Certainty relations between local and nonlocal observables

Abstract

We demonstrate that for an arbitrary number of identical particles, each defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder of relations of complementarity between local, and every conceivable kind of joint (or nonlocal) measurements. E.g., the more accurate we can know (by a measurement) some joint property of three qubits (projecting the state onto a tripartite entangled state), the less accurate some other property, local to the three qubits, become. We also show that the corresponding complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces.

4 pages, no figures

References in corpus (4)

• Mutually unbiased binary observable sets on N qubits
• On the structure of the sets of mutually unbiased bases for N qubits
• Mutually Unbiased Bases and Trinary Operator Sets for N Qutrits
• Information theoretic approach to single-particle and two-particle interference in multi-path interferometers

Cited by in corpus (4)

• Complex joint probabilities as expressions of determinism in quantum mechanics
• Entropic formulation of the uncertainty principle for the number and annihilation operators
• Uncertainty and certainty relations for complementary qubit observables in terms of Tsallis' entropies
• Uncertainty and certainty relations for the Pauli observables in terms of the Rényi entropies of order $\alpha \in (0;1]$