scholarly journals Bipartite quantum measurements with optimal single-sided distinguishability

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 442
Author(s):  
Jakub Czartowski ◽  
Karol Życzkowski
Keyword(s):  
Composite System ◽  
Edge Length ◽  
Regular Simplex ◽  
Optimal Basis ◽  
Joint Measurement ◽  
Qubit System ◽  
Local Quantum ◽  
Complete Set ◽  
State Tomography ◽  
The One

We analyse orthogonal bases in a composite N×N Hilbert space describing a bipartite quantum system and look for a basis with optimal single-sided mutual state distinguishability. This condition implies that in each subsystem the N2 reduced states form a regular simplex of a maximal edge length, defined with respect to the trace distance. In the case N=2 of a two-qubit system our solution coincides with the elegant joint measurement introduced by Gisin. We derive explicit expressions of an analogous constellation for N=3 and provide a general construction of N2 states forming such an optimal basis in HN⊗HN. Our construction is valid for all dimensions for which a symmetric informationally complete (SIC) generalized measurement is known. Furthermore, we show that the one-party measurement that distinguishes the states of an optimal basis of the composite system leads to a local quantum state tomography with a linear reconstruction formula. Finally, we test the introduced tomographical scheme on a complete set of three mutually unbiased bases for a single qubit using two different IBM machines.

scholarly journals Local Information as an Essential Factor for Quantum Entanglement

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 728
Author(s):  
Zhaofeng Su
Keyword(s):  
Quantum Entanglement ◽  
Quantum Information Processing ◽  
Local Information ◽  
Essential Factor ◽  
Qubit System ◽  
Local Vectors ◽  
Correlation Parameters ◽  
The One ◽  
Local Parameters

Quantum entanglement is not only a fundamental concept in quantum mechanics but also a special resource for many important quantum information processing tasks. An intuitive way to understand quantum entanglement is to analyze its geometric parameters which include local parameters and correlation parameters. The correlation parameters have been extensively studied while the role of local parameters have not been drawn attention. In this paper, we investigate the question how local parameters of a two-qubit system affect quantum entanglement in both quantitative and qualitative perspective. Firstly, we find that the concurrence, a measure of quantum entanglement, of a general two-qubit state is bounded by the norms of local vectors and correlations matrix. Then, we derive a sufficient condition for a two-qubit being separable in perspective of local parameters. Finally, we find that different local parameters could make a state with fixed correlation matrix separable, entangled or even more qualitatively entangled than the one with vanished local parameters.

scholarly journals On the connection between quark propagation and hadronization

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Alberto Accardi ◽  
Andrea Signori
Keyword(s):  
Sum Rules ◽  
Mass Term ◽  
Final State ◽  
Mass Generation ◽  
Gauge Invariant ◽  
Dynamical Generation ◽  
Dynamical Quark Mass ◽  
Complete Set ◽  
Fragmentation Functions ◽  
The One

AbstractWe investigate the properties and structure of the recently discussed “fully inclusive jet correlator”, namely, the gauge-invariant field correlator characterizing the final state hadrons produced by a free quark as this propagates in the vacuum. Working at the operator level, we connect this object to the single-hadron fragmentation correlator of a quark, and exploit a novel gauge invariant spectral decomposition technique to derive a complete set of momentum sum rules for quark fragmentation functions up to twist-3 level; known results are recovered, and new sum rules proposed. We then show how one can explicitly connect quark hadronization and dynamical quark mass generation by studying the inclusive jet’s gauge-invariant mass term. This mass is, on the one hand, theoretically related to the integrated chiral-odd spectral function of the quark, and, on the other hand, is experimentally accessible through the E and $${\widetilde{E}}$$ E ~ twist-3 fragmentation function sum rules. Thus, measurements of these fragmentation functions in deep inelastic processes provide one with an experimental gateway into the dynamical generation of mass in Quantum Chromodynamics.

Most robust and fragile two-qubit entangled states under deploarizing channels

2013 ◽  
Vol 13 (7&8) ◽  
pp. 645-660
Author(s):  
Chao-Qian Pang ◽  
Fu-Lin Zhang ◽  
Yue Jiang ◽  
Mai-Lin Liang ◽  
Jing-Ling Chen
Keyword(s):  
Evolution Equation ◽  
Numerical Calculations ◽  
Entangled States ◽  
Fragile States ◽  
Qubit System ◽  
Uniform Channel ◽  
Pure States ◽  
The One ◽  
Major Factors ◽  
The Impact

For a two-qubit system under local depolarizing channels, the most robust and most fragile states are derived for a given concurrence or negativity. For the one-sided channel, the pure states are proved to be the most robust ones, with the aid of the evolution equation for entanglement given by Konrad \emph{et al.} [Nat. Phys. 4, 99 (2008)]. Based on a generalization of the evolution equation for entanglement, we classify the ansatz states in our investigation by the amount of robustness, and consequently derive the most fragile states. For the two-sided channel, the pure states are the most robust for a fixed concurrence. Under the uniform channel, the most fragile states have the minimal negativity when the concurrence is given in the region $[1/2,1]$. For a given negativity, the most robust states are the ones with the maximal concurrence, and the most fragile ones are the pure states with minimum of concurrence. When the entanglement approaches zero, the most fragile states under general nonuniform channels tend to the ones in the uniform channel. Influences on robustness by entanglement, degree of mixture, and asymmetry between the two qubits are discussed through numerical calculations. It turns out that the concurrence and negativity are major factors for the robustness. When they are fixed, the impact of the mixedness becomes obvious. In the nonuniform channels, the most fragile states are closely correlated with the asymmetry, while the most robust ones with the degree of mixture.

Periodic distributions of dislocations

1964 ◽  
Vol 280 (1383) ◽  
pp. 528-544 ◽  
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Edge Length ◽  
Internal Stresses ◽  
Periodic Distribution ◽  
Stress And Deformation ◽  
The One ◽  
Distribution Of Dislocations ◽  
Distributed Dislocations ◽  
Three Dimensional Space

First, explicit expressions are obtained for the state of stress and deformation due to a periodic distribution of dislocations with respect to three-dimensional space and time. Further, equilibrium conditions for continuously distributed dislocations are derived from the law of energy conservation. The conditions are applied to determine several equilibrium states of periodic distributions. It was found that the distributions of edge and screw dislocations must have a phase difference of ½π when all the Burgers vectors are limited to the one direction. A sudden application of constant stress will cause the dislocations to move spontaneously to their new equilibrium positions. Also, an expression for dislocation velocity is established. In addition, expressions for internal stresses due to the periodic distribution of dislocations are used to find the stress field induced by a Frank network of dislocations. It was found that the normal stress acting on planes parallel to the network has a maximum value at a distance equal to one-half of the edge length of the hexagon of the net. The stress is propor­tional to the sum of the edge components of the three Burgers vectors at a node of the net­work, and decreases exponentially with distance from the network plane.

Quantum-state tomography for quadrupole nuclei and its application on a two-qubit system

2004 ◽  
Vol 69 (4) ◽  
Author(s):  
F. A. Bonk ◽  
R. S. Sarthour ◽  
E. R. deAzevedo ◽  
J. D. Bulnes ◽  
G. L. Mantovani ◽  
...  
Keyword(s):  
Quantum State ◽  
Quantum State Tomography ◽  
Qubit System ◽  
State Tomography

A spectral representation of the linear multivelocity transport problem

2016 ◽  
Vol 23 (3) ◽  
pp. 329-341
Author(s):  
Mariam Avalishvili ◽  
Dazmir Shulaia
Keyword(s):  
Characteristic Equation ◽  
Spectral Representation ◽  
Transport Theory ◽  
Transport Problem ◽  
Spectral Integral ◽  
Complete Set ◽  
The Difference ◽  
The One ◽  
Original Characteristic ◽  
Linear Transport Theory

AbstractThe transformation of the original characteristic equation of the multivelocity linear transport theory was carried out by expanding the scattering function for the problem to be solved as a spectral integral over a complete set of eigenfunctions for the previously solved transport problem. The obtained equation represents a singular integral equation containing a spectral integral over the spectrum of the solved problem, whose kernel depends on the difference between the scattering of the problem to be solved and that of the already solved problem. We consider also the examples illustrating the validity of such a transformation. M. Kanal and J. Davies made a similar transformation of the characteristic equation of the one-velocity transport theory.

scholarly journals Consistent higher order $$ \sigma \left(\mathcal{GG}\to h\right) $$, $$ \Gamma \left(h\to \mathcal{GG}\right) $$ and Γ(h → γγ) in geoSMEFT

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Tyler Corbett ◽  
Adam Martin ◽  
Michael Trott
Keyword(s):  
Background Field ◽  
Field Method ◽  
Effective Field ◽  
Leading Order ◽  
The Standard Model ◽  
Gauge Fixing ◽  
Complete Set ◽  
Background Field Method ◽  
The One ◽  
Geometric Formulation

Abstract We report consistent results for Γ(h → γγ), $$ \sigma \left(\mathcal{GG}\to h\right) $$ σ GG → h and $$ \Gamma \left(h\to \mathcal{GG}\right) $$ Γ h → GG in the Standard Model Effective Field Theory (SMEFT) perturbing the SM by corrections $$ \mathcal{O}\left({\overline{\upsilon}}_T^2/16{\pi}^2{\Lambda}^2\right) $$ O υ ¯ T 2 / 16 π 2 Λ 2 in the Background Field Method (BFM) approach to gauge fixing, and to $$ \mathcal{O}\left({\overline{\upsilon}}_T^4/{\Lambda}^4\right) $$ O υ ¯ T 4 / Λ 4 using the geometric formulation of the SMEFT. We combine and modify recent results in the literature into a complete set of consistent results, uniforming conventions, and simultaneously complete the one loop results for these processes in the BFM. We emphasize calculational scheme dependence present across these processes, and how the operator and loop expansions are not independent beyond leading order. We illustrate several cross checks of consistency in the results.

scholarly journals Quantum Darwinism in a Composite System: Objectivity versus Classicality

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 995
Author(s):  
Barış Çakmak ◽  
Özgür E. Müstecaplıoğlu ◽  
Mauro Paternostro ◽  
Bassano Vacchini ◽  
Steve Campbell
Keyword(s):  
Hilbert Space ◽  
Quantum System ◽  
Quantum Discord ◽  
Composite System ◽  
Analytical Expression ◽  
Composite Systems ◽  
Composite Quantum System ◽  
Qubit System ◽  
Quantum Darwinism ◽  
Decoherence Free Subspace

We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an N-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an analytical expression for the dynamics is obtained. It demonstrates that part of the system Hilbert space redundantly proliferates its information to the environment, while the remaining subspace is decoupled and preserves clear non-classical signatures. For measurements performed on the system, we establish that a non-zero quantum discord is shared between the composite system and the environment, thus violating the conditions of strong Darwinism. However, due to the asymmetry of quantum discord, the information shared with the environment is completely classical for measurements performed on the environment. Our results imply a dichotomy between objectivity and classicality that emerges when considering composite systems.

scholarly journals General non-leptonic ∆F = 1 WET at the NLO in QCD

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Jason Aebischer ◽  
Christoph Bobeth ◽  
Andrzej J. Buras ◽  
Jacky Kumar ◽  
Mikołaj Misiak
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
High Energy ◽  
Effective Field ◽  
Effective Theory ◽  
Leading Order ◽  
The Standard Model ◽  
Complete Set ◽  
The One

Abstract We reconsider the complete set of four-quark operators in the Weak Effective Theory (WET) for non-leptonic ∆F = 1 decays that govern s → d and b → d, s transitions in the Standard Model (SM) and beyond, at the Next-to-Leading Order (NLO) in QCD. We discuss cases with different numbers Nf of active flavours, intermediate threshold corrections, as well as the issue of transformations between operator bases beyond leading order to facilitate the matching to high-energy completions or the Standard Model Effective Field Theory (SMEFT) at the electroweak scale. As a first step towards a SMEFT NLO analysis of K → ππ and non-leptonic B-meson decays, we calculate the relevant WET Wilson coefficients including two-loop contributions to their renormalization group running, and express them in terms of the Wilson coefficients in a particular operator basis for which the one-loop matching to SMEFT is already known.

scholarly journals A fixed point algorithm for improving fidelity of quantum gates

2020 ◽  
Author(s):  
Paulo Sergio Pereira da Silva ◽  
Pierre Rouchon ◽  
Hector Bessa Silveira
Keyword(s):  
Fixed Point ◽  
Approximate Solution ◽  
Computational Effort ◽  
Banach Fixed Point Theorem ◽  
Fixed Point Algorithm ◽  
Piecewise Constant ◽  
System A ◽  
Piecewise Constant Control ◽  
Qubit System ◽  
The One

This work considers the problem of quantum gate generation for controllable quantum systems with drift.  It is assumed that an approximate solution called seed is pre-computed  by some known algorithm. This work presents a method, called   Fixed-Point Algorithm (FPA)  that is able to improve arbitrarily the fidelity of the given seed. When  the infidelity of the seed is small enough and the approximate solution is attractive in  the context of a tracking control problem (that is verified with probability one, in some sense), the Banach Fixed Point Theorem allows to prove the exponential convergence of the FPA. Even when the FPA  does not converge, several iterated applications of the FPA  may produce the desired fidelity. The FPA produces only small corrections in the control pulses and preserves the original bandwidth  of the seed. The computational effort of each step of the FPA corresponds to the one of the numerical integration of a stabilized closed loop system. A piecewise-constant and a smooth numerical implementations are developed. Several numerical experiments with a N-qubit system  illustrates the effectiveness of the method in several different applications including the conversion of piecewise-constant control pulses into smooth ones and the reduction of their bandwidth.

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