Schmidt Decomposition of Multipartite States

• URL: http://arxiv.org/abs/2411.02473v1
• Date: Mon, 04 Nov 2024 17:01:28 GMT
• Title: Schmidt Decomposition of Multipartite States
• Authors: Mithilesh Kumar,
• Abstract summary: Schmidt decomposition of a quantum state has a lot of properties useful in the study of entanglement. We obtain necessary and sufficient conditions for the existence of Schmidt decompositions of multipartite states. We provide an efficient algorithm to obtain the decomposition for a Schmidt decomposable multipartite state.
• Score: 0.0
• License:
• Abstract: Quantum states can be written in infinitely many ways depending on the choices of basis. Schmidt decomposition of a quantum state has a lot of properties useful in the study of entanglement. All bipartite states admit Schmidt decomposition, but this does not extend to multipartite systems. We obtain necessary and sufficient conditions for the existence of Schmidt decompositions of multipartite states. Moreover, we provide an efficient algorithm to obtain the decomposition for a Schmidt decomposable multipartite state.

Related papers

• On properties of Schmidt Decomposition [0.0]
  We review properties of bipartite Schmidt decompositions and study which of them extend to multipartite states. We show that it is NP-complete to partition a multipartite state that attains the highest Schmidt number.
  arXiv  Detail & Related papers  (2024-11-08T17:03:22Z)
• Entanglement distribution in pure non-Gaussian tripartite states: a Schmidt decomposition approach [0.0]
  We study entanglement in a system of three coupled quantum harmonic oscillators. We use the Schmidt decomposition to analyze how the entanglement is distributed among the three subsystems.
  arXiv  Detail & Related papers  (2024-09-27T17:15:15Z)
• Families of Schmidt-number witnesses for high dimensional quantum states [0.9790236766474201]
  Schmidt number is a quantity on the dimension entanglement of a bipartite state. We show the distance between a bipartite state and the set of states with Schmidt number less than k.
  arXiv  Detail & Related papers  (2024-03-01T03:25:53Z)
• High Schmidt number concentration in quantum bound entangled states [0.135975510645475]
  We introduce efficient analytical tools for calculating the Schmidt number for a class of bipartite states. We construct a Schmidt number three PPT state in five dimensional systems and a family of states with a Schmidt number of $(d+1)/2$ for odd $d$-dimensional systems.
  arXiv  Detail & Related papers  (2024-02-20T12:33:57Z)
• The Schmidt rank for the commuting operator framework [58.720142291102135]
  The Schmidt rank is a measure for the entanglement dimension of a pure bipartite state. We generalize the Schmidt rank to the commuting operator framework. We analyze bipartite states and compute the Schmidt rank in several examples.
  arXiv  Detail & Related papers  (2023-07-21T14:37:33Z)
• Multipartite entanglement theory with entanglement-nonincreasing operations [91.3755431537592]
  We extend the resource theory of entanglement for multipartite systems beyond the standard framework of local operations and classical communication. We demonstrate that in this adjusted framework, the transformation rates between multipartite states are fundamentally dictated by the bipartite entanglement entropies of the respective quantum states.
  arXiv  Detail & Related papers  (2023-05-30T12:53:56Z)
• Tensor Network Efficiently Representing Schmidt Decomposition of Quantum Many-Body States [6.941759751222217]
  Schmidt network state (Schmidt TNS) efficiently represents the Schmidt decomposition of finite- and even infinite-size quantum states. We show that the MPS encoding the Schmidt coefficients is weakly entangled even when the entanglement entropy of the state is strong. This justifies the efficiency of using MPS to encode the Schmidt coefficients, and promises an exponential speedup on the full-state sampling tasks.
  arXiv  Detail & Related papers  (2022-10-15T02:34:43Z)
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver [89.80359585967642]
  Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
  arXiv  Detail & Related papers  (2022-03-15T09:46:45Z)
• Quantum Discrimination of Two Noisy Displaced Number States [68.2727599930504]
  We first consider the quantum discrimination of two noiseless displaced number states. We then address the problem of discriminating between two noisy displaced number states.
  arXiv  Detail & Related papers  (2020-12-09T16:56:16Z)
• Genuine Network Multipartite Entanglement [62.997667081978825]
  We argue that a source capable of distributing bipartite entanglement can, by itself, generate genuine $k$-partite entangled states for any $k$. We provide analytic and numerical witnesses of genuine network entanglement, and we reinterpret many past quantum experiments as demonstrations of this feature.
  arXiv  Detail & Related papers  (2020-02-07T13:26:00Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.