Analytical bounds for non-asymptotic asymmetric state discrimination
- URL: http://arxiv.org/abs/2207.10699v3
- Date: Tue, 21 Nov 2023 19:20:29 GMT
- Title: Analytical bounds for non-asymptotic asymmetric state discrimination
- Authors: Jason L. Pereira, Leonardo Banchi, Stefano Pirandola
- Abstract summary: Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other.
We give explicit expressions bounding the set of achievable errors using the trace norm, the fidelity, and the quantum Chernoff bound.
Unlike bounds, our bounds give error values instead of exponents, so can give more precise results when applied to finite-copy state discrimination problems.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Two types of errors can occur when discriminating pairs of quantum states.
Asymmetric state discrimination involves minimizing the probability of one type
of error, subject to a constraint on the other. We give explicit expressions
bounding the set of achievable errors, using the trace norm, the fidelity, and
the quantum Chernoff bound. The upper bound is asymptotically tight and the
lower bound is exact for pure states. Unlike asymptotic bounds, our bounds give
error values instead of exponents, so can give more precise results when
applied to finite-copy state discrimination problems.
Related papers
- Barycentric bounds on the error exponents of quantum hypothesis exclusion [7.812210699650153]
We study the optimal error probability of quantum state exclusion from an information-theoretic perspective.
We extend our analysis to the more complicated task of quantum channel exclusion.
arXiv Detail & Related papers (2024-07-18T17:27:36Z) - Quantum hypothesis testing between qubit states with parity [7.586817293358619]
Two types of decision errors in a Quantum hypothesis testing (QHT) can occur.
We show that the minimal probability of type-II error occurs when the null hypothesis is accepted when it is false.
We replace one of the two pure states with a maximally mixed state, and similarly characterize the behavior of the minimal probability of type-II error.
arXiv Detail & Related papers (2022-12-04T08:30:25Z) - Local approximation for perfect discrimination of quantum states [0.0]
Quantum state discrimination involves identifying a given state out of a set of possible states.
In the case of multipartite systems when the parties are constrained to use multiple rounds of local operations and classical communication (LOCC), perfect state discrimination is often impossible.
arXiv Detail & Related papers (2022-07-07T21:12:47Z) - Experimental demonstration of optimal unambiguous two-out-of-four
quantum state elimination [52.77024349608834]
A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements.
Here we implement a quantum state elimination measurement which unambiguously rules out two of four pure, non-orthogonal quantum states.
arXiv Detail & Related papers (2022-06-30T18:00:01Z) - Super-exponential distinguishability of correlated quantum states [0.0]
A super-exponential decrease for both types of error probabilities is only possible in the trivial case.
We show that a qualitatively different behaviour can occur when there is correlation between the samples.
arXiv Detail & Related papers (2022-03-30T17:49:19Z) - Optimal variance-reduced stochastic approximation in Banach spaces [114.8734960258221]
We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space.
We establish non-asymptotic bounds for both the operator defect and the estimation error.
arXiv Detail & Related papers (2022-01-21T02:46:57Z) - Tight Exponential Analysis for Smoothing the Max-Relative Entropy and
for Quantum Privacy Amplification [56.61325554836984]
The max-relative entropy together with its smoothed version is a basic tool in quantum information theory.
We derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance.
arXiv Detail & Related papers (2021-11-01T16:35:41Z) - Spectral clustering under degree heterogeneity: a case for the random
walk Laplacian [83.79286663107845]
This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree.
In the special case of a degree-corrected block model, the embedding concentrates about K distinct points, representing communities.
arXiv Detail & Related papers (2021-05-03T16:36:27Z) - Quantum Discrimination of Two Noisy Displaced Number States [68.2727599930504]
We first consider the quantum discrimination of two noiseless displaced number states.
We then address the problem of discriminating between two noisy displaced number states.
arXiv Detail & Related papers (2020-12-09T16:56:16Z) - 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) - Asymptotic relative submajorization of multiple-state boxes [0.0]
Pairs of states are the basic objects in the resource theory of asymmetric distinguishability (Wang and Wilde, 2019), where free operations are arbitrary quantum channels that are applied to both states.
We consider boxes of a fixed finite number of states and study an extension of the relative submajorization preorder to such objects.
This preorder characterizes error probabilities in the case of testing a composite null hypothesis against a simple alternative hypothesis, as well as certain error probabilities in state discrimination.
arXiv Detail & Related papers (2020-07-22T08:29:52Z)
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.