers. We show that, by choosing von Neumann entropy of reduced density operator or Schmidt rank as entanglement measure, even the 'weakest' entangling power is generically very close to its maximal possible entanglement generation. In other words, maximum, average and minimum entangling powers are generically close. We then study minimum entangling power with respect to other Lipschitiz-continuous entanglement measures and generalize our results to multipartite quantum systems. As a straightforward application, a random quantum gate will almost surely be an intrinsically fault-tolerant entangling device that will always transform every low-entangled state to near-maximally entangled state.Comment: 26 pages, subsection III.A.2 revised, authors list updated, comments are welcom

Corrosion Resistance of Duplex Stainless Steels and MMFX Microcomposite Steel for Reinforced Concrete Bridge Decks

Chloride-induced corrosion of reinforcing steel in concrete is one of the major durability concerns in reinforced concrete structures. In Northern America, the cost of maintenance and replacement for highway bridges due to corrosion damage is measured in billions of dollars. Of corrosion protection systems, reinforcing steels with inherently good corrosion resistance have received increased attention. In this study, the corrosion performance of duplex stainless steels, including 2101 and 2205 duplex steels in both “as-rolled” and pickled conditions, and MMFX microcomposite steel were compared with the corrosion performance of conventional and epoxy-coated steel using laboratory tests. These tests include rapid macrocell tests, corrosion potential tests, bench-scale tests (the Southern Exposure and cracked beam tests), and two modified versions of the Southern Exposure test to determine the critical chloride threshold. The rapid macrocell tests were modified by replacing the simulated concrete pore solutions at the anode and cathode every five weeks to limit the effects of changes in the pH of the solutions. The corrosion resistance of the steels was evaluated based on the corrosion rates, corrosion potentials, mat-to-mat resistances, and critical chloride thresholds measured in these tests. Based on laboratory results, along with data from bridge deck surveys and field experience, the service lives of the steels for bridges decks were estimated and the cost effectiveness was compared based on a life-cycle cost analysis. Results show that, in all rapid macrocell tests, replacing the test solution helps maintain the pH and reduces the corrosion rate and loss of steel. It is recommended that the test solution be replaced every five weeks. Statistically, effective chloride thresholds for reinforcing steel can be determined based on chloride samples from modified Southern Exposure and beam specimens. Results show that conventional steel has the lowest corrosion resistance, with chloride thresholds ranging from 0.91 to 1.22 kg/m3 (1.53 to 2.05 lb/yd3) on a water-soluble basis. Epoxy-coated steel [with four 3.2-mm (0.125-in.) diameter holes in the coating in each test bar to simulate defects of 0.2 to 1% of the bar area] has good corrosion resistance, with corrosion losses ranging from 0.4 to 6% of the values for conventional steel. MMFX microcomposite steel exhibits higher corrosion resistance than conventional steel, with corrosion losses between 16% and 66% and chloride thresholds, 3.70 to 4.07 kg/m3 (4.72 to 6.86 lb/yd3), equal to three to four times the value of conventional steel. Bridge decks containing MMFX steel will be less cost effective than decks containing epoxy-coated steel. Pickled 2101 steel and nonpickled and pickled 2205 steel exhibit significantly better corrosion resistance than conventional steel, with corrosion losses, respectively, ranging from 0.4% to 2%, 0.4% to 5%, and 0.2% to 0.5% of the value of conventional steel. Conservatively, the chloride thresholds of the steels are more than 10 times the value of conventional steel. Overall, 2205 steel has better corrosion resistance than 2101 steel, and pickled bars are more corrosion resistant than nonpickled bars. Pickled 2205 steel exhibits the best corrosion resistance of all the steels tested, while nonpickled 2101 steel has similar corrosion resistance to MMFX steel. The life cycle cost analyses show that in most cases bridge decks containing duplex stainless steels provide lower total life-cycle costs than bridge decks containing conventional, epoxy-coated, or MMFX steel. Pickled 2101 steel represents the lowest cost option

Existence of Universal Entangler

A gate is called entangler if it transforms some (pure) product states to entangled states. A universal entangler is a gate which transforms all product states to entangled states. In practice, a universal entangler is a very powerful device for generating entanglements, and thus provides important physical resources for accomplishing many tasks in quantum computing and quantum information. This Letter demonstrates that a universal entangler always exists except for a degenerated case. Nevertheless, the problem how to find a universal entangler remains open.Comment: 4 page

Correlations in excited states of local Hamiltonians

Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least enough for the calculation of the ground state and excited state energies. Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine ${>}k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for non-degenerate excited states. In fact, for fermionic systems, it has been conjectured that any non-degenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any non-degenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. It means that correlations in excited states of local Hamiltonians could be dramatically different from those in ground states. We further show that any non-degenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix)

Discontinuity of maximum entropy inference and quantum phase transitions

In this paper, we discuss the connection between two genuinely quantum phenomena-the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit

Discontinuity of Maximum Entropy Inference and Quantum Phase Transitions

In this paper, we discuss the connection between two genuinely quantum phenomena --- the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit.Comment: Major revision. 26 pages, 12 figure