The complexity of entanglement embezzlement

• URL: http://arxiv.org/abs/2410.19051v1
• Date: Thu, 24 Oct 2024 18:00:33 GMT
• Title: The complexity of entanglement embezzlement
• Authors: Tal Schwartzman,
• Abstract summary: We study the circuit complexity of embezzlement using sequences of states that enable arbitrary precision for the process. Our results imply that circuit complexity acts as a physical obstruction to perfect embezzlement.
• Score: 0.0
• License:
• Abstract: Embezzlement of entanglement is the counterintuitive process in which entanglement is extracted from a resource system using local unitary operations, with almost no detectable change in the resource's state. It has recently been argued that any state of a relativistic quantum field theory can serve as a resource for perfect embezzlement. We study the circuit complexity of embezzlement, using sequences of states that enable arbitrary precision for the process, commonly called universal embezzling families. In addition, we argue that this approach provides a well-defined model for the complexity of embezzlement from quantum field theories. Our results show that, under fairly general assumptions, lower bounds on the complexity increase with the precision of the process or embezzled entanglement, diverging as these become infinite. Consequently, the findings imply that circuit complexity acts as a physical obstruction to perfect embezzlement. Supplementary to the main results, we derive lower bounds for common models of circuit complexity for state preparation, based on the difference between the Schatten norms of the initial and final states.

Related papers

• Complexity-constrained quantum thermodynamics [0.2796197251957244]
  We show that the minimum thermodynamic work required to reset an arbitrary state, via a complexity-constrained process, is quantified by the state's complexity entropy. The complexity entropy quantifies a trade-off between the work cost and complexity cost of resetting a state. We identify information-theoretic applications of the complexity entropy.
  arXiv  Detail & Related papers  (2024-03-07T19:00:01Z)
• The Complexity of Being Entangled [0.0]
  Nielsen's approach to quantum state complexity relates the minimal number of quantum gates required to prepare a state to the length of geodesics computed with a certain norm on the manifold of unitary transformations. For a bipartite system, we investigate binding complexity, which corresponds to norms in which gates acting on a single subsystem are free of cost.
  arXiv  Detail & Related papers  (2023-11-07T19:00:02Z)
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling [49.1574468325115]
  A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient. We develop a single- parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics. We establish that scaling predictions are matched by a privileged process, and serve as bounds for other dynamical scrambling scenarios, allowing one to quantify inefficient or incomplete scrambling on all timescales.
  arXiv  Detail & Related papers  (2023-10-17T15:41:50Z)
• An Analysis of On-the-fly Determinization of Finite-state Automata [65.268245109828]
  We establish an abstraction of on-the-fly determinization of finite-state automata and demonstrate how it can be applied to bound the automatons. A special case of our findings is that automata with many non-deterministic transitions almost always admit a determinization of complexity.
  arXiv  Detail & Related papers  (2023-08-27T11:51:27Z)
• Catalytic and asymptotic equivalence for quantum entanglement [68.8204255655161]
  Many-copy entanglement manipulation procedures allow for highly entangled pure states from noisy states. We show that using an entangled catalyst cannot enhance the singlet distillation rate of a distillable quantum state. Our findings provide a comprehensive understanding of the capabilities and limitations of both catalytic and state transformations of entangled states.
  arXiv  Detail & Related papers  (2023-05-05T12:57:59Z)
• Circuit Complexity through phase transitions: consequences in quantum state preparation [0.0]
  We analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition.
  arXiv  Detail & Related papers  (2023-01-11T19:00:10Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Bounds on quantum evolution complexity via lattice cryptography [0.0]
  We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries.
  arXiv  Detail & Related papers  (2022-02-28T16:20:10Z)
• Detailed Account of Complexity for Implementation of Some Gate-Based Quantum Algorithms [55.41644538483948]
  In particular, some steps of the implementation, as state preparation and readout processes, can surpass the complexity aspects of the algorithm itself. We present the complexity involved in the full implementation of quantum algorithms for solving linear systems of equations and linear system of differential equations.
  arXiv  Detail & Related papers  (2021-06-23T16:33:33Z)
• On estimating the entropy of shallow circuit outputs [49.1574468325115]
  Estimating the entropy of probability distributions and quantum states is a fundamental task in information processing. We show that entropy estimation for distributions or states produced by either log-depth circuits or constant-depth circuits with gates of bounded fan-in and unbounded fan-out is at least as hard as the Learning with Errors problem.
  arXiv  Detail & Related papers  (2020-02-27T15:32:08Z)
• Aspects of The First Law of Complexity [0.0]
  We investigate the first law of complexity proposed in arXiv:1903.04511, i.e., the variation of complexity when the target state is perturbed. Based on Nielsen's geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit.
  arXiv  Detail & Related papers  (2020-02-13T21:15:57Z)

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.