**Beam Me Up, Scotty**

By **Rose Walters
**

Over the course of the 20th and 21st centuries, few technological advancements have captivated the science fiction imagination as much as teleportation. While far from achieving the capability of Captain Kirk’s transporter, quantum teleportation stands to have a practical impact on information transfer protocols, including long-distance quantum communication and secure quantum networks.

In 1993, C.H. Bennett and others published the first paper expounding the theoretical possibility of quantum teleportation and laid the groundwork for a decades-long process of achieving and refining such a quantum mechanical feat[1]. Based on John S. Bell’s seminal 1964 paper — written during his brief stint at the University of Wisconsin-Madison — quantum teleportation enables complete long distance information transfer through a combination of quantum measurement and operation and classical communication. Unlike classical bits, quantum bits, or qubits, can exist in both the usual 0 and 1 logic states as well as in a superposition of both 0 and 1 simultaneously. The four Bell states are maximally entangled qubit pairs in which information is contained exclusively in the pair: not all information can be known about either of the individual qubits. These maximally entangled states, also called Einstein-Podolsky-Rosen (EPR) pairs, are ironically both the basis of Einstein’s objections to quantum mechanics and Bell’s evidence for that same quantum mechanical nonlocality against which Einstein protested. Einstein specifically objects to “spooky action at a distance,” which is the apparent violation of special relativity where a manipulation of one entangled particle generates a seemingly instantaneous reaction by the other, distant particle [2].

The canonical quantum teleportation protocol uses two parties, Alice and Bob, whose respective qubits A and B are prepared in a Bell state, one of four particular, maximally entangled states of two qubits. Alice also possesses a third qubit, initialized in an unknown state, which is the one that will be teleported to Bob. Akin to its science fiction analogue — where the transporter kills and recopies its user every time one is teleported — in order to teleport the particle, Alice must perform a destructive Bell measurement (the original state cannot be preserved) on her qubit A and also the one that will be teleported, which is subsequently received by Bob. This Bell measurement reveals information about the entangled pair’s state but destroys its quantum mechanical nature. Furthermore, due to the entanglement of A and B, it also projects Bob’s qubit into a specific quantum state based upon the outcome of Alice’s measurement. Alice sends a classical two-bit message telling Bob the outcome of her measurement (this resolves the EPR paradox’s apparent violation of special relativity), after which Bob applies the proper local quantum logic operation on qubit B to recover the original unknown input state[1].

Free space teleportation over a lab bench (about one meter) was first achieved five years after Bennett’s theorization, when Furusawa et al. achieved a 58% fidelity transportation. In quantum computing, fidelity is a measure of the degree to which the final state, in this case the teleported state, matches the ideal state expected as a result of the operations performed[3]. Since then, improvements have been made in free space teleportation, exemplified by a 2015 teleportation of over 16 m with an average fidelity of 89%. Using a teleportation scheme that calls for two particles instead of three, therefore allowing for a full Bell measurement, the experimenters exploited the theoretical possibility of perfect Bell measurements to achieve excellent fidelity[4].

This mention of the theoretical potential for perfect Bell measurements leads us to one significant practical limitation of quantum teleportation: the difficulty of fully distinguishing between the Bell states. As the current standard of Bell detection, using photodetection and linear optics, can only distinguish between two of the four Bell states, there is an upper limit for Bell measurement efficiency at 50%. In an effort to resolve the gap between theory – which states that with linear optics and *n *qubits one can approach 100% Bell-efficiency as *n *approaches infinity – and experiment, Hussain A. Zaidi and Peter Van Loock achieved over 60% unambiguous discrimination of Bell states. They did so with only linear optical elements, which never add frequency components or modify frequencies with respect to others in the system, and single-mode squeeze operators, which add pairs of photons, thus preserving the overall sign of the qubits’ spatial coordinates[5].

Teleportation over optical fiber, which stands to have perhaps the most immediate impact on communications networks, has especially suffered from these low detection efficiencies, where high photon loss and internal decoherence, or the destruction of stored quantum information, further limit the maximum transmission possibility. In 2015, Takeuse et al. used superconducting nanowire single-photon detectors in order to teleport qubits over an astonishing 100 km of fiber[6]. Somewhat more practically, in 2016 another research group used a Calgary fiber network to teleport photons over 6.2 km[7]. As we move towards teleportation over many kilometers with standard optical fiber, the reality of a quantum network becomes closer than ever.

Despite current practical limitations, recent research in both free space and optical fiber quantum teleportation has improved by orders of magnitude over early implementation efforts. With quantum computing capable of processing superpositions of logic states, these future networks offer the possibility for much higher efficiency computing over a distributed network, all relying on entangled photonic teleportation — that “spooky action at a distance”[7].

## REFERENCES

- Bennett CH, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters WK. Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels. Phys. Rev. Lett. 1993 March 29; 70 (13): 1895-899.
- Bell, JS. On the Einstein Podolsky Rosen Paradox. Physics. 1964 Novemebr 4; 1 (3): 195-200.
- Furusawa A, Sorensen JL, Braunstein SL, Fuchs CA, Kimble HJ, Polzik ES. Unconditional Quantum Teleportation. Science. 1998 October 23; 282 (5389): 706-09.
- Jin X, Ren J, Yang B, Yi Z, Zhou F, Xu X, et al. Experimental Free-space Quantum Teleportation. Nature Photonics. 2010 May 16. 4 (6): 376-81.
- Zaidi HA, Van Loock P. Beating the One-Half Limit of Ancilla-Free Linear Optics Bell Measurements. Phys. Rev. Lett. 2013 January 15. 110 (26): 110.26 (2013): 260501.
- Takesue H, Dyer SD, Stevens MJ, Verma V, Mirin RP, Nam SW. Quantum Teleportation over 100 km of Fiber Using Highly Efficient Superconducting Nanowire Single-photon Detectors. Optica. 2015. 2 (10): 832.
- Valivarthi R, Puigibert MG, Zhou Q, Aguilar GH, Verma VB, Marsili F, Shaw MD, Nam SW, Oblak D, Tittel W. Quantum Teleportation across a Metropolitan Fibre Network. Nature Photonics. 2016 September 19. 10 (10): 676-80.