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arXiv:1405.0063 · Physical Review A

Superoscillations underlying remote state preparation for relativistic fields

Ran Ber, Oded Kenneth, Benni Reznik

Published May 14, 2015• 8 citations
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Abstract

We present a physical (gedanken) implementation of a generalized remote state preparation of relativistic quantum field states for an arbitrary set of observers. The prepared states are created in regions that are outside the future light cone of the generating region. The mechanism, which is based on utilizing the vacuum state of a relativistic quantum field as a resource, sheds light on the well known Reeh-Schlieder theorem, indicating its strong connection with the mathematical phenomenon of superoscillations.

DOI
10.1103/physreva.91.052312

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We present a physical (gedanken) implementation of a generalized remote state preparation of relativistic quantum field states for an arbitrary set of observers. The prepared states are created in regions that are outside the future light cone of the generating region. The mechanism, which is based on utilizing the vacuum state of a relativistic quantum field as a resource, sheds light on the well known Reeh-Schlieder theorem, indicating its strong connection with the mathematical phenomenon of superoscillations.
We present a physical (gedanken) implementation of a generalized remote state preparation of relativistic quantum field states for an arbitrary set of observers. The prepared states are created in regions which are outside the future light-cone of the generating region. The mechanism, which is based on utilizing the vacuum state of a relativistic quantum field as a resource, sheds new light on the well known Reeh-Schlieder theorem, indicating its strong connection with the mathematical phenomenon of superoscillations.
Many of the "counterintuitive" features of relativistic quantum field theory have their formal root in the Reeh-Schlieder theorem, which in particular entails that local operations applied to the vacuum state can produce any state of the entire field.It is of great interest then that I.E.Segal and, more recently, G. Fleming (in a paper entitled "Reeh-Schlieder meets Newton-Wigner") have proposed an alternative "Newton-Wigner" localization scheme that avoids the Reeh-Schlieder theorem.In this paper, I reconstruct the Newton-Wigner localization scheme and clarify the limited extent to which it avoids the counterintuitive consequences of the Reeh-Schlieder theorem.I also argue that there is no coherent interpretation of the Newton-Wigner localization scheme that renders it free from act-outcome correlations at spacelike separation.
We review what it means for a relativistic particle to be localized and argue that the most useful approach is through local measurement. This perspective ties localization directly to relativistic causality and measurable outcomes in spacetime. Strict localization in quantum field theory is formalized by states that give the same expectation value as vacuum for all local observables outside some spacetime region. With this formalism, single photons cannot be strictly localized, but coherent states can. The structure and interpretation of local observables and local operator algebras are discussed in connection with the Reeh-Schlieder theorem. Since probabilities of local measurement outcomes cannot vanish in vacuum, particle detection events must be phrased carefully. Key characteristics of strictly localized states are surveyed alongside concrete strategies for constructing them. The relationship between localization, causality, and on-demand sources is analyzed, finding that strictly localized states can represent localized, propagating information in quantum field theory. Explicit examples of localized photonic states are presented with an emphasis on quantum optics, including states that approximate single photons and (entangled) Bell states.
We put forward two novel and perfect protocols for preparing an arbitrary single–particle state and simultaneously implementing a rotation operator or an arbitrary unitary operator on that particle. There are schemes for either only teleporting particles or only remotely controlling quantun particles. If one has to remotely control a prepared quantum, then he/ she has to first do remote state preparation and then executes the remote control on the prepared quantum. Both operations ware done separately on two sets of entanglements. However, this intuitive solution is inefficient because many resources are wasted. Thus, we attempt to complete both operations by sharing one three–particle Greenberger–Horne– Zeilinger (GHZ) state. Comparing our two protocols with the corresponding intuitive solutions, respectively, the results show that our protocols are more efficient than the corresponding intuitive solutions. Only Pauli operators, controlled–NOT gate, Bell–state measurement, single–qubit measurement, Einstein–Podolsky–Rosen (EPR) state and GHZ state are used in our schemes, so these schemes are easily realized in physical experiment.
By using a partial polarizer to apply a generalized polarization measurement to one photon of a polarization entangled pair, we remotely prepare single photons in arbitrary polarization qubits. Specifically, we are able to produce a range of states of any desired degree of mixedness or purity, over (and within) the entire Poincare sphere, with a typical fidelity exceeding 99.5%. Moreover, by using non-degenerate entangled pairs as a resource, we can prepare states in multiple wavelengths. Finally, we discuss the states remotely preparable given a particular two-qubit resource state.