Limitations of Classically-Simulable Measurements for Quantum State
Discrimination
- URL: http://arxiv.org/abs/2310.11323v1
- Date: Tue, 17 Oct 2023 15:01:54 GMT
- Title: Limitations of Classically-Simulable Measurements for Quantum State
Discrimination
- Authors: Chengkai Zhu, Zhiping Liu, Chenghong Zhu, Xin Wang
- Abstract summary: We investigate the limitations of classically-simulable measurements, specifically POVMs with positive discrete Wigner functions.
Our results reveal similarities and distinctions between the quantum resource theory of magic states and entanglement in quantum state discrimination.
- Score: 7.749391145337816
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In the realm of fault-tolerant quantum computing, stabilizer operations play
a pivotal role, characterized by their remarkable efficiency in classical
simulation. This efficiency sets them apart from non-stabilizer operations
within the computational resource theory. In this work, we investigate the
limitations of classically-simulable measurements, specifically POVMs with
positive discrete Wigner functions which include all stabilizer measurements,
in distinguishing quantum states. We demonstrate that any pure magic state and
its orthogonal complement of odd prime dimension cannot be unambiguously
distinguished by POVMs with positive discrete Wigner functions, regardless of
how many copies of the states are supplied. We also give the asymptotic error
probability for distinguishing the Strange state and its orthogonal complement.
Moreover, we prove that every set of orthogonal pure stabilizer states can be
unambiguously distinguished via POVMs with positive discrete Wigner functions,
which is different from the existence of an unextendible product basis in
entanglement theory. Our results reveal intrinsic similarities and distinctions
between the quantum resource theory of magic states and entanglement in quantum
state discrimination. The results emphasize the inherent limitations of
classically-simulable measurements and contribute to a deeper understanding of
the quantum-classical boundary.
Related papers
- Efficient classical simulation of quantum computation beyond Wigner positivity [0.0]
We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits.
arXiv Detail & Related papers (2024-07-14T22:25:13Z) - Embezzling entanglement from quantum fields [41.94295877935867]
Embezzlement of entanglement refers to the counterintuitive possibility of extracting entangled quantum states from a reference state of an auxiliary system.
We uncover a deep connection between the operational task of embezzling entanglement and the mathematical classification of von Neumann algebras.
arXiv Detail & Related papers (2024-01-14T13:58:32Z) - Magic in generalized Rokhsar-Kivelson wavefunctions [0.0]
We study magic, as quantified by the stabilizer Renyi entropy, in a class of models known as generalized Rokhsar-Kive systems.
We find that the maximum of the SRE generically occurs at a cusp away from the quantum critical point, where the derivative suddenly changes sign.
arXiv Detail & Related papers (2023-11-14T19:00:05Z) - Variational quantum simulation using non-Gaussian continuous-variable
systems [39.58317527488534]
We present a continuous-variable variational quantum eigensolver compatible with state-of-the-art photonic technology.
The framework we introduce allows us to compare discrete and continuous variable systems without introducing a truncation of the Hilbert space.
arXiv Detail & Related papers (2023-10-24T15:20:07Z) - Indistinguishability of identical bosons from a quantum information
theory perspective [0.0]
We present a general theory of indistinguishability of identical bosons in experiments consisting of passive linear optics followed by particle number detection.
We identify the expectation value of the projector onto the $N$-particle symmetric subspace as an operationally meaningful measure of indistinguishability.
We show that these states are diagonal in the computational basis up to a permutationally invariant unitary.
arXiv Detail & Related papers (2023-07-13T08:45:51Z) - 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) - Quasi-probabilities of work and heat in an open quantum system [0.0]
We discuss an approach to determine averages of the work, dissipated heat and variation of internal energy of an open quantum system driven by an external classical field.
We obtain a quasi-characteristic function and a quasi-probability density function for the corresponding observables.
We use this feature to show that in the limit of strong dissipation, the quantum features vanish and interpret this as the emergence of the classical limit of the energy exchange process.
arXiv Detail & Related papers (2021-10-12T06:55:39Z) - On the properties of the asymptotic incompatibility measure in
multiparameter quantum estimation [62.997667081978825]
Incompatibility (AI) is a measure which quantifies the difference between the Holevo and the SLD scalar bounds.
We show that the maximum amount of AI is attainable only for quantum statistical models characterized by a purity larger than $mu_sf min = 1/(d-1)$.
arXiv Detail & Related papers (2021-07-28T15:16:37Z) - Bose-Einstein condensate soliton qubit states for metrological
applications [58.720142291102135]
We propose novel quantum metrology applications with two soliton qubit states.
Phase space analysis, in terms of population imbalance - phase difference variables, is also performed to demonstrate macroscopic quantum self-trapping regimes.
arXiv Detail & Related papers (2020-11-26T09:05:06Z) - Extremal quantum states [0.41998444721319206]
We peruse quantumness from a variety of viewpoints, concentrating on phase-space formulations.
The symmetry-transcending properties of the Husimi $Q$ function make it our basic tool.
We use these quantities to formulate extremal principles and determine in this way which states are the most and least "quantum"
arXiv Detail & Related papers (2020-10-09T18:00:02Z) - Efficient simulatability of continuous-variable circuits with large
Wigner negativity [62.997667081978825]
Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures.
We identify vast families of circuits that display large, possibly unbounded, Wigner negativity, and yet are classically efficiently simulatable.
We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.
arXiv Detail & Related papers (2020-05-25T11:03:42Z)
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.