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Journal of Mathematical Physics

Remote state preparation using Einstein–Podolsky–Rosen representations

Siendong Huang

Published Oct 1, 2018• 1 citation
Publisher

Abstract

Because Einstein–Podolsky–Rosen states are well-defined on the Weyl algebra, their canonical cyclic representations are suitable for demonstrating the process of remote state preparation. Local projection-valued measurements and the corresponding recovery unitary operator are formulated in this representation, whereupon generalized equatorial states are prepared remotely and faithfully.

DOI
10.1063/1.5025651

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Because Einstein–Podolsky–Rosen states are well-defined on the Weyl algebra, their canonical cyclic representations are suitable for demonstrating the process of remote state preparation. Local projection-valued measurements and the corresponding recovery unitary operator are formulated in this representation, whereupon generalized equatorial states are prepared remotely and faithfully.
Known quantum pure states of a qudit can be remotely prepared onto a group of particles of qubits exactly or probabilistically with the aid of two-level Einstein--Podolsky--Rosen states. We present a protocol for such kind of remote state preparation. We are mainly focused on the remote preparation of the ensembles of equatorial states and those of states in real Hilbert space. In particular, a kind of states of qudits in real Hilbert space have been shown to be remotely prepared in faith without the limitation of the input space dimension.
We propose several schemes for the joint remote preparation of four-qubit cluster-type states with real coefficients and complex coefficients by using six Einstein–Podolsky–Rosen (EPR) pairs and two six-qubit entangled states as quantum channels respectively. In these schemes, two senders share the original state which they wish to help the receiver to remotely prepare. It is shown that, only if two senders collaborate with each other, and perform four-qubit projective measurements on their own qubits respectively, the receiver can reconstruct the original state by means of some appropriate unitary operations.
Summary form only given. Optical hybrid quantum information processing aims at mixing the traditionally separated discrete (DV) and continuous variable (CV) tools and concepts. In this approach, both DV states, such as single photons, and CV states, for example Schrödinger cats states: |cat ±〉 ∝ |α〉 ± | - α〉, are used. Having succeeded in experimentally generating hybrid entanglement of light for flying qubits [2], we will report on two protocols using this resource: the remote preparation of arbitrary CV qubits as well as the first demonstration of Einstein-Podolsky-Rosen (EPR) steering in the context of hybrid quantum information.
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.