Quantum Teleportation: A Brief Overview of How it Functions and itsPossible Uses

Sean Boland

Abstract— As the conventional means of communication age,more ways than ever are being found to exploit them. In thedigital world, cryptography continues to become more prevalentand more widely known, leading toward increasingly largernumbers of both successful and harmful attacks on ’secure’information. Such attacks not only call for more research intothe fields of cryptography and security systems, but also intonew ways of communication. With the creation of machinesthat can successfully utilize quantum mechanics to teleportinformation instantaneously and without leaving a messageto intercept, a new form of highly secure communication isarriving at exactly the time it is needed. Though there arelimitations due to currently available technology, quantumteleportation serves as a groundbreaking basis to an importantand advanced technological leap forward.

I. INTRODUCTION

Communication throughout history has always been inter-ceptable. Ever since humans first thought to keep informationsecret, others have strived to discover those secrets. Fromeavesdropping to wire-tapping to backdoors that bypassencryptions, people who steal information have been creatingever more complicated means to keep up in the figurativearms race between them and those who create the securityand cryptographic systems themselves.

Before writing, information would either be discussedin secure locations, or relayed by messengers, and otherswho desired to steal the information would eavesdrop onthe party’s conversation or intercept said messenger. Afterthe creation of formal writing systems, messages could besent without their carriers knowing what they contained, butseeing as these methods were still interceptable, ciphers orother ways of hiding the information were created. Around500 BC, Demaratus, a deposed king of Sparta, sent warningto Greece of an imminent attack from the Persian empireby writing it in wood and covering the message with wax,creating a wax tablet with an unimportant correspondenceon the front, as was a common form of communication forthe time. During his time as a Roman general, Julius Caesarcreated one of the earliest known ciphers as a way to encryptmessages to his troops, simply shifting the alphabet by a setnumber of letters in order to make the messages unreadablewithout sitting down and deciphering them; something a spywould not have time to do without being noticed[1]. In moredesperate situations, messages were hidden in public view,such as certain letters in a public document having beenprinted in a different typeface to spell a message, or JeremiahDenton blinking in Morse code during a television broadcastto warn the United States that he and the other capturedsoldiers in the Vietnam war were being tortured.

Skipping ahead to the advent of computers and the in-ternet, because of the nature of the internet, messages anddocuments could now be read without the original sender’sor recipient’s knowledge, and new, more complicated, formsof cryptography had to be created to secure the data. Keycryptography is a prevalent form of cryptography originallyconceived in the late 19th century that was adapted andimproved upon for use with computer systems. The basisof key encryption is that the values of each character in amessage are manipulated in some way by a key to encryptthe message in such a way that only someone with the samekey (in single-key encryption), or a specific, private key (intwo-key encryption) can decrypt and read the message. Thistype of cryptography is used for digital signatures, passwordencryption, and end-to-end encryption. The largest current(external) threats to key-systems are known as man-in-the-middle attacks[2]. These are situations in which a third partyimpersonates the recipient in some way so that the messageis encrypted with a key known to the attacker, who decryptsthe message, and then re-encrypts it with a key shared withthe real recipient before sending it to them. Because boththe sender and recipient of the messages believe that theyare sending messages to each other, and because they areboth receiving messages as if nothing is wrong, they arenever made aware of the third party whom is also receivingand decrypting their messages.

Counteracting such man-in-the-middle attacks is wherequantum cryptography, or more specifically, quantum tele-portation and quantum key-exchanges could revolutionizecommunication yet again.

II. EXPLAINING QUANTUM CRYPTOGRAPHY

A. Quantum Teleportation

Quantum teleportation is the instantaneous transfer ofinformation from one point to another. This differs fromnormal forms of information transference or communicationin that the information does not travel from one location toanother, but rather ceases to exist in one location, and springsinto existence in another, set location. This is achievedthrough the use of a particle phenomenon known as quantumentanglement.

Quantum entanglement is a physical phenomenon thatoccurs when particles (a pair in this case) are linked in sucha way that the quantum state of one cannot be describedseparately from the quantum state of the other and must bedescribed as if the particles were one and the same, even ifthey are separated by huge distances. Once a pair of quantum

entangled photons are separated, any change in one will beinstantaneously made in the other as well.

For example, in the “Quantum Teleportation over 100 Kmof Fiber Using Highly Efficient Superconducting NanowireSingle-photon Detectors” experiment[3], the original, entan-gled photons are created at random to hit the detectors eitherone nanosecond early or late, so their states are either ‘early’or ‘late’, representing the 1’s and 0’s of bits. However,since in this case it is unknown which state the photonsare in as they are unmeasured, they are considered both. Ina situation which is effectively the quantum equivalent ofSchrodinger’s cat, the very act of measuring the state of aparticle defines the state of that particle. This is known as aquantum superposition, where the peaks of the states’ wavescan either be in phase, where they line up and multiply eachother, or out of phase, where the waves cancel each otherout. This is a property that is unique to quantum bits, or‘quibits’ as opposed to conventional, binary bits.

Fig. 1. A visual representation of the experiment, courtesy of Kelly Irvineand the National Institute of Standards and Technology[4].

The experiment begins by generating a photon of anunknown state and then splitting it into two photons whichare quantum entangled. The output photon is sent through 60miles of optical fiber to its destination, while its entangledphoton is sent into a collision with a new input photon ofwhich the state is known, so it is either early or late. Whenthe two photons collide, they are both destroyed, but notbefore the entangled photon takes on the state opposite tothat of the input photon. Since the entangled photon’s statewas changed, the output photon’s state was also changed atthe exact time the change occurred 60 miles away.

Because the information never traveled through any chan-nels to show the message at the output photon, methodssuch as intercepting the information through surveillanceor wiretap methods along the route of information flow isimpossible. The only way for someone to discover the outputwould be to see it at either its origin or destination.

B. Quantum Key-ExchangeWhere quantum teleportation truly shines is when it is

added to the traditional key exchange problem, turning itinto the quantum key exchange problem.

To extend the range of communication with quantumteleportation, waystations or repeaters would have to becreated at distance intervals along the route of communi-cation. These repeaters would act in much the same wayas conventional repeaters do for boosting cell phone signalsover long distances. One downside that may come to mindwould be that these repeaters create places for a third party tointercept messages between two people. However, quantumteleportation thwarts the normal man-in-the-middle attack.

Using the BB84 protocol by Charles H. Bennett and GillesBrassard[5][6], Alice, the sender, will send Bob, the receiver,a message consisting of a stream of randomly polarizedphotons. A polarized photon is one of the pairs of stateswithin one of the conjugate state pairs that represent binarynumbers. In figure 2, the states are represented as ↑ = 0, →= 1 for one conjugate (+), and ↗ = 0, ↘ = 1 for the other(x). Bob will then pass Alice’s stream of photons through hisown randomly polarized filter and tell her the polarizations ofthe photons that he gets. If the wrong conjugate was chosento measure one of the photons in, the result has a 50% chanceto be either arrow in the pair, so Alice will tell him whicharrows (photons) made it through his filter correctly, and theresulting set of arrows will represent their shared key.

When an eavesdropping third party, Eve, is placed into aposition to intercept Alice’s photon stream to Bob, however,this changes. Eve must also use a randomly polarized filterto pass Alice’s photon stream through, but since the photonswere destroyed when she measured them, she must also sendthe results she received as a stream of photons to Bob. If shechooses the wrong filter for any of Alice’s photons and sendsthat result to Bob, Bob could choose the same filter that Alicehad, but have a 50% chance to get the wrong arrow, whichis exactly what happens in figure 2.

Fig. 2. A chart showing an example of the BB84 protocol in action, withEve in the center, trying to eavesdrop.

In the figure above, there were two instances where Evechose the wrong filter and Bob the correct one, in one ofthese, Bob received the wrong arrow (photon state), but inthe other, received the correct one by chance. This error inthe results should not have existed, as Bob chose the correctfilter, and there should have been no way for him to receivethe incorrect state. This means that Alice and Bob have beenmade aware of Eve’s existence, will not use the created key,

and can choose to create a new key later or on a differentchannel in order to avoid her.

Because attempting to intercept a quantum key gives Evea 50% chance for each filter to be wrong, and Bob a 50%chance to get the wrong photon state from that filter if hechooses the correct filter, Eve’s chance of detection is 25%per photon. This may also be written as a formula:

1− (3/4)number of photons

So, in attempting to intercept the photon stream fromfigure 2, Eve had a 90% chance of being detected, and ifAlice and Bob doubled the number of photons in the streamto 16, she would have a 99% chance of being detected.

The very nature of quantum teleportation invalidates acurrently successful form of anonymous information gath-ering almost entirely with just 16 photons. Though a keyof less than or equal length of 16 bits would be easilycrackable through other means if used to encrypt messageson conventional channels.

III. QUANTUM DECRYPTION

In contemporary cryptology, all key cryptographic systemsare based on the concept of integer factorization beingimpossible (or at least infeasible) to solve with contemporarycomputer systems for large integers that are the productsof only a few prime numbers such as 300-digit primes[7].Many contemporary cryptographic systems are based on thecomplexity of the algorithm that could be used to decryptthem. For example, though Shor’s algorithm can break aninteger into its prime factors, it is a quantum algorithm, andsubsequently could only run on a quantum computer.

If a quantum computer were used for decryption, however,it would be able to decode messages, without using a key,in polynomial time, as well as decode any other systemsbased on the difficulty of solving large integers. Such sys-tems would include email encryption, secure webpages, andnumerous other data types on the internet. Decrypting thesesystems would have widespread and problematic implica-tions for privacy and security on computer systems.

There are types of encryption that currently exist and arenot solvable as of yet through quantum algorithms, however,and would remain secure even with quantum computers inuse, such as the McEliece cryptosystem[8]. Also, quantumcryptography would come into use along with quantumdecryption methods, and would protect even key-encryptedinformation from both contemporary and quantum decryp-tion simply due to the information not existing in any placesbeside those of the sender’s and receiver’s computers. It isalso unknown what encryption methods could be created byutilizing a quantum computer.

IV. LIMITATIONS

Though impressive even as they exist today, quantum tele-portation, cryptography, and computing unfortunately havemajor downsides that keep them from being feasible to usein present day.

A. Quantum Decoherence

When a quantum system is not kept in perfect isolationfrom its surroundings, the process of quantum decoherencebegins, the system’s coherence begins to decay irreversibly,and the quantum behavior that allows for the system to workis lost. As decoherence progresses, quantum entanglementsare created between the system and its surroundings, causingthe system to begin to share or transfer its information tothem[9][10].

B. Success Rate

Though the 60-mile quantum teleportation experiment[3]

was successful, there were issues with how many times aset of entangled photons would fail to even survive to thepoint of teleportation, as well as how many photons wereactually teleported. According to the researchers themselves,because of the manner in which the experiment focused onspecific combinations of quantum states, teleportation waspossible, at best, only successful 25% of the time. In the end,the researchers, teleported 83% of the possible transmissionssuccessfully, and while it did prove that the teleportation wasindeed quantum-based, that still leaves almost one-fifth ofthe currently possible teleportations as lost, which wouldbe an unreasonable amount for key-exchange or moderncommunication systems such as text messaging or email.

“Only about 1 percent of photons make it all the waythrough 100 km of fiber.” - Marty Stevens[11].

C. Upkeep

Though currently possible, multiple quantum teleportationrepeaters are largely infeasible due to what would be highupkeep costs. For quantum teleportation to work, supercon-ductivity is required[3]. So, quantum repeaters would needto house large, powerful, energy-draining freezers in orderto keep the superconductive wires at the one-degree aboveabsolute-zero needed for teleportation to succeed.

V. CURRENT USES

• University of Calgary researchers in Canada have re-cently successfully used quantum teleportation over 6kilometers of actual city infrastructure rather than in alab setting. They used unused cables under the city ofCalgary to do so[13].

• Researches at Google were able to use Google’s Quan-tum Dream quantum computer to successfully modeland produce the first completely scalable quantum sim-ulation of a hydrogen molecule. This could lead to moremolecules being modeled, allowing us to better under-stand particle-level physics, chemistry, and medicine,leading to breakthroughs in all fields[14].

• Some of the information that Edward Snowden leakedabout the NSA in 2014 shows that the agency wasattempting to build “a cryptologically useful quantumcomputer” for cracking most contemporary encryptiontypes. According to documents given the WashingtonPost, the computer was and possibly still is ”part of a

$79.7 million research program titled ‘Penetrating HardTargets.’”[15]

• In August, China successfully launched the first everquantum satellite into space. The satellite was created“to establish ultra-secure quantum communications” byusing quantum teleportation to transmit complex cryp-tographic keys between Earth and space, as well asinvestigate quantum phenomena[16].

VI. CONCLUSIONS

Despite current limitations due to modern technology,quantum teleportation, cryptography, and computers onlystand to improve in the coming years. As of today, quantumteleportation has been proven both possible and feasible inurban environments as well as labs, quantum cryptographyis able to create traditionally undecryptable means of digitalcommunication, and quantum computers have grown to thepoint of being able to map the building blocks of matteritself. Even with some justified reasons for concern in thefield of cryptology, quantum computers will prove only toadvance the field once the transition period is over. As thefield of quantum computing theory continues to grow, it willboth benefit and forever change all fields of science, not justcomputer science.

REFERENCES

[1] Suetonius. ”Life of Julius Caesar.” De Vita Caesarum (The TwelveCaesars). 121 AD. Print.

[2] Kohno, Tadayoshi, Niels Ferguson, and Bruce Schneier. CryptographyEngineering: Design Principles and Practical Applications. Indianapo-lis, IN: Wiley Pub., 2010. Print.

[3] Takesue, Hiroki, Shellee D. Dyer, Martin J. Stevens, Varun Verma,Richard P. Mirin, and Sae Woo Nam. ”Quantum Teleportation over100 Km of Fiber Using Highly Efficient Superconducting NanowireSingle-photon Detectors.” Optica 2.10 (2015): 832. Web.

[4] Irvine, Kelly. ”Quantum teleportation infographic.” NIST. NationalInstitute of Standards and Technology. Web.

[5] C. H. Bennett and G. Brassard. ”Quantum cryptography: Public keydistribution and coin tossing”. In Proceedings of IEEE InternationalConference on Computers, Systems and Signal Processing, volume175, page 8. New York, 1984. Print.

[6] Bennett, Charles H. ”Quantum Cryptography Using Any TwoNonorthogonal States.” Physical Review Letters 68.21 (1992): 3121-124. Web.

[7] Lenstra, Arjen K. ”Integer Factoring.” Designs, Codes and Cryptog-raphy 19.2/3 (2000): 101-28. Web.

[8] Bernstein, Daniel J. ”Introduction to Post-quantum Cryptography.”Post-Quantum Cryptography (2009): 1-14. Web.

[9] Zeh, H. D. ”On the Interpretation of Measurement in QuantumTheory.” Foundations of Physics 1.1 (1970): 69-76. Web.

[10] Schlosshauer, Maximilian. ”Decoherence, the Measurement Problem,and Interpretations of Quantum Mechanics.” Reviews of ModernPhysics 76.4 (2005): 1267-305. Web.

[11] Ost, Laura. ”NIST Team Breaks Distance Record for Quantum Tele-portation.” NIST. National Institute of Standards and Technology, 21Sept. 2016. Web.

[12] Brassard, Gilles, Samuel L. Braunstein, and Richard Cleve. ”Telepor-tation as a Quantum Computation.” Physica D: Nonlinear Phenomena120.1-2 (1998): 43-47. Web.

[13] Valivarthi, Raju, Marcel.li Grimau Puigibert, Qiang Zhou, Gabriel H.Aguilar, Varun B. Verma, Francesco Marsili, Matthew D. Shaw, SaeWoo Nam, Daniel Oblak, and Wolfgang Tittel. ”Quantum Teleporta-tion across a Metropolitan Fibre Network.” Nature Photonics 10.10(2016): 676-80. Web.

[14] O’Malley, P. J. J., R. Babbush, I. D. Kivlichan, J. Romero, J. R.Mcclean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding,B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. G.Fowler, E. Jeffrey, E. Lucero, A. Megrant, J. Y. Mutus, M. Neeley,C. Neill, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T. C.White, P. V. Coveney, P. J. Love, H. Neven, A. Aspuru-Guzik, and J.M. Martinis. ”Scalable Quantum Simulation of Molecular Energies.”Physical Review X 6.3 (2016): n. pag. Web.

[15] Rich, Steven, and Barton Gellman. ”NSA Seeks to Build QuantumComputer That Could Crack Most Types of Encryption.” The Wash-ington Post. WP Company, 02 Jan. 2014. Web.

[16] ”China Launches First-ever Quantum Communication Satellite.” ChinaLaunches First-ever Quantum Communication Satellite - Xinhua —English.news.cn. Xinhua News, 16 Aug. 2016. Web.