Using the Schmidt Decomposition to Determine Quantum Entanglement

• URL: http://arxiv.org/abs/2511.14648v1
• Date: Tue, 18 Nov 2025 16:40:23 GMT
• Title: Using the Schmidt Decomposition to Determine Quantum Entanglement
• Authors: Lane Boswell, Ying Cao,
• Abstract summary: Entanglement is at the very core of quantum information theory.<n>In quantum mechanics, particles can be in superposition, meaning they are in multiple different states at once.<n> Entanglement allows for the massive increase in computing power.
• Score: 4.015543785704653
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum information theory is a rapidly growing area of math and physics that combines two independent theories, quantum mechanics and information theory. Quantum entanglement is a concept that was first proposed in the EPR paradox. In quantum mechanics, particles can be in superposition, meaning they are in multiple different states at once. It is not until the particle is measured that it is forced into a single state. However, it is possible that particles can be tied to other particles, meaning that the measurement of one particle will determine the measurement of the other particle. Entanglement is at the very core of quantum information theory. It is one of the core pieces that allows for the massive increase in computing power. For this paper, we decided to focus on demonstrating the mathematical method (the Schmidt decomposition) for determining if a system is entangled, and a demonstration of quantum entanglement's use (quantum teleportation) as well as a quick look at how to extend the uses of the Schmidt decomposition.

Related papers

• Will we ever quantize the center of mass of macroscopic systems? A case for a Heisenberg cut in quantum mechanics [0.0]
  The concept of quantum particles derives from quantum field theory.<n>Wave mechanics can describe the center of mass of systems at or above the Planck scale.
  arXiv  Detail & Related papers  (2026-01-28T12:03:26Z)
• Counterfactuals in Macroscopic Quantum Physics: Irreversibility, Measurement and Locality [0.0]
  We argue that measurement, irreversibility and locality can all appear to challenge the universality of quantum theory.<n>We find novel features of quantum thermodynamics relating to irreversibility, information erasure and coherence.<n>This reveals new ways of characterising the quantum information stored in entanglement and quantum branching structure.
  arXiv  Detail & Related papers  (2025-05-28T20:14:17Z)
• The Quantum Ratio [0.0]
  The concept of the Quantum Ratio was born out of the efforts to find a simple but universal criterion if the center of mass behaves quantum mechanically or classically.<n>The ratio is defined as the ratio between the quantum fluctuation range, which is the spatial extension of the pure-state CM wave function, and the linear size of the body.<n>An important notion following from the introduction of quantum ratio is that the elementary particles (thus the electron and the photon) are quantum mechanical.
  arXiv  Detail & Related papers  (2025-02-17T14:15:36Z)
• The construction of quantum mechanics from electromagnetism. Part II: the Hydrogen atom [0.0]
  We extend the description to the hydrogen atom testing the correctness and accuracy of the general description.<n>We briefly discuss why the concept of isolation built in Schr"odinger's time evolution is not acceptable and how it immediately results in the well known measurement paradoxes of quantum mechanics.
  arXiv  Detail & Related papers  (2024-11-14T13:08:44Z)
• A Theory of Quantum Jumps [44.99833362998488]
  We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
  arXiv  Detail & Related papers  (2024-04-16T11:00:46Z)
• Schr\"odinger cat states of a 16-microgram mechanical oscillator [54.35850218188371]
  The superposition principle is one of the most fundamental principles of quantum mechanics. Here we demonstrate the preparation of a mechanical resonator with an effective mass of 16.2 micrograms in Schr"odinger cat states of motion. We show control over the size and phase of the superposition and investigate the decoherence dynamics of these states.
  arXiv  Detail & Related papers  (2022-11-01T13:29:44Z)
• Is there evidence for exponential quantum advantage in quantum chemistry? [45.33336180477751]
  The idea to use quantum mechanical devices to simulate other quantum systems is commonly ascribed to Feynman. It may be prudent to assume exponential speedups are not generically available for this problem.
  arXiv  Detail & Related papers  (2022-08-03T16:33:57Z)
• A Mechanical Implementation and Diagrammatic Calculation of Entangled Basis States [0.0]
  We give for the first time a diagrammatic calculational tool of quantum entanglement. When two or more particles are correlated in a certain way, no matter how far apart they are in space, their states remain correlated. Our results seem to advocate the idea that quantum entanglement generates the extra dimensions of the gravitational theory.
  arXiv  Detail & Related papers  (2021-12-20T00:31:48Z)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• The Time-Evolution of States in Quantum Mechanics [77.34726150561087]
  It is argued that the Schr"odinger equation does not yield a correct description of the quantum-mechanical time evolution of states of isolated (open) systems featuring events. A precise general law for the time evolution of states replacing the Schr"odinger equation is formulated within the so-called ETH-Approach to Quantum Mechanics.
  arXiv  Detail & Related papers  (2021-01-04T16:09:10Z)
• Operational Resource Theory of Imaginarity [48.7576911714538]
  We show that quantum states are easier to create and manipulate if they only have real elements. As an application, we show that imaginarity plays a crucial role for state discrimination.
  arXiv  Detail & Related papers  (2020-07-29T14:03:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.