Conjectured Strong Complementary Information Tradeoff

Conjectured strong complementary-correlations tradeoff

We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when one party measures a single observable and the other party measures one of two observables. The uncertainty relation does not follow from Maassen-Uffink uncertainty relation and is much stronger than Hall uncertainty relation derived from the latter. The second uncertainty relation bounds the sum of two mutual informations when each party measures one of two…

Uncertainty is complementary to Complementarity

For any ideal two-path interferometer it is shown that the wave-particle duality of quantum mechanics implies Heisenberg's uncertainty relation and vice versa. It is conjectured that complementarity and uncertainty are two aspects of the same general principle.

Noise and Disturbance of Qubit Measurements: An Information-Theoretic Characterisation

Information-theoretic definitions for the noise associated with a quantum measurement and the corresponding disturbance to the state of the system have recently been introduced [F. Buscemi et al., Phys. Rev. Lett. 112, 050401 (2014)]. These definitions are invariant under relabelling of measurement outcomes, and lend themselves readily to the formulation of state-independent uncertainty relations both for the joint estimate of observables (noise-noise relations) and the noise-disturbance tradeoff. Here we derive such relations for incompatible qubit observables, which we prove to be tight in t…

State-Dependent Approach to Entropic Measurement-Disturbance Relations

Heisenberg's intuition was that there should be a tradeoff between measuring a particle's position with greater precision and disturbing its momentum. Recent formulations of this idea have focused on the question of how well two complementary observables can be jointly measured. Here, we provide an alternative approach based on how enhancing the predictability of one observable necessarily disturbs a complementary one. Our measurement-disturbance relation refers to a clear operational scenario and is expressed by entropic quantities with clear statistical meaning. We show that our relation is …

Complementary contributions of indeterminism and signalling to quantum correlations

Simple quantitative measures of indeterminism and signalling, $I$ and $S$, are defined for models of statistical correlations. It is shown that any such model satisfies a generalised Bell-type inequality, with tight upper bound B(I,S). This upper bound explicitly quantifies the complementary contributions required from indeterminism and signalling, for modelling any given violation of the standard Bell-CHSH inequality. For example, all models of the maximum quantum violation must either assign no more than 80% probability of occurrence to some underlying event, and/or allow a nonlocal change o…

量子比特维度加法器中噪声与带状限制之间的权衡

Tradeoff between noise and banding in a quantum adder with qudits

本文研究任意维度量子加法器的资源需求，证明受控旋转门数量上界，并揭示噪声下带状限制使恒定深度近似电路更优，同时提出用一维自旋链实现量子加法的方案。