A general theory of comparison of quantum channels (and beyond)

• URL: http://arxiv.org/abs/2002.04240v2
• Date: Wed, 17 Feb 2021 09:21:45 GMT
• Title: A general theory of comparison of quantum channels (and beyond)
• Authors: Anna Jen\v{c}ov\'a
• Abstract summary: We show that approximate simulability can be characterized by comparing outcome probabilities in certain tests. Results are applied to several specific cases of simulability of quantum channels.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a general theory of comparison of quantum channels, concerning with the question of simulability or approximate simulability of a given quantum channel by allowed transformations of another given channel. We introduce a modification of conditional min-entropies, with respect to the set F of allowed transformations, and show that under some conditions on F, these quantities characterize approximate simulability. If F is the set of free superchannels in a quantum resource theory of processes, the modified conditional min-entropies form a complete set of resource monotones. If the transformations in F consist of a preprocessing and a postprocessing of specified forms, approximate simulability is also characterized in terms of success probabilities in certain guessing games, where a preprocessing of a given form can be chosen and the measurements are restricted. These results are applied to several specific cases of simulability of quantum channels, including postprocessings, preprocessings and processing of bipartite channels by LOCC superchannels and by partial superchannels, as well as simulability of sets of quantum measurements. These questions are first studied in a general setting that is an extension of the framework of general probabilistic theories (GPT), suitable for dealing with channels. Here we prove a general theorem that shows that approximate simulability can be characterized by comparing outcome probabilities in certain tests. This result is inspired by the classical Le Cam randomization criterion for statistical experiments and contains its finite dimensional version as a special case.

Related papers

• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• Studying Stabilizer de Finetti Theorems and Possible Applications in Quantum Information Processing [0.0]
  In quantum information theory, if a quantum state is invariant under permutations of its subsystems, its marginal can be approximated by a mixture of powers of a state on a single subsystem. Recently, it has been discovered that a similar observation can be made for a larger symmetry group than permutations. This naturally raises the question if similar improvements could be found for applications where this symmetry appears.
  arXiv  Detail & Related papers  (2024-03-15T17:55:12Z)
• Random covariant quantum channels [2.9741863650371805]
  Group symmetries inherent in quantum channels often make them tractable. We introduce natural probability distributions for covariant quantum channels. We discuss the threshold phenomenon for positive partial transpose and entanglement breaking properties.
  arXiv  Detail & Related papers  (2024-03-06T12:39:30Z)
• Normal quantum channels and Markovian correlated two-qubit quantum errors [77.34726150561087]
  We study general normally'' distributed random unitary transformations. On the one hand, a normal distribution induces a unital quantum channel. On the other hand, the diffusive random walk defines a unital quantum process.
  arXiv  Detail & Related papers  (2023-07-25T15:33:28Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Simulating all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories [0.0]
  Non-signalling quantum channels may be simulated via affine combinations of local operations in bipartite scenarios. We show that such useful quasi-stochastic characterizations of channels may be unified and applied to the broader class of multipartite non-signalling channels.
  arXiv  Detail & Related papers  (2022-04-22T11:16:18Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  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.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Generating random quantum channels [1.0499611180329802]
  Several techniques of generating random quantum channels, which act on the set of $d$-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show under which conditions they become mathematically equivalent. Additional results focus on the spectral gap and other spectral properties of random quantum channels and their invariant states.
  arXiv  Detail & Related papers  (2020-11-05T17:35:30Z)
• Theory of Ergodic Quantum Processes [0.0]
  We consider general ergodic sequences of quantum channels with arbitrary correlations and non-negligible decoherence. We compute the entanglement spectrum across any cut, by which the bipartite entanglement entropy can be computed exactly. Other physical implications of our results are that most Floquet phases of matter are metastable and that noisy random circuits in the large depth limit will be trivial as far as their quantum entanglement is concerned.
  arXiv  Detail & Related papers  (2020-04-29T18:00:03Z)
• 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)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

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.