A New High-Dimensional Quantum Entropic Uncertainty Relation with Applications

• URL: http://arxiv.org/abs/2005.04773v2
• Date: Sat, 23 May 2020 20:47:21 GMT
• Title: A New High-Dimensional Quantum Entropic Uncertainty Relation with Applications
• Authors: Walter O. Krawec
• Abstract summary: We derive a new quantum entropic uncertainty relation, bounding the conditional smooth quantum min entropy based on the result of a measurement. Our relation works for systems of arbitrary finite dimension.
• Score: 1.827510863075184
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we derive a new quantum entropic uncertainty relation, bounding the conditional smooth quantum min entropy based on the result of a measurement using a two outcome POVM and the failure probability of a classical sampling strategy. Our relation works for systems of arbitrary finite dimension. We apply it to analyze a new source independent quantum random number generation protocol and show our relation provides optimistic results compared to prior work.

Related papers

• Generalized quantum asymptotic equipartition [11.59751616011475]
  We prove that all operationally relevant divergences converge to the quantum relative entropy between two sets of quantum states. In particular, both the smoothed min-relative entropy between two sequential processes of quantum channels can be lower bounded by the sum of the regularized minimum output channel divergences. We apply our generalized AEP to quantum resource theories and provide improved and efficient bounds for entanglement distillation, magic state distillation, and the entanglement cost of quantum states and channels.
  arXiv  Detail & Related papers  (2024-11-06T16:33:16Z)
• One-Shot Min-Entropy Calculation And Its Application To Quantum Cryptography [21.823963925581868]
  We develop a one-shot lower bound calculation technique for the min-entropy of a classical-quantum state. It gives an alternative tight finite-data analysis for the well-known BB84 quantum key distribution protocol. It provides a security proof for a novel source-independent continuous-variable quantum random number generation protocol.
  arXiv  Detail & Related papers  (2024-06-21T15:11:26Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Anticipative measurements in hybrid quantum-classical computation [68.8204255655161]
  We present an approach where the quantum computation is supplemented by a classical result. Taking advantage of its anticipation also leads to a new type of quantum measurements, which we call anticipative. In an anticipative quantum measurement the combination of the results from classical and quantum computations happens only in the end.
  arXiv  Detail & Related papers  (2022-09-12T15:47:44Z)
• Jarzynski-like Equality of Nonequilibrium Information Production Based on Quantum Cross Entropy [0.8367938108534343]
  We employ the one-time measurement scheme to derive a Jarzynski-like equality of nonequilibrium information production. The derived equality further enables one to explore the roles of the quantum cross entropy in quantum communications, quantum machine learning and quantum thermodynamics.
  arXiv  Detail & Related papers  (2022-09-05T04:47:10Z)
• Experimental violations of Leggett-Garg's inequalities on a quantum computer [77.34726150561087]
  We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
  arXiv  Detail & Related papers  (2021-09-06T14:35:15Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Quantum Sampling for Optimistic Finite Key Rates in High Dimensional Quantum Cryptography [1.5469452301122175]
  We revisit so-called sampling-based entropic uncertainty relations, deriving newer, more powerful, relations and applying them to source-independent quantum random number generators and high-dimensional quantum key distribution protocols. These sampling-based approaches to entropic uncertainty, and their application to quantum cryptography, hold great potential for deriving proofs of security for quantum cryptographic systems.
  arXiv  Detail & Related papers  (2020-12-08T01:32:59Z)
• Entropic Uncertainty Relations and the Quantum-to-Classical transition [77.34726150561087]
  We aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations. We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities.
  arXiv  Detail & Related papers  (2020-03-04T14:01:17Z)
• An optimal measurement strategy to beat the quantum uncertainty in correlated system [0.6091702876917281]
  Uncertainty principle undermines the precise measurement of incompatible observables. Entanglement, another unique feature of quantum physics, was found may help to reduce the quantum uncertainty.
  arXiv  Detail & Related papers  (2020-02-23T05:27:36Z)
• 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)

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.