Violation of local uncertainty relations as a signature of entanglement

  title={Violation of local uncertainty relations as a signature of entanglement},
  author={Holger F. Hofmann and Shigeki Takeuchi},
  journal={Physical Review A},
Entangled states represent correlations between two separate systems that are too precise to be represented by products of local quantum states. We show that this limit of precision for the local quantum states of a pair of N-level systems can be defined by an appropriate class of uncertainty relations. The violation of such local uncertainty relations may be used as an experimental test of entanglement generation. 
Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement
The uncertainty principle tells us that two associated properties of a particle cannot be simultaneously known with infinite precision. However, if the particle is entangled with a quantum memory,
Experimental investigation of the entanglement-assisted entropic uncertainty principle
Heisenberg’s uncertainty principle limits the precision with which we can measure two complementary properties of a quantum system. Entanglement, it has previously been proposed, can relax these
The separability versus entanglement problem
We present a review of the problem of finding out whether a quantum state of two or more parties is entangled or separable. After a formal definition of entangled states, we present a few criteria
Estimating entanglement through local correlations
  • I. Sainz, G. Björk
  • Physics
    International Conference on Coherent and Nonlinear Optics
  • 2007
A bipartite, arbitrary-dimensional entanglement measure based on local correlations of any set of generators of the corresponding algebras is proposed. An explicit relation with the I- and
Multipartite entanglement criterion via generalized local uncertainty relations
A sufficient criterion for the entanglement of four-partite quantum systems is presented in terms of the local uncertainty relations and the approach is generalized to general multipartite Entanglement cases.
Entanglement criterion independent on observables for multipartite Gaussian states based on uncertainty principle
The uncertainty principle is applied to improve the LUR criteria to obtain entanglement criteria for multipartite Gaussian states, which are independent on observalbes.
Entanglement detection
Entanglement conditions for four-mode states via the uncertainty relations in conjunction with partial transposition
From the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for
Uncertainty relations and entanglement in fermion systems
The violation of uncertainty relations is used as a signature of entanglement for both pure and mixed states of two identical fermions. In the case of fermions with a four-dimensional single-particle
Entanglement of Local Hidden States
Steering criteria are conditions whose violation excludes the possibility of describing the observed measurement statistics with local hidden state (LHS) models. When the available data do not allow


Recently, we have found that some bound entanglemed states violate a non-symmetric local uncertainty relation ͓see H.F. Hofmann
  • Phys. Rev. A
͓22͔ Note that this precise correlation is also the essential feature of entanglement in quantum teleportation, as discussed in H.F. Hofmann
  • Phys. Rev. A
807 ͑1935͒; 23, 823 ͑1935͒; 23, 844 ͑1935͒; in Quantum Theory and Measurement
  • Naturwissenschaften
  • 1983