An old technique helps Bob correctly decode Alice’s entangled message qubits
 Alice would like to transmit a stream of quantum information to Bob. She shares entanglement in the form of ebits before quantum communication begins. Red qubits belong to Alice and… Click here for more information. |
The Viterbi Algorithm, the elegant
41-year-old logical tool for rapidly eliminating dead end possibilities
in data transmission, has a new application to go alongside its
ubiquitous daily use in cell phone communications, bioinformatics,
speech recognition and many other areas of information technology.
In
a recent set of papers two investigators from the University of
Southern California school that bears the name of the algorithm’s
inventor say it can play a key role in quantum communication.
Mark
Wilde, a graduate student in the USC Viterbi School of Engineering,
collaborated with his faculty advisor Todd Brun on the work. The
research is also his thesis, for which he will receive a PhD from the
School’s Ming Hsieh Department of Electrical Engineering in August.
Brun,
an associate professor in the Hsieh Department, is also deputy director
of the USC Center for Quantum Information Science & Technology.
The
quantum communication applications Wilde and Brun explored are for an
environment in which a sender "Alice" (the traditional sender name) is
trying to send a quantum message to a receiver named (again by
tradition) "Bob" using a stream of pairs of "entangled" photons.
"Such
[entangled] photons," in the words of the recent New Scientist story,
"obey the strange principles of quantum physics, whereby disturbing the
state of one will instantly disturb the other, no matter how much
distance there is in between them."
Use of such a system has
been proposed for a variety of uses, including space based
communication, and progress is being made on the physical devices that
might create entanged photons for messages. But noise is created in the
transmission of quantum data, an issue the USC work addresses using the
time-hallowed Viterbi algorithm.
In the system considered by
Wilde and Brun, Alice encodes each quantum bit of the message with the
help of an ebit, an entangled qubit. She sends her part of the encoded
quantum message over a noisy quantum communication channel, a process
that can introduce errors.
From his side, Bob receives what
Alice sent and combines her transmitted qubits with his half of the
ebits. He measures all of the qubits, processes the results of the
measurements, performs recovery operations, and finally decodes them,
receiving the message qubits Alice sent. At the conclusion of the
process Bob will have the transmitted quantum information error-free.
The
above description is a condensed and simplified paraphrase of what is
in fact a much more complex process, a ballet in which Alice and Bob
can exploit ancilla or helper qubits, gauge or noisy qubits, and ebits
to transmit both quantum and classical information.
But the
bottom line question coming out remains, how does Bob know that the
dancers were following the music, that the message he now has was
transmitted correctly?
The fact that the noisy quantum
communication channel can be modeled as a sequential process of steps,
each step of which changes the state of the system, offers an opening.
The Viterbi algorithm is, precisely, a way of analyzing the products of
such progressions, called "Markov processes."
In Wilde and
Brun’s analysis, Bob watches the step coming out of his measurement
process, testing them against statistical probabilities, using standard
Viterbi tools.
Cell phones use similar programming to correct for errors in the transmission of digital voice data.
The
result: Bob can reliably spot errors, and knows which message qubits
are bogus before he opens the message – crucial, because opening it
destroys it; and if it is garbled, he has nothing.
With thanks to the University of Southern California
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