Lower bounds on the error probability of multiple quantum channel
discrimination by the Bures angle and the trace distance
- URL: http://arxiv.org/abs/2107.03948v2
- Date: Mon, 1 Aug 2022 13:04:05 GMT
- Title: Lower bounds on the error probability of multiple quantum channel
discrimination by the Bures angle and the trace distance
- Authors: Ryo Ito and Ryuhei Mori
- Abstract summary: We derive the lower bounds of the error probability based on the triangle inequalities of the Bures angle and the trace distance.
We prove the optimality of Grover's search if the number of marked elements is fixed to some integer $ell$.
We also present several numerical results in which our lower bounds based on the trace distance outperform recently obtained lower bounds.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum channel discrimination is a fundamental problem in quantum
information science. In this study, we consider general quantum channel
discrimination problems, and derive the lower bounds of the error probability.
Our lower bounds are based on the triangle inequalities of the Bures angle and
the trace distance. As a consequence of the lower bound based on the Bures
angle, we prove the optimality of Grover's search if the number of marked
elements is fixed to some integer $\ell$. This result generalizes Zalka's
result for $\ell=1$. We also present several numerical results in which our
lower bounds based on the trace distance outperform recently obtained lower
bounds.
Related papers
- Lower Bounds on Error Exponents via a New Quantum Decoder [14.304623719903972]
We show new lower bounds on the error exponent on the classical-quantum and the entanglement-assisted channel coding problem.
Our bounds are expressed in terms of measured (for the one-shot bounds) and sandwiched (for the bounds) channel R'enyi mutual information of order between 1/2 and 1.
arXiv Detail & Related papers (2023-10-13T11:22:49Z) - Approximate degree lower bounds for oracle identification problems [19.001036556917818]
We introduce a framework for proving approximate degree lower bounds for certain oracle identification problems.
Our lower bounds are driven by randomized communication upper bounds for the greater-than and equality functions.
arXiv Detail & Related papers (2023-03-07T14:30:28Z) - Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
We study the problem of designing worst-case to average-case reductions for quantum algorithms.
We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
arXiv Detail & Related papers (2022-12-06T22:01:49Z) - Analytical bounds for non-asymptotic asymmetric state discrimination [0.0]
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.
arXiv Detail & Related papers (2022-07-21T18:21:04Z) - Computable lower bounds on the entanglement cost of quantum channels [8.37609145576126]
A class of lower bounds for the entanglement cost of any quantum state was recently introduced in [arXiv:2111.02438].
Here we extend their definitions to point-to-point quantum channels, establishing a lower bound for the quantum entanglement cost of any channel.
This leads to a bound that is computable as a semidefinite program and that can outperform previously known lower bounds.
arXiv Detail & Related papers (2022-01-23T13:05:36Z) - 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) - Excluding false negative error in certification of quantum channels [68.8204255655161]
This work focuses on the scenario when the false negative error cannot occur, even if it leads to the growth of the probability of false positive error.
We establish a condition when it is possible to exclude false negative error after a finite number of queries to the quantum channel in parallel.
arXiv Detail & Related papers (2021-06-04T09:41:11Z) - On Lower Bounds for Standard and Robust Gaussian Process Bandit
Optimization [55.937424268654645]
We consider algorithm-independent lower bounds for the problem of black-box optimization of functions having a bounded norm.
We provide a novel proof technique for deriving lower bounds on the regret, with benefits including simplicity, versatility, and an improved dependence on the error probability.
arXiv Detail & Related papers (2020-08-20T03:48:14Z) - Discrimination of Ohmic thermal baths by quantum dephasing probes [68.8204255655161]
We evaluate the minimum error probability achievable by three different kinds of quantum probes, namely a qubit, a qutrit and a quantum register made of two qubits.
A qutrit probe outperforms a qubit one in the discrimination task, whereas a register made of two qubits does not offer any advantage.
arXiv Detail & Related papers (2020-08-06T08:51:51Z) - Ultimate limits for multiple quantum channel discrimination [0.966840768820136]
This paper studies the problem of hypothesis testing with quantum channels.
We establish a lower limit for the ultimate error probability affecting the discrimination of an arbitrary number of quantum channels.
We also show that this lower bound is achievable when the channels have certain symmetries.
arXiv Detail & Related papers (2020-07-29T03:08:48Z) - Boundaries of quantum supremacy via random circuit sampling [69.16452769334367]
Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling.
We examine the constraints of the observed quantum runtime advantage in a larger number of qubits and gates.
arXiv Detail & Related papers (2020-05-05T20:11:53Z)
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.