scholarly journals A Tight Uniform Continuity Bound for the Arimoto-Rényi Conditional Entropy and its Extension to Classical-Quantum States

2022 ◽  
pp. 1-1
Author(s):  
Michael G Jabbour ◽  
Nilanjana Datta
Keyword(s):  
Conditional Entropy ◽  
Uniform Continuity ◽  
Quantum States ◽  
Classical Quantum

scholarly journals Computing conditional entropies for quantum correlations

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Peter Brown ◽  
Hamza Fawzi ◽  
Omar Fawzi
Keyword(s):  
Quantum Key Distribution ◽  
Detection Efficiency ◽  
Conditional Entropy ◽  
Key Distribution ◽  
Quantum Correlations ◽  
Upper Bounds ◽  
Cryptographic Protocols ◽  
Quantum States ◽  
Security Proofs

AbstractThe rates of quantum cryptographic protocols are usually expressed in terms of a conditional entropy minimized over a certain set of quantum states. In particular, in the device-independent setting, the minimization is over all the quantum states jointly held by the adversary and the parties that are consistent with the statistics that are seen by the parties. Here, we introduce a method to approximate such entropic quantities. Applied to the setting of device-independent randomness generation and quantum key distribution, we obtain improvements on protocol rates in various settings. In particular, we find new upper bounds on the minimal global detection efficiency required to perform device-independent quantum key distribution without additional preprocessing. Furthermore, we show that our construction can be readily combined with the entropy accumulation theorem in order to establish full finite-key security proofs for these protocols.

Dynamics of Interacting Classical and Quantum Systems

2011 ◽  
Vol 18 (04) ◽  
pp. 339-351 ◽  
Author(s):  
Dariusz Chruściński ◽  
Andrzej Kossakowski ◽  
Giuseppe Marmo ◽  
E. C. G. Sudarshan
Keyword(s):  
Characteristic Feature ◽  
Quantum Dynamics ◽  
Quantum Discord ◽  
Main Idea ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Quantum States ◽  
Algebra Of Observables ◽  
Classical Quantum ◽  
True Quantum

We analyze the dynamics of coupled classical and quantum systems. The main idea is to treat both systems as true quantum ones and impose a family of superselection rules which imply that the corresponding algebra of observables of one subsystem is commutative and hence may be treated as a classical one. Equivalently, one may impose a special symmetry which restricts the algebra of observables to the 'classical' subalgebra. The characteristic feature of classical-quantum dynamics is that it leaves invariant a subspace of classical-quantum states, that is, it does not create quantum correlations as measured by the quantum discord.

scholarly journals Effectively classical quantum states for open systems

2000 ◽  
Vol 273 (4) ◽  
pp. 223-231 ◽  
Author(s):  
Ph. Blanchard ◽  
R. Olkiewicz
Keyword(s):  
Open Systems ◽  
Quantum States ◽  
Classical Quantum

Entangled versus classical quantum states

2001 ◽  
Vol 280 (1-2) ◽  
pp. 7-16 ◽  
Author(s):  
Ph. Blanchard ◽  
L. Jakóbczyk ◽  
R. Olkiewicz
Keyword(s):  
Quantum States ◽  
Classical Quantum

QUANTUM ENTROPY AND INFORMATION IN DISCRETE ENTANGLED STATES

2001 ◽  
Vol 04 (02) ◽  
pp. 137-160 ◽  
Author(s):  
VIACHESLAV P. BELAVKIN ◽  
MASANORI OHYA
Keyword(s):  
Conditional Entropy ◽  
Von Neumann Entropy ◽  
Entangled States ◽  
Commutative Case ◽  
Maximal Abelian Subalgebra ◽  
Von Neumann ◽  
Abelian Subalgebra ◽  
Different Types ◽  
Classical Quantum ◽  
Entropic Measure

Quantum entanglements, describing truly quantum couplings, are studied and classified for discrete compound states. We show that classical-quantum correspondences such as quantum encodings can be treated as d-entanglements leading to a special class of separable compound states. The mutual information for the d-compound and for q-compound (entangled) states leads to two different types of entropies for a given quantum state. The first one is the von Neumann entropy, which is achieved as the supremum of the information over all d-entanglements, and the second one is the dimensional entropy, which is achieved at the standard entanglement, the true quantum entanglement, coinciding with a d-entanglement only in the commutative case. The q-conditional entropy and q-capacity of a quantum noiseless channel, defined as the supremum over all entanglements, is given as the logarithm of the dimensionality of the input von Neumann algebra. It can double the classical capacity, achieved as the supremum over all semiquantum couplings (d-entanglements, or encodings), which is bounded by the logarithm of the dimensionality of a maximal Abelian subalgebra. The entropic measure for essential entanglement is introduced.

scholarly journals QUANTUM LOCKING OF CLASSICAL CORRELATIONS AND QUANTUM DISCORD OF CLASSICAL-QUANTUM STATES

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1643-1651 ◽  
Author(s):  
S. BOIXO ◽  
L. AOLITA ◽  
D. CAVALCANTI ◽  
K. MODI ◽  
A. WINTER
Keyword(s):  
Quantum State ◽  
Quantum Discord ◽  
Quantum States ◽  
Unconditional Security ◽  
Classical Quantum ◽  
Classical Correlations ◽  
Locking Protocol ◽  
Quantum Protocol

A locking protocol between two parties is as follows: Alice gives an encrypted classical message to Bob which she does not want Bob to be able to read until she gives him the key. If Alice is using classical resources, and she wants to approach unconditional security, then the key and the message must have comparable sizes. But if Alice prepares a quantum state, the size of the key can be comparatively negligible. This effect is called quantum locking. Entanglement does not play a role in this quantum advantage. We show that, in this scenario, the quantum discord quantifies the advantage of the quantum protocol over the corresponding classical one for any classical-quantum state.

scholarly journals CHARACTERIZING QUANTUMNESS VIA ENTANGLEMENT CREATION

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1701-1713 ◽  
Author(s):  
SEVAG GHARIBIAN ◽  
MARCO PIANI ◽  
GERARDO ADESSO ◽  
JOHN CALSAMIGLIA ◽  
PAWEŁ HORODECKI
Keyword(s):  
Relative Entropy ◽  
Special Class ◽  
Entanglement Swapping ◽  
Quantum States ◽  
Bipartite Entanglement ◽  
Separable States ◽  
Classical Quantum ◽  
Qubit States

In [Piani et al., PRL106 (2011) 220403], an activation protocol was introduced which maps the general non-classical (multipartite) correlations between given systems into bipartite entanglement between the systems and local ancillae by means of a potentially highly entangling interaction. Here, we study how this activation protocol can be used to entangle the starting systems themselves via entanglement swapping through a measurement on the ancillae. Furthermore, we bound the relative entropy of quantumness (a naturally arising measure of non-classicality in the scheme of Piani et al. above) for a special class of separable states, the so-called classical–quantum states. In particular, we fully characterize the classical–quantum two-qubit states that are maximally non-classical.

scholarly journals A Quantum Money Solution to the Blockchain Scalability Problem

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 297 ◽  
Author(s):  
Andrea Coladangelo ◽  
Or Sattath
Keyword(s):  
Quantum Cryptography ◽  
Quantum Communication ◽  
Payment System ◽  
Quantum States ◽  
Public Key ◽  
Smart Contracts ◽  
Monetary Incentives ◽  
Smart Contract ◽  
Formal Tool ◽  
Classical Quantum

We put forward the idea that classical blockchains and smart contracts are potentially useful primitives not only for classical cryptography, but for quantum cryptography as well. Abstractly, a smart contract is a functionality that allows parties to deposit funds, and release them upon fulfillment of algorithmically checkable conditions, and can thus be employed as a formal tool to enforce monetary incentives. In this work, we give the first example of the use of smart contracts in a quantum setting. We describe a simple hybrid classical-quantum payment system whose main ingredients are a classical blockchain capable of handling stateful smart contracts, and quantum lightning, a strengthening of public-key quantum money introduced by Zhandry [55]. Our hybrid payment system employs quantum states as banknotes and a classical blockchain to settle disputes and to keep track of the valid serial numbers. It has several desirable properties: it is decentralized, requiring no trust in any single entity; payments are as quick as quantum communication, regardless of the total number of users; when a quantum banknote is damaged or lost, the rightful owner can recover the lost value.

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