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Entangling without Entanglement

T. Cubitt, F. Verstraete, W. Dür, J. I. Cirac. Entangling without Entanglement. “Separable State can be used to Distribute Entanglement” (to appear in PRL vol. 91 , issue 3). L ocal O perations & C lassical C ommunication. Send entangled ancilla particle.

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Entangling without Entanglement

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  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

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