Optimal measurements for relative quantum information

Bartlett, Stephen D.; Rudolph, Terry; Spekkens, Robert W.

doi:10.1103/physreva.70.032321

Cited by 63 publications

(141 citation statements)

References 29 publications

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“…Indeed, the notion of entanglement is affected by the additional restrictions [7,8], and new protocols arise, e.g., perfect data hiding [9] becomes possible [7]. On the other hand, it has been shown [7,10] that the extra resource of a shared reference frame (i.e., a nonlocal state) allows to overcome the restrictions imposed by the SSR (note that [10] also adressed non-Abelian SSR); conversely, private reference frames restrict the possible operations of an eavesdropper and can thus be employed for cryptographic tasks [11].…”

Section: Introductionmentioning

confidence: 99%

Quantum entanglement theory in the presence of superselection rules

2004

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Superselection rules severly constrain the operations which can be implemented on a distributed quantum system. While the restriction to local operations and classical communication gives rise to entanglement as a nonlocal resource, particle number conservation additionally confines the possible operations and should give rise to a new resource. In [Phys. Rev. Lett. 92, 087904 (2004), quant-ph/0310124] we showed that this resource can be quantified by a single additional number, the superselection induced variance (SiV) without changing the concept of entanglement. In this paper, we give the results on pure states in greater detail; additionally, we provide a discussion of mixed state nonlocality with superselection rules where we consider both formation and distillation. Finally, we demonstrate that SiV is indeed a resource, i.e., that it captures how well a state can be used to overcome the restrictions imposed by the superselection rule.

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Section: Introductionmentioning

confidence: 99%

Quantum entanglement theory in the presence of superselection rules

2004

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“…Bartlett et al have shown that in the absence of a reference for spatial orientation the communication of classical and quantum information using spin particles is still possible provided the spins are entangled and the information is encoded in SSR-invariant subsystems [10]. They have also shown how a private shared reference for spatial orientation can be used for secret communications [11]. The effects of finite references has been studied in a variety of ways.…”

Section: Introductionmentioning

confidence: 99%

Optimal reference states for maximum accessible entanglement under the local-particle-number superselection rule

2009

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Global conservation laws imply superselection rules (SSR) which restrict the operations that are possible on any given state. Imposing the additional constraint of local operations and classical communication (LOCC) forbids the transfer of quantum systems between spatially separated sites. In the case of particle conservation this imposes a SSR for local particle number. That is, the coherences between subspaces of fixed particle number at each site are not accessible and any state is therefore equivalent to its projection onto these subspaces. The accessible entanglement under the SSR is less than (or equal to) that available in the absence of the SSR. An ancilla can be used as a reference system to increase the amount of accessible entanglement. We examine the relationship between local particle number uncertainty and the accessible entanglement and consider the optimal reference states for recovering entanglement from certain systems. In particular we derive the optimal ancilla state for extracting entanglement for a single shared particle and make steps towards the optimum for general systems. We also show that a reference for phase angle is fundamentally different to a reference for the SSR associated with particle conservation.

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“…of secret bits that can be exchanged once a private SRF is established [6]. Such a tight balance provides a new understanding of reference frames as a communication resource.…”

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confidence: 99%

“…In fact, we can relate the above protocol with the cryptographic protocol of Ref. [6], where a private SRF is used to communicate a secret string of bits. While in our case we have asymptotically N qbits + 3 log N secret bits −→ private SRF , (10) in the case of Ref.…”

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confidence: 99%