The Trivial Bound of Entropic Uncertainty Relations
- URL: http://arxiv.org/abs/2208.00242v5
- Date: Thu, 19 Jan 2023 21:44:53 GMT
- Title: The Trivial Bound of Entropic Uncertainty Relations
- Authors: Minu J. Bae
- Abstract summary: Entropic uncertainty relations are underpinning to compute the quantitative security bound in quantum cryptographic applications.
This paper draws one case of the POVM-versioned standard entropic uncertainty relation yielding the trivial bound.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Entropic uncertainty relations are underpinning to compute the quantitative
security bound in quantum cryptographic applications, such as quantum random
number generation (QRNG) and quantum key distribution (QKD). All security
proofs derive a relation between the information accessible to the legitimate
group and the maximum knowledge that an adversary may have gained, Eve, which
exploits entropic uncertainty relations to lower bound Eve's uncertainty about
the raw key generated by one party, Alice. The standard entropic uncertainty
relations is to utilize the smooth min- and max-entropies to show these
cryptographic applications' security by computing the overlap of two
incompatible measurements or positive-operator valued measures (POVMs). This
paper draws one case of the POVM-versioned standard entropic uncertainty
relation yielding the trivial bound since the maximum overlap in POVMs always
produces the trivial value, "one." So, it fails to tie the smooth min-entropy
to show the security of the quantum cryptographic application.
Related papers
- Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities [79.9629927171974]
Uncertainty in Large Language Models (LLMs) is crucial for applications where safety and reliability are important.
We propose Kernel Language Entropy (KLE), a novel method for uncertainty estimation in white- and black-box LLMs.
arXiv Detail & Related papers (2024-05-30T12:42:05Z) - Entropic Uncertainty for Biased Measurements [1.827510863075184]
We derive a new entropic uncertainty relation for certain quantum states and for instances where the two measurement bases are no longer mutually unbiased.
We show that our new bound can produce higher key-rates under several scenarios when compared with prior work using standard entropic uncertainty relations.
arXiv Detail & Related papers (2023-05-16T19:01:16Z) - An entropic uncertainty principle for mixed states [0.0]
We provide a family of generalizations of the entropic uncertainty principle.
Results can be used to certify entanglement between trusted parties, or to bound the entanglement of a system with an untrusted environment.
arXiv Detail & Related papers (2023-03-20T18:31:53Z) - Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees.
Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation.
We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
arXiv Detail & Related papers (2022-03-30T02:02:16Z) - 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) - Geometry of Banach spaces: a new route towards Position Based
Cryptography [65.51757376525798]
We study Position Based Quantum Cryptography (PBQC) from the perspective of geometric functional analysis and its connections with quantum games.
The main question we are interested in asks for the optimal amount of entanglement that a coalition of attackers have to share in order to compromise the security of any PBQC protocol.
We show that the understanding of the type properties of some more involved Banach spaces would allow to drop out the assumptions and lead to unconditional lower bounds on the resources used to attack our protocol.
arXiv Detail & Related papers (2021-03-30T13:55:11Z) - Maximum Entropy Reinforcement Learning with Mixture Policies [54.291331971813364]
We construct a tractable approximation of the mixture entropy using MaxEnt algorithms.
We show that it is closely related to the sum of marginal entropies.
We derive an algorithmic variant of Soft Actor-Critic (SAC) to the mixture policy case and evaluate it on a series of continuous control tasks.
arXiv Detail & Related papers (2021-03-18T11:23:39Z) - R\'{e}nyi formulation of uncertainty relations for POVMs assigned to a
quantum design [0.0]
Information entropies provide powerful and flexible way to express restrictions imposed by the uncertainty principle.
In this paper, we obtain uncertainty relations in terms of min-entropies and R'enyi entropies for POVMs assigned to a quantum design.
arXiv Detail & Related papers (2020-04-12T09:44:44Z) - Improved tripartite uncertainty relation with quantum memory [5.43508370077166]
Uncertainty principle is a striking and fundamental feature in quantum mechanics.
In quantum information theory, this uncertainty principle is popularly formulized in terms of entropy.
We present an improvement of tripartite quantum-memory-assisted entropic uncertainty relation.
arXiv Detail & Related papers (2020-04-09T03:54:51Z) - On estimating the entropy of shallow circuit outputs [49.1574468325115]
Estimating the entropy of probability distributions and quantum states is a fundamental task in information processing.
We show that entropy estimation for distributions or states produced by either log-depth circuits or constant-depth circuits with gates of bounded fan-in and unbounded fan-out is at least as hard as the Learning with Errors problem.
arXiv Detail & Related papers (2020-02-27T15:32:08Z)
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.