1 / 13

Leveraging Separable States for Entanglement Distribution in Quantum Communication

This study explores using separable states to distribute entanglement in quantum communication. Examining the concept of separability in quantum states, the paper delves into entanglement generation through local operations & classical communications. It discusses the implications of not entangling the mediator and highlights how entanglement 'flows' between particles. The role of ancilla particles in mediating interactions is explored, emphasizing the importance of separability in ancilla states. The text also touches upon perturbation theory, evolution under time-steps, and the interdependence of entanglement properties in bipartite partitions for pure and mixed states.

wedwards
Download Presentation

Leveraging Separable States for Entanglement Distribution in Quantum Communication

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. T. Cubitt, F. Verstraete, W. Dür, J. I. Cirac EntanglingwithoutEntanglement “Separable State can be used to Distribute Entanglement” (to appear in PRL vol. 91, issue 3)

  2. Local Operations & Classical Communication • Send entangled ancilla particle • Send separable ancilla particle Entangling two distant particles 6 4 4 6

  3. What does “separable” mean for the messenger? • Choose strongest possible meaning: • For pure states: = • For mixed states: B B • Implies separability tracing out one particle: C C C  A A A B Define “separable”?

  4. Alice and Bob prepare initial state: • Alice applies CNOT to A and a: • Bob applies CNOT to B and a: Don’t Entangle the Messenger

  5. Chain with nearest neighbour interactions • If we think of rates of entanglement generation as ‘flows’… B B B B B B • Can and be entangled without entangling the ancilla ? A A A A A a a a a a • …can entanglement ‘flow’ be 0 between & and & , yet be non-zero between and ? How does entanglement ‘flow’?

  6. Interactions are often mediated by an ‘ancilla’ particle • Ion traps: interactions between ions mediated by phonons • Cavity QED: interactions between atoms mediated by photons in the cavity • Fundamentally, all interactions are mediated by the gauge bosons of particle physics Physical relevance

  7. > • Continuous case is stronger than discrete case. • Evolution can be discretized by Trotter formula B A a • Immediately gives a discrete procedure. Continuous and discrete cases

  8. Evolve under for an infinitesimal time-step: • Start with separable state • Condition on separability of ancilla is then • Multiplying by gives • So Pure states:impossibility proof Separable

  9. Expand in perturbation theory: B • As achieve effect for e.g. initial state . A a • Want ancilla to really be separable, not just arbitrarily small entanglement as Don’t entangle the mediator Trivial?

  10. Use mixed initial state: • After evolution ( ): Separable in ( )- Entangled in ( )- B B B B • Choose  large enough to destroy all entanglement with . (States near maximally mixed state are separable). a A A A A a a a • Choose  small enough such that mixing does not destroy - entanglement. Just add a dash of noise

  11. For pure states, entanglement properties of bipartite partitions are inter-dependent &  B B B A A • For mixed states, partitions are independent B B C C C C C C & & A A A A B Entanglement properties of partitions

  12. Alice and Bob prepare initial state: • Alice applies CNOT to A and a: A A A B B B C C C • Bob applies CNOT to B and a: Theoreticalinsight

  13. Separable states can be used to distribute entanglement • Forces us to abandon any intuitive ideas of entanglement being sent through a quantum channel • Upsets notions of entanglement flow • (At least for general – i.e. mixed – states…) Conclusions“Wacky but Lovely” – Seth Lloyd

More Related