Reconstructing the whole from its parts

• URL: http://arxiv.org/abs/2209.14154v1
• Date: Wed, 28 Sep 2022 15:04:22 GMT
• Title: Reconstructing the whole from its parts
• Authors: Daniel Uzc\'ategui Contreras, Dardo Goyeneche
• Abstract summary: We analytically determine global quantum states from a wide class of self-consistent marginal reductions in any multipartite scenario. We show that any self-consistent set of multipartite marginal reductions is compatible with the existence of a global quantum state, after passing through a depolarizing channel.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum marginal problem consists in deciding whether a given set of marginal reductions is compatible with the existence of a global quantum state or not. In this work, we formulate the problem from the perspective of dynamical systems theory and study its advantages with respect to the standard approach. The introduced formalism allows us to analytically determine global quantum states from a wide class of self-consistent marginal reductions in any multipartite scenario. In particular, we show that any self-consistent set of multipartite marginal reductions is compatible with the existence of a global quantum state, after passing through a depolarizing channel. This result reveals that the complexity associated to the marginal problem can be drastically reduced when restricting the attention to sufficiently mixed marginals. We also formulate the marginal problem in a compressed way, in the sense that the total number of scalar constraints is smaller than the one required by the standard approach. This fact suggests an exponential speedup in runtime when considering semi-definite programming techniques to solve it, in both classical and quantum algorithms. Finally, we reconstruct $n$-qubit quantum states from all the $\binom{n}{k}$ marginal reductions to $k$ parties, generated from randomly chosen mixed states. Numerical simulations reveal that the fraction of cases where we can find a global state equals 1 when $5\leq n\leq12$ and $\lfloor(n-1)/\sqrt{2}\rfloor\leq k\leq n-1$, where $\lfloor\cdot\rfloor$ denotes the floor function.

Related papers

• Quasi-quantum states and the quasi-quantum PCP theorem [0.21485350418225244]
  We show that solving the $k$-local Hamiltonian over the quasi-quantum states is equivalent to optimizing a distribution of assignment over a classical $k$-local CSP. Our main result is a PCP theorem for the $k$-local Hamiltonian over the quasi-quantum states in the form of a hardness-of-approximation result.
  arXiv  Detail & Related papers  (2024-10-17T13:43:18Z)
• Quantum Error Suppression with Subgroup Stabilisation [3.4719087457636792]
  Quantum state purification is the functionality that, given multiple copies of an unknown state, outputs a state with increased purity. We propose an effective state purification gadget with a moderate quantum overhead by projecting $M$ noisy quantum inputs to their subspace. Our method, applied in every short evolution over $M$ redundant copies of noisy states, can suppress both coherent and errors by a factor of $1/M$, respectively.
  arXiv  Detail & Related papers  (2024-04-15T17:51:47Z)
• The Power of Unentangled Quantum Proofs with Non-negative Amplitudes [55.90795112399611]
  We study the power of unentangled quantum proofs with non-negative amplitudes, a class which we denote $textQMA+(2)$. In particular, we design global protocols for small set expansion, unique games, and PCP verification. We show that QMA(2) is equal to $textQMA+(2)$ provided the gap of the latter is a sufficiently large constant.
  arXiv  Detail & Related papers  (2024-02-29T01:35:46Z)
• Generating Entanglement by Quantum Resetting [0.0]
  We consider a closed quantum system subjected to Poissonian resetting with rate $r$ to its initial state. We show that quantum resetting provides a simple and effective mechanism to enhance entanglement between two parts of an interacting quantum system.
  arXiv  Detail & Related papers  (2023-07-14T17:12:08Z)
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees [0.0]
  We provide theoretical guarantees for efficient learning of quantum many-body states and their properties, with model-independent applications. Our results provide theoretical guarantees for efficient learning of quantum many-body states and their properties, with model-independent applications.
  arXiv  Detail & Related papers  (2023-04-10T02:22:36Z)
• Nonlocality under Computational Assumptions [51.020610614131186]
  A set of correlations is said to be nonlocal if it cannot be reproduced by spacelike-separated parties sharing randomness and performing local operations. We show that there exist (efficient) local producing measurements that cannot be reproduced through randomness and quantum-time computation.
  arXiv  Detail & Related papers  (2023-03-03T16:53:30Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Canonically consistent quantum master equation [68.8204255655161]
  We put forth a new class of quantum master equations that correctly reproduce the state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics.
  arXiv  Detail & Related papers  (2022-05-25T15:22:52Z)
• Random quantum circuits transform local noise into global white noise [118.18170052022323]
  We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially. If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
  arXiv  Detail & Related papers  (2021-11-29T19:26:28Z)
• Entanglement marginal problems [0.0]
  entanglement marginal problem consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. We propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals admitting a fully separable extension. Our results even extend to infinite systems, such as translation-invariant systems in 1D, as well as higher spatial dimensions with extra symmetries.
  arXiv  Detail & Related papers  (2020-06-16T10:48:56Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

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.