6,084 research outputs found
Heisenberg's uncertainty principle
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle. (c) 2007 Elsevier B.V. All rights reserved
Measurement uncertainty relations
Measurement uncertainty relations are quantitative bounds on the errors in an
approximate joint measurement of two observables. They can be seen as a
generalization of the error/disturbance tradeoff first discussed heuristically
by Heisenberg. Here we prove such relations for the case of two canonically
conjugate observables like position and momentum, and establish a close
connection with the more familiar preparation uncertainty relations
constraining the sharpness of the distributions of the two observables in the
same state. Both sets of relations are generalized to means of order
rather than the usual quadratic means, and we show that the optimal constants
are the same for preparation and for measurement uncertainty. The constants are
determined numerically and compared with some bounds in the literature. In both
cases the near-saturation of the inequalities entails that the state (resp.
observable) is uniformly close to a minimizing one.Comment: This version 2 contains minor corrections and reformulation
A Tight High-Order Entropic Quantum Uncertainty Relation With Applications
We derive a new entropic quantum uncertainty relation involving min-entropy.
The relation is tight and can be applied in various quantum-cryptographic
settings.
Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit
Commitment are presented and the uncertainty relation is used to prove the
security of these protocols in the bounded quantum-storage model according to
new strong security definitions.
As another application, we consider the realistic setting of Quantum Key
Distribution (QKD) against quantum-memory-bounded eavesdroppers. The
uncertainty relation allows to prove the security of QKD protocols in this
setting while tolerating considerably higher error rates compared to the
standard model with unbounded adversaries. For instance, for the six-state
protocol with one-way communication, a bit-flip error rate of up to 17% can be
tolerated (compared to 13% in the standard model).
Our uncertainty relation also yields a lower bound on the min-entropy key
uncertainty against known-plaintext attacks when quantum ciphers are composed.
Previously, the key uncertainty of these ciphers was only known with respect to
Shannon entropy.Comment: 21 pages; editorial changes, additional applicatio
- …