Local unitary decomposition of tripartite arbitrary leveled qudit stabilizer states into $p$-level-qudit EPR and GHZ state

• URL: http://arxiv.org/abs/2507.09416v1
• Date: Sat, 12 Jul 2025 22:51:08 GMT
• Title: Local unitary decomposition of tripartite arbitrary leveled qudit stabilizer states into $p$-level-qudit EPR and GHZ state
• Authors: Yat Wong, Liang Jiang,
• Abstract summary: We study the entanglement structure of tripartite stabilizer states on $N$ qudits of dimension $D$, distributed across parties $A$, $B$, and $C$, under arbitrary local unitaries.
• Score: 2.165197150310128
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the entanglement structure of tripartite stabilizer states on $N$ qudits of dimension $D$, distributed across parties $A$, $B$, and $C$, under arbitrary local unitaries. Prior work by Bravyi et al. and Looi et al. showed that qubit and squarefree qudit stabilizer states can be transformed via local Clifford unitaries into tensor products of GHZ states, EPR pairs, and unentangled qudits [arXiv:quant-ph/0504208, arXiv:1107.1761]. We generalize this to arbitrary integer $D$ by introducing local unitaries beyond the Clifford group, enabling decomposition of prime-power qudit stabilizer states into $p$-level GHZ states, EPR pairs, and unentangled qudits. Our algorithm leverages subsystem phase matrices to characterize entanglement and applies to quantum protocols requiring efficient entanglement distribution.

Related papers

• General detectability measure [53.64687146666141]
  Distinguishing resource states from resource-free states is a fundamental task in quantum information.<n>We derived the optimal exponential decay rate of the failure probability for detecting a given $n$-tensor product state.
  arXiv  Detail & Related papers  (2025-01-16T05:39:22Z)
• Enhancing Quantum State Reconstruction with Structured Classical Shadows [22.432806329828782]
  We introduce a projected classical shadow (PCS) method with guaranteed performance for QST based on Haar-random projective measurements.<n>PCS extends the standard CS method by incorporating a projection step onto the target subspace.<n>For matrix product operator states, we demonstrate that the PCS method can recover the ground-truth state with $O(n2)$ total state copies.
  arXiv  Detail & Related papers  (2025-01-06T17:09:38Z)
• LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations [0.025206105035672277]
  We generalize the proof of stability of topological order, due to Bravyi, Hastings and Michalakis, to Hamiltonians corresponding to low-density parity check codes. We show that LDPC codes very generally define stable gapped quantum phases, even in the non-Euclidean setting.
  arXiv  Detail & Related papers  (2024-11-04T18:52:44Z)
• Exploiting Exogenous Structure for Sample-Efficient Reinforcement Learning [44.17068570786194]
  We study Exo-MDPs, a structured class of Markov Decision Processes (MDPs)<n> Exogenous states evolve independently of the agent's actions, while endogenous states evolve deterministically based on both state components and actions.<n> Exo-MDPs are useful for applications including inventory control, portfolio management, and ride-sharing.
  arXiv  Detail & Related papers  (2024-09-22T18:45:38Z)
• Superdense Coding and Stabiliser Codes with Ising-coupled Entanglement [0.0]
  A new class of quantum states is introduced by demanding that the computational measurement statistics approach the Boltzmann distribution of higher-order strongly coupled Ising models. The states, referred to as $n$-coupled states, are superpositions of even or odd parity $n$-qubit states, generalize Bell states, and form an orthonormal basis for the $n$-qubit Hilbert space.
  arXiv  Detail & Related papers  (2024-04-09T16:54:34Z)
• The role of shared randomness in quantum state certification with unentangled measurements [36.19846254657676]
  We study quantum state certification using unentangled quantum measurements. $Theta(d2/varepsilon2)$ copies are necessary and sufficient for state certification. We develop a unified lower bound framework for both fixed and randomized measurements.
  arXiv  Detail & Related papers  (2024-01-17T23:44:52Z)
• Sufficient condition for universal quantum computation using bosonic circuits [44.99833362998488]
  We focus on promoting circuits that are otherwise simulatable to computational universality. We first introduce a general framework for mapping a continuous-variable state into a qubit state. We then cast existing maps into this framework, including the modular and stabilizer subsystem decompositions.
  arXiv  Detail & Related papers  (2023-09-14T16:15:14Z)
• Learning t-doped stabilizer states [0.0]
  We present a learning algorithm aimed at learning states obtained from computational basis states by Clifford circuits doped with a finite number $t$ of $T$-gates. The algorithm learns an exact tomographic description of $t$-doped stabilizer states in terms of Pauli observables.
  arXiv  Detail & Related papers  (2023-05-24T17:57:10Z)
• Local predictability and coherence versus distributed entanglement in entanglement swapping from partially entangled pure states [0.0]
  We study the relation between $P$, $C$ and the distributed entanglement in the entanglement swapping protocol (ESP) We use IBM's quantum computers to verify some instances of these general theoretical results.
  arXiv  Detail & Related papers  (2022-11-14T17:05:50Z)
• Transformations of Stabilizer States in Quantum Networks [0.0]
  We study party-local Clifford transformations among stabilizer states. Traits arise as a physically motivated extension of local operations in quantum networks. We show that PLC transformations among graph states are equivalent to a generalization of the well-known local complementation.
  arXiv  Detail & Related papers  (2022-03-08T17:04:58Z)
• Constructions of $k$-uniform states from mixed orthogonal arrays [18.378398718548016]
  We study $k$-uniform states in heterogeneous systems whose local dimensions are mixed. We present two constructions of $2$-uniform states in heterogeneous systems. We show that some $k$-uniform bases can not be distinguished by local operations and classical communications.
  arXiv  Detail & Related papers  (2020-06-07T08:35:22Z)
• Communication-Efficient Distributed SVD via Local Power Iterations [33.95814240875917]
  We develop an algorithm that we call textttLocalPower for improving communication efficiency. We conduct experiments to demonstrate the effectiveness of textttLocalPower
  arXiv  Detail & Related papers  (2020-02-19T05:58:23Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.