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arXiv:1411.7173 · Physical Review A

Full-Bloch-sphere teleportation of spinor Bose-Einstein condensates and spin ensembles

Alexey N. Pyrkov, Tim Byrnes

Published Dec 23, 2014• 39 citations
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Abstract

Quantum teleportation is the transfer of quantum information between two locations by the use of shared entanglement. Current teleportation schemes broadly fall under one of two categories, either qubit or continuous-variable teleportation. Spin coherent states on spin ensembles can be teleported under the continuous-variable approximation for states with small deviations from a given polarization. However, for spin-coherent states with large deviations, no convenient teleportation protocol exists. Recently, we introduced a teleportation scheme where a spin-coherent state lying on the equator of the Bloch sphere is teleported between distant parties [A. N. Pyrkov and T. Byrnes, New J. Phys. 16, 073038 (2014)]. Here we generalize the protocol to a spin-coherent state with an arbitrary position on the Bloch sphere. Our proposed scheme breaks classical bounds based on communication in the unconditional case and quantum state estimation with postselection.

DOI
10.1103/physreva.90.062336

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Quantum teleportation is the transfer of quantum information between two locations by the use of shared entanglement. Current teleportation schemes broadly fall under one of two categories, either qubit or continuous-variable teleportation. Spin coherent states on spin ensembles can be teleported under the continuous-variable approximation for states with small deviations from a given polarization. However, for spin-coherent states with large deviations, no convenient teleportation protocol exists. Recently, we introduced a teleportation scheme where a spin-coherent state lying on the equator of the Bloch sphere is teleported between distant parties [A. N. Pyrkov and T. Byrnes, New J. Phys. 16, 073038 (2014)]. Here we generalize the protocol to a spin-coherent state with an arbitrary position on the Bloch sphere. Our proposed scheme breaks classical bounds based on communication in the unconditional case and quantum state estimation with postselection.
We introduce a quantum teleportation scheme that transfers a spin coherent state between two locations using entanglement. In the scheme an unknown spin coherent state lying on the equator of the Bloch sphere, such as realized in a coherent two-component Bose–Einstein condensate, is teleported onto a distant spin coherent state using only elementary operations and measurements. The scheme works in the regime beyond the standard continuous variables approximation based on the Holstein–Primakoff transformation. We analyze the error of the protocol with the number of particles N in the spin coherent state under decoherence and find that it scales favorably with N . The simplicity of the operations involved and the robustness under decoherence should make the protocol suitable under realistic experimental conditions.
Quantum teleportation is one of the most enigmatic protocols realized so far in the area of quantum information, allowing for the transfer of quantum information assisted by an entangled state. It was a subject of science fiction 20 years ago, but now is a fundamental experimental protocol and quantum primitive for quantum information processing tasks. There have been many successful realizations of teleportation ranging from those using photons, atoms, and hybrid systems and long-range teleportation beyond 100km has already been achieved multiple times. These however typically involve explicitly single particle systems or effective few-particle systems. For larger (visible to the naked eye) objects involving many particles, teleportation is typically more difficult due to the fast decoherence such macroscopic objects suffer. In this case, the entanglement disappears almost as soon as it is created, making it useless for such tasks. More recently, teleportation was accomplished in the continuous variables (CV) framework between two atomic ensembles [1]. As remarkable as these achievements are, teleportation schemes that are known today (qubit/CV) do not allow us to teleport more complex quantum states at the macroscopic level. For example, while it is possible in principle to extend teleportation to multiple qubits, on a macroscopic level this is prohibitively complicated and highly susceptible to decoherence. For atomic ensemble CV based schemes, the teleported states are restricted to small displacements from the completely Sx-polarized state on the Bloch sphere.
We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a smaller number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a nonmaximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's laboratory in terms of the composition of the completely positive maps corresponding to the shared resource state and a joint positive operator-valued measure (POVM) performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is perfectly possible with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with Werner states and show that even when Werner states become separable, the amount of teleported coherence is nonzero, implying the possibility of teleportation of coherence without entanglement.
In the present paper, a quantum teleportation protocol for split-squeezed Bose-Einstein Condensates is proposed that transfers a spin coherent state between two locations using entanglement introduced by squeezing interactions. One axis squeezing is used for this purpose, two axis anti squeezing further reduces the noise. The protocol uses continuous variable quadrature measurements that works for short interaction times in the Holstein-Primakoff approximation. The performance of the protocol is also analyzed by calculating the fidelity to show that it exceeds the classical bound.
We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a lesser number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a non-maximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's lab in terms of the composition of the completely positive maps corresponding to the shared resource state and joint POVM performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is possible perfectly with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with the Werner states and show that even when the Werner states become separable, the amount of teleported coherence is non-zero, implying the possibility of teleportation of coherence without entanglement.
We develop methods for performing quantum teleportation of the total spin variables of an unknown state, using quantum nondemolition measurements, spin projection measurements, and classical communication. While, theoretically, teleportation of high-dimensional states can be attained with the assumption of generalized Bell measurements, this is typically experimentally nontrivial to implement. We introduce two protocols and show that on average, the teleportation succeeds in teleporting the spin variables of a spin coherent state with average zero angular error in the ideal case, beating classical strategies based on quantum state estimation. In a single run of the teleportation, there is an angular error at the level of $\ensuremath{\sim}0.1$ radians for large ensembles. A potential physical implementation for the scheme is with atomic ensembles and quantum nondemolition measurements performed with light. We analyze the decoherence of the protocols and find that the protocol is robust even in the limit of large ensemble sizes.