Conjectured strong complementary information tradeoff.

  title={Conjectured strong complementary information tradeoff.},
  author={Joseph M. Renes and Jean-Christian Boileau},
  journal={Physical review letters},
  volume={103 2},
We conjecture a new entropic uncertainty principle governing the entropy of complementary observations made on a system given side information in the form of quantum states, generalizing the entropic uncertainty relation of Maassen and Uffink [Phys. Rev. Lett. 60, 1103 (1988)]. We prove a special case for certain conjugate observables by adapting a similar result found by Christandl and Winter pertaining to quantum channels [IEEE Trans. Inf. Theory 51, 3159 (2005)], and discuss possible… 
Continuous Variable Entropic Uncertainty Relations in the Presence of Quantum Memory
We generalize entropic uncertainty relations in the presence of quantum memory [Nature Physics 6 (659), 2010], and [Physical Review Letters 106 (110506), 2011] in two directions. First, we consider
A framework for non-asymptotic quantum information theory
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography, and introduces the purified distance, a novel metric for unnormalized quantum states, and explores various properties of these entropies, including data-processing inequalities, chain rules and their classical limits.
Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities
Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy
Quantum Side Information: Uncertainty Relations, Extractors, Channel Simulations
This thesis provides an information theoretic analysis by discussing entropic uncertainty relations with quantum side information and develops various kinds of quantum channel simulation results by using classical and quantum randomness extractors that also work with respect to quantum side Information.
Quantum complementarity through entropic certainty principles
We approach the physical implications of the noncommutative nature of complementary observable algebras (COAs) from an information theoretic perspective. In particular, we derive a general entropic
Entropic uncertainty and measurement reversibility
The entropic uncertainty relation with quantum side information (EUR-QSI) from [Berta et al., Nat. Phys. 6, 659 (2010)] is a unifying principle relating two distinctive features of quantum mechanics:
Uncertainty relations from simple entropic properties.
This work shows that a single technique applies to several entropic quantities, including the von Neumann entropy, min- and max-entropies, and the Rényi entropies.
The smooth entropy formalism for von Neumann algebras
In particular, it is proved the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.
Improved tripartite uncertainty relation with quantum memory
An improvement of tripartite quantum-memory-assisted entropic uncertainty relation is presented, which shows that the bound derived by this method will be tighter than the lower bound in [Phys. Rev. Lett. 103, 020402 (2009].
Relative entropic uncertainty relation for scalar quantum fields
This work presents the first entropic uncertainty relation for a scalar quantum field theory and demonstrates its behavior by considering few particle excitations and the thermal state and shows that the relation implies the multidimensional Heisenberg uncertainty relation.


Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality
We give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von Neumann entropy. By combining a result of Petz characterising the equality
Random quantum codes from Gaussian ensembles and an uncertainty relation
Using random Gaussian vectors and an information-uncertainty relation, we give a proof that the coherent information is an achievable rate for entanglement transmission through a noisy quantum
Uncertainty, monogamy, and locking of quantum correlations
The results lead to the conclusion that both measures can drop by an arbitrary amount when only a single qubit of a local system is lost.
Physical underpinnings of privacy
A new definition of private states is given in terms of one party's potential knowledge of two complementary measurements made on the other and this is used to construct a general method of private state distillation using quantum error-correcting codes.
Monogamy of quantum entanglement and other correlations
It has been observed by numerous authors that a quantum system being entangled with another one limits its possible entanglement with a third system: this has been dubbed the ``monogamous nature of
Security of quantum key distribution using d-level systems.
The information gained by a potential eavesdropper applying a cloning-based individual attack is derived, along with an upper bound on the error rate that ensures unconditional security against coherent attacks.
Quantum computation and quantum information
  • T. Paul
  • Physics
    Mathematical Structures in Computer Science
  • 2007
This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal
Generalized entropic uncertainty relations.
A new class of uncertainty relations is derived for pairs of observables in a finite-dimensional Hilbert space which do not have any common eigenvector. This class contains an ``entropic''
Locking classical correlations in quantum States.
There are (2n+1)-qubit states for which a one-bit message doubles the optimal classical mutual information between measurement results on the subsystems, from n/2 bits to n bits.
Small accessible quantum information does not imply security.
It is shown that even if this so-called accessible information is small, the key S might not be secure enough to be used in applications such as one-time pad encryption.