Peter Heuer - 10/21/2013
Quantum Cryptography Using Single and Entangled Photon Sources
The end goal of any code is to transmit information from one person, Alice, to a receiver,
Bob, without the message being intercepted by an eavesdropper, Eve. Classical codes can use a
key held by both Alice and Bob to prevent Eve from understanding their correspondence.
However, this type of code can be easily defeated if Eve manages to intercept the encryption key
itself. Classically, there is no way for Alice and Bob to be absolutely sure that the key was not
intercepted.
Quantum key distribution seeks to solve this problem by exploiting the quantum
mechanical properties of individual photons. One of the most famous examples of this process is
the BB84 protocol. Alice encodes a bit of information on a single photon by transmitting it in
one of two choices of basis. The photon then travels to Bob, who measures in one of the two
basis chosen at random. After the transmission, Alice and Bob compare the list of basis they used
over a classical communication channel. When their basis agreed they take those measured
values as zeros and ones, which becomes the key for their code. By comparing the remaining
photons, Bob can check that Eve has not intercepted the communication. If she has, the
remaining photons will be in a different polarization state than Bob would have expected. If this
is the case, Bob and Alice will know to try sending the key again, this time over a more secure
channel.
This process relies on Alice's ability to emit a single photon at a time. This is difficult
because, like all bosons, photons prefer to bunch together in groups that share the same
characteristics. If the quantum key was sent using bunches of photons, Eve could simply measure
one photon from each bunch to reconstruct the message allowing the rest of the photons to reach
Bob in their original state, leaving no sign of her intervention. A stream of photons that are truly
spatially separated is said to be antibunched.
An attenuated laser beam contains bunched photons and is therefore insufficient for
secure quantum communication. True single photon sources are created by using the
fluorescence lifetimes of single emitting structure to separate the emitted photons. These
structures are known as single emitters. Two of the most common single emitters are colloidal
quantum dots and diamond color centers.
Colloidal quantum dots are small pockets of a semiconductor with a small band gap
embedded within a larger semiconductor with a larger band gap. The structures combine to
create discrete energy levels that can be excited and emit light much like an atom. A single
quantum dot can be excited by focusing a laser onto it, causing it to emit photons separated by its
fluorescence lifetime, which are often on the order of nanoseconds. However, quantum dots have
several properties that make them unwieldy sources for quantum communication. Single
quantum dots sometimes become inactive for some period of time and then reactivate; a
phenomenon known as blinking. Even worse, dots can die completely, which is called bleaching.
In either case, Alice would have to refocus her laser on a new quantum dot to continue the
message, which would be extremely inconvenient.
Nanodiamond color centers are a promising single emitter that may eventually replace
quantum dots. Color centers are defects in the carbon lattice most commonly consisting of an
empty space with the adjacent carbon replaced with a nitrogen atom. All diamonds have these
defects, but the small size of nanodiamonds limits the effects of refraction due the high index of
refraction of diamond. When illuminated, color centers fluoresce much like a quantum dot.
Unlike quantum dots, color centers do not bleach or blink, making them more much more stable.
However, since color centers are natural rather than manufactured, it is harder to create uniform
single emitters that can be used interchangeably.
Both quantum dots and nanodiamonds produce photons on demand. However, quantum
key distribution can be done with probabilistically emitted photons as long as Alice can still
measure what polarizations are being sent. This cannot be done by simply measuring the photons
before sending them to Bob, as this would collapse their wave function, leaving Eve free to
intercept them unnoticed. However, entangled photons can be used to get around this restriction.
When two photons are polarization entangled, a measurement of the polarization of one photon
determines with certainty the polarization of the other photon. In the E91 protocol, Alice
produces a pair of polarization entangled photons. As photons pairs are produced, she measures
the polarization of one in some basis and sends the other to Bob, who does the same. After some
number of photons has been sent, Alice and Bob determine the key by comparing their choices
of basis and their measured results. As with the BB84 protocol, Alice and Bob can tell if Eve has
intercepted the message by checking the statistics of the photons received.
Entangled photons can be created through the process of parametric down conversion in a
non-linear Beta-barium borate (BBO) crystal. When a pump beam is incident on the crystal,
there is a small probability that a given photon will split into two photons with each vertical and
horizontal polarization. The horizontal and vertical photons are produced with trajectories
distributed around two separate cones. However, where these cones meet there is an equal
probability of measuring receiving either polarization. The two beams where these cones
intersect contain entangled photons.
Many other potential quantum key distribution protocols and photon sources exist in
addition to those mentioned above. These techniques have been tested both in the laboratory as
well as over long distances. Their eventual adoption requires only the development of longer
lasting, more stable and tunable single emitters.
References
M. D. Eisaman, J. Fan, A. Migdall, & S. V. Polyakov (2011) "Single-photon sources and
detectors" Review of Scientific Insturments 82 (071101-1)
R. Ursin et al. (2007) "Entanglement-based quantum communication over 144km" Nature Vol. 3,
481-486