Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Athens Journal of Sciences

Assembling Large Entangled States in the Rényi-Ingarden-Urbanik Entropy Measure under the SU(2)-Dynamics Decomposition for Systems Built from Two-Level Subsystems

Francisco Delgado

Published Jun 1, 2019• 1 citation
Publisher

Abstract

Quantum Information is a discipline derived from Quantum Mechanics which uses quantum systems to exploit their states as information recipients.Normally, these states are conformed by two-level systems to reproduce the binary nature underlying the classical computation structure.Quantum evolution is then controlled to reproduce convenient information processing operations.Evolution could be hard to be controlled.SU(2) decomposition procedure lets to set a binary structure of processing when a convenient basis is selected to set the dynamics description.In this work, we exploit this procedure for a generic Hamiltonian in order to set the process to reduce arbitrary states into simplest ones.For this work, we use customary SU(2) operations on local and entangled states.These operations are described in the development.They involve 1, 2 and 4-local operations meaning the number of quantum parties involved, in agreement with the decomposition procedure scope.This task is complex in spite the difficulty to set a general way to manipulate the entanglement in the system.We are particularly interested on the application of stochastic procedures based in SU(2) decomposition operations to achieve that goal.In order to have a measure of the advancement of the last task, we use the Rényi-Ingarden-Urbanik entropy to describe the whole spectrum of entanglement in the large systems through the assembling/disassembling of the state.

DOI
10.30958/ajs.6-2-1

Related papers

SU(2) Decomposition for the Quantum Information Dynamics in 2d-Partite Two-Level Quantum Systems

Francisco Delgado

The gate array version of quantum computation uses logical gates adopting convenient forms for computational algorithms based on the algorithms classical computation. Two-level quantum systems are the basic elements connecting the binary nature of classical computation with the settlement of quantum processing. Despite this, their design depends on specific quantum systems and the physical interactions involved, thus complicating the dynamics analysis. Predictable and controllable manipulation should be addressed in order to control the quantum states in terms of the physical control parameters. Resources are restricted to limitations imposed by the physical settlement. This work presents a formalism to decompose the quantum information dynamics in S U ( 2 2 d ) for 2 d -partite two-level systems into 2 2 d - 1 S U ( 2 ) quantum subsystems. It generates an easier and more direct physical implementation of quantum processing developments for qubits. Easy and traditional operations proposed by quantum computation are recovered for larger and more complex systems. Alternating the parameters of local and non-local interactions, the procedure states a universal exchange semantics on the basis of generalized Bell states. Although the main procedure could still be settled on other interaction architectures by the proper selection of the basis as natural grammar, the procedure can be understood as a momentary splitting of the 2 d information channels into 2 2 d - 1 pairs of 2 level quantum information subsystems. Additionally, it is a settlement of the quantum information manipulation that is free of the restrictions imposed by the underlying physical system. Thus, the motivation of decomposition is to set control procedures easily in order to generate large entangled states and to design specialized dedicated quantum gates. They are potential applications that properly bypass the general induced superposition generated by physical dynamics.

Entropy•Aug 17, 2018•4 citations

Minimal Rényi–Ingarden–Urbanik Entropy of Multipartite Quantum States

Marco Enríquez, Zbigniew Puchała, Karol Życzkowski

We study the entanglement of a pure state of a composite quantum system consisting of several subsystems with d levels each. It can be described by the Rényi–Ingarden–Urbanik entropy Sq of a decomposition of the state in a product basis, minimized over all local unitary transformations. In the case q = 0, this quantity becomes a function of the rank of the tensor representing the state, while in the limit q → ∞, the entropy becomes related to the overlap with the closest separable state and the geometric measure of entanglement. For any bipartite system, the entropy S1 coincides with the standard entanglement entropy. We analyze the distribution of the minimal entropy for random states of three- and four-qubit systems. In the former case, the distribution of the three-tangle is studied and some of its moments are evaluated, while in the latter case, we analyze the distribution of the hyperdeterminant. The behavior of the maximum overlap of a three-qudit system with the closest separable state is also investigated in the asymptotic limit.

arXiv:1506.04788•Entropy•Jul 20, 2015•16 citations

Elementary SU(2) Operations to Manipulate the Entropy in Large 2-Level Quantum Systems

Francisco Delgado

Abstract SU(2) operations are recurrently required in quantum information because of their simplicity. The SU(2) formalism states that quantum systems can be controlled easily, step by step, by means of such operations if convenient vector bases (normally composed by entangled states) are used as grammar. In this work, we explore the entanglement gained under such operations for the classes GHZ and W, as two well known representatives of maximal entangled states for larger systems.

Journal of Physics Conference Series•Apr 1, 2020•0 citations

Generation of large quantum entangled states in 2d-partite systems using SU(2) decomposition

Francisco Delgado

This work presents a procedure to generate large entangled states on 2d-partite two level systems via factorization using SU(2) decomposition of its information dynamics under certain natural entangling interactions in ion traps and light-matter systems.

Quantum Information and Measurement (QIM)•Jan 1, 2017•2 citations

Quantum Information Dynamics

Jeffrey Yepez

Presented is a study of quantum entanglement from the perspective of the theory of quantum information dynamics. We consider pairwise entanglement and present an analytical development using joint ladder operators, the sum of two single-particle fermionic ladder operators. This approach allows us to write down analytical representations of quantum algorithms and to explore quantum entanglement as it is manifested in a system of qubits.;We present a topological representation of quantum logic that views entangled qubit spacetime histories (or qubit world lines) as a generalized braid, referred to as a super-braid. The crossing of world lines may be either classical or quantum mechanical in nature, and in the latter case most conveniently expressed with our analytical expressions for entangling quantum gates. at a quantum mechanical crossing, independent world lines can become entangled. We present quantum skein relations that allow complicated superbraids to be recursively reduced to alternate classical histories. If the superbraid is closed, then one can decompose the resulting superlink into an entangled superposition of classical links. Also, one can compute a superlink invariant, for example the Jones polynomial for the square root of a knot.;We present measurement-based quantum computing based on our joint number operators. We take expectation values of the joint number operators to determine kinetic-level variables describing the quantum information dynamics in the qubit system at the mesoscopic scale. We explore the issue of reversibility in quantum maps at this scale using a quantum Boltzmann equation. We then present an example of quantum information processing using a qubit system comprised of nuclear spins. We also discuss quantum propositions cast in terms of joint number operators.;We review the well known dynamical equations governing superfluidity, with a focus on self-consistent dynamics supporting quantum vortices in a Bose-Einstein condensate (BEC). Furthermore, we review the mutual vortex-vortex interaction and the consequent Kelvin wave instability. We derive an effective equation of motion for a Fermi condensate that is the basis of our qubit representation of superfluidity.;We then present our quantum lattice gas representation of a superfluid. We explore aspects of our model with two qubits per point, referred to as a Q2 model, particularly its usefulness for carrying out practical quantum fluid simulations. We find that it is perhaps the simplest yet most comprehensive model of superfluid dynamics. as a prime application of Q2, we explore the power-law regions in the energy spectrum of a condensate in the low-temperature limit. We achieved the largest quantum simulations to date of a BEC and, for the first time, Kolmogorov scaling in superfluids, a flow regime heretofore only obtainably by classical turbulence models.;Finally, we address the subject of turbulence regarding information conservation on the small scales (both mesoscopic and microscopic) underlying the flow dynamics on the large hydrodynamic (macroscopic) scale. We present a hydrodynamic-level momentum equation, in the form of a Navier-Stokes equation, as the basis for the energy spectrum of quantum turbulence at large scales. Quantum turbulence, in particular the representation of fluid eddies in terms of a coherent structure of polarized quantum vortices, offers a unique window into the heretofore intractable subject of energy cascades.

•Jan 1, 2010•1 citation

Bell gems naturally split dynamics information from $SU(2^{2d}) \rightarrow U(1)^{2^{2d-1}-1} \times SU(2)^{2^{2d-1}}$

Francisco Delgado

Quantum Computation and Quantum Information are continuously growing research areas which are based on nature and resources of quantum mechanics, as superposition and entanglement. In its gate array version, the use of convenient and appropriate gates is essential. But while those proposed gates adopt convenient forms for computational algorithms, in the practice, their design depends on specific quantum systems and stuff being used. Gates design is restricted to properties and limitations of interactions and physical elements being involved, where Quantum Control plays a deep role. Quantum complexity of multipartite systems and their interactions requires a tight control to manipulate their quantum states, either local and non-local ones, but still a reducibility procedure should be addressed. This work shows how a general $2d$-partite two level spin system in $SU(2d)$ could be decomposed in $2^{n-1}$ subsystems on $SU(2)$, letting establish control operations. In particular, it is shown that Bell gems basis is a set of natural states on which decomposition happen naturally under some interaction restrictions. Thus, alternating the direction of local interaction terms in the Hamiltonian, this procedure states a universal exchange semantics on those basis. The structure developed could be understood as a splitting of the $2d$ information channels into $2^{2d-1}$ pairs of $2$ level information subsystems.

arXiv:1510.01348•Jan 1, 2015•0 citations
Quantum Information is a discipline derived from Quantum Mechanics which uses quantum systems to exploit their states as information recipients.Normally, these states are conformed by two-level systems to reproduce the binary nature underlying the classical computation structure.Quantum evolution is then controlled to reproduce convenient information processing operations.Evolution could be hard to be controlled.SU(2) decomposition procedure lets to set a binary structure of processing when a convenient basis is selected to set the dynamics description.In this work, we exploit this procedure for a generic Hamiltonian in order to set the process to reduce arbitrary states into simplest ones.For this work, we use customary SU(2) operations on local and entangled states.These operations are described in the development.They involve 1, 2 and 4-local operations meaning the number of quantum parties involved, in agreement with the decomposition procedure scope.This task is complex in spite the difficulty to set a general way to manipulate the entanglement in the system.We are particularly interested on the application of stochastic procedures based in SU(2) decomposition operations to achieve that goal.In order to have a measure of the advancement of the last task, we use the Rényi-Ingarden-Urbanik entropy to describe the whole spectrum of entanglement in the large systems through the assembling/disassembling of the state.
The gate array version of quantum computation uses logical gates adopting convenient forms for computational algorithms based on the algorithms classical computation. Two-level quantum systems are the basic elements connecting the binary nature of classical computation with the settlement of quantum processing. Despite this, their design depends on specific quantum systems and the physical interactions involved, thus complicating the dynamics analysis. Predictable and controllable manipulation should be addressed in order to control the quantum states in terms of the physical control parameters. Resources are restricted to limitations imposed by the physical settlement. This work presents a formalism to decompose the quantum information dynamics in S U ( 2 2 d ) for 2 d -partite two-level systems into 2 2 d - 1 S U ( 2 ) quantum subsystems. It generates an easier and more direct physical implementation of quantum processing developments for qubits. Easy and traditional operations proposed by quantum computation are recovered for larger and more complex systems. Alternating the parameters of local and non-local interactions, the procedure states a universal exchange semantics on the basis of generalized Bell states. Although the main procedure could still be settled on other interaction architectures by the proper selection of the basis as natural grammar, the procedure can be understood as a momentary splitting of the 2 d information channels into 2 2 d - 1 pairs of 2 level quantum information subsystems. Additionally, it is a settlement of the quantum information manipulation that is free of the restrictions imposed by the underlying physical system. Thus, the motivation of decomposition is to set control procedures easily in order to generate large entangled states and to design specialized dedicated quantum gates. They are potential applications that properly bypass the general induced superposition generated by physical dynamics.
We study the entanglement of a pure state of a composite quantum system consisting of several subsystems with d levels each. It can be described by the Rényi–Ingarden–Urbanik entropy Sq of a decomposition of the state in a product basis, minimized over all local unitary transformations. In the case q = 0, this quantity becomes a function of the rank of the tensor representing the state, while in the limit q → ∞, the entropy becomes related to the overlap with the closest separable state and the geometric measure of entanglement. For any bipartite system, the entropy S1 coincides with the standard entanglement entropy. We analyze the distribution of the minimal entropy for random states of three- and four-qubit systems. In the former case, the distribution of the three-tangle is studied and some of its moments are evaluated, while in the latter case, we analyze the distribution of the hyperdeterminant. The behavior of the maximum overlap of a three-qudit system with the closest separable state is also investigated in the asymptotic limit.
Presented is a study of quantum entanglement from the perspective of the theory of quantum information dynamics. We consider pairwise entanglement and present an analytical development using joint ladder operators, the sum of two single-particle fermionic ladder operators. This approach allows us to write down analytical representations of quantum algorithms and to explore quantum entanglement as it is manifested in a system of qubits.;We present a topological representation of quantum logic that views entangled qubit spacetime histories (or qubit world lines) as a generalized braid, referred to as a super-braid. The crossing of world lines may be either classical or quantum mechanical in nature, and in the latter case most conveniently expressed with our analytical expressions for entangling quantum gates. at a quantum mechanical crossing, independent world lines can become entangled. We present quantum skein relations that allow complicated superbraids to be recursively reduced to alternate classical histories. If the superbraid is closed, then one can decompose the resulting superlink into an entangled superposition of classical links. Also, one can compute a superlink invariant, for example the Jones polynomial for the square root of a knot.;We present measurement-based quantum computing based on our joint number operators. We take expectation values of the joint number operators to determine kinetic-level variables describing the quantum information dynamics in the qubit system at the mesoscopic scale. We explore the issue of reversibility in quantum maps at this scale using a quantum Boltzmann equation. We then present an example of quantum information processing using a qubit system comprised of nuclear spins. We also discuss quantum propositions cast in terms of joint number operators.;We review the well known dynamical equations governing superfluidity, with a focus on self-consistent dynamics supporting quantum vortices in a Bose-Einstein condensate (BEC). Furthermore, we review the mutual vortex-vortex interaction and the consequent Kelvin wave instability. We derive an effective equation of motion for a Fermi condensate that is the basis of our qubit representation of superfluidity.;We then present our quantum lattice gas representation of a superfluid. We explore aspects of our model with two qubits per point, referred to as a Q2 model, particularly its usefulness for carrying out practical quantum fluid simulations. We find that it is perhaps the simplest yet most comprehensive model of superfluid dynamics. as a prime application of Q2, we explore the power-law regions in the energy spectrum of a condensate in the low-temperature limit. We achieved the largest quantum simulations to date of a BEC and, for the first time, Kolmogorov scaling in superfluids, a flow regime heretofore only obtainably by classical turbulence models.;Finally, we address the subject of turbulence regarding information conservation on the small scales (both mesoscopic and microscopic) underlying the flow dynamics on the large hydrodynamic (macroscopic) scale. We present a hydrodynamic-level momentum equation, in the form of a Navier-Stokes equation, as the basis for the energy spectrum of quantum turbulence at large scales. Quantum turbulence, in particular the representation of fluid eddies in terms of a coherent structure of polarized quantum vortices, offers a unique window into the heretofore intractable subject of energy cascades.
Bell gems naturally split dynamics information from SU(22d)→U(1)22d−1−1×SU(2)22d−1SU(2^{2d}) \rightarrow U(1)^{2^{2d-1}-1} \times SU(2)^{2^{2d-1}}SU(22d)→U(1)22d−1−1×SU(2)22d−1
Quantum Computation and Quantum Information are continuously growing research areas which are based on nature and resources of quantum mechanics, as superposition and entanglement. In its gate array version, the use of convenient and appropriate gates is essential. But while those proposed gates adopt convenient forms for computational algorithms, in the practice, their design depends on specific quantum systems and stuff being used. Gates design is restricted to properties and limitations of interactions and physical elements being involved, where Quantum Control plays a deep role. Quantum complexity of multipartite systems and their interactions requires a tight control to manipulate their quantum states, either local and non-local ones, but still a reducibility procedure should be addressed. This work shows how a general 2d2d2d-partite two level spin system in SU(2d)SU(2d)SU(2d) could be decomposed in 2n−12^{n-1}2n−1 subsystems on SU(2)SU(2)SU(2), letting establish control operations. In particular, it is shown that Bell gems basis is a set of natural states on which decomposition happen naturally under some interaction restrictions. Thus, alternating the direction of local interaction terms in the Hamiltonian, this procedure states a universal exchange semantics on those basis. The structure developed could be understood as a splitting of the 2d2d2d information channels into 22d−12^{2d-1}22d−1 pairs of 222 level information subsystems.