Stochastic approximate state conversion for entanglement and general quantum resource theories

• URL: http://arxiv.org/abs/2111.12646v3
• Date: Tue, 9 Apr 2024 13:16:30 GMT
• Title: Stochastic approximate state conversion for entanglement and general quantum resource theories
• Authors: Tulja Varun Kondra, Chandan Datta, Alexander Streltsov,
• Abstract summary: An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
• Score: 41.94295877935867
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum resource theories provide a mathematically rigorous way of understanding the nature of various quantum resources. An important problem in any quantum resource theory is to determine how quantum states can be converted into each other within the physical constraints of the theory. The standard approach to this problem is to study approximate or probabilistic transformations. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. Here, we investigate this intermediate regime, providing limits on both, the fidelity and the probability of state transitions. We derive limitations on the transformations, which are valid in all quantum resource theories, by providing bounds on the maximal transformation fidelity for a given transformation probability. As an application, we show that these bounds imply an upper bound on the asymptotic rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels, which goes beyond the previously known bounds of channel manipulations. Furthermore, we completely solve the question of stochastic-approximate state conversion via local operations and classical communication in the following two cases: (i) Both initial and target states are pure bipartite entangled states of arbitrary dimensions. (ii) The target state is a two-qubit entangled state and the initial state is a pure bipartite state.

Related papers

• A solution of the generalised quantum Stein's lemma [6.1642231492615345]
  We prove that the Stein exponent associated with entanglement testing equals the regularised relative entropy of entanglement. As a by-product, we prove that the same Stein exponent can also be achieved when the null hypothesis is only approximately i.i.d.
  arXiv  Detail & Related papers  (2024-08-12T18:00:01Z)
• Quantum Speed Limits for Implementation of Unitary Transformations [0.0]
  We provide bounds on the speed limit of quantum evolution by unitary operators in arbitrary dimensions. We will discuss the application of these bounds in several classes of transformations that are of interest to quantum information processing.
  arXiv  Detail & Related papers  (2024-06-06T11:17:21Z)
• 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)
• Is there a finite complete set of monotones in any quantum resource theory? [39.58317527488534]
  We show that there does not exist a finite set of resource monotones which completely determines all state transformations. We show that totally ordered theories allow for free transformations between all pure states.
  arXiv  Detail & Related papers  (2022-12-05T18:28:36Z)
• Real quantum operations and state transformations [44.99833362998488]
  Resource theory of imaginarity provides a useful framework to understand the role of complex numbers. In the first part of this article, we study the properties of real'' (quantum) operations in single-party and bipartite settings. In the second part of this article, we focus on the problem of single copy state transformation via real quantum operations.
  arXiv  Detail & Related papers  (2022-10-28T01:08:16Z)
• Tight constraints on probabilistic convertibility of quantum states [0.0]
  Two general approaches to characterising the manipulation of quantum states by means of probabilistic protocols constrained by the limitations of some quantum resource theory. First, we give a general necessary condition for the existence of a physical transformation between quantum states, obtained using a recently introduced resource monotone based on the Hilbert projective metric. We show it to tightly characterise single-shot probabilistic distillation in broad types of resource theories, allowing an exact analysis of the trade-offs between the probabilities and errors in distilling maximally resourceful states.
  arXiv  Detail & Related papers  (2021-12-21T16:14:55Z)
• 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)
• Gaussian conversion protocols for cubic phase state generation [104.23865519192793]
  Universal quantum computing with continuous variables requires non-Gaussian resources. The cubic phase state is a non-Gaussian state whose experimental implementation has so far remained elusive. We introduce two protocols that allow for the conversion of a non-Gaussian state to a cubic phase state.
  arXiv  Detail & Related papers  (2020-07-07T09:19:49Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

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.