A closed timelike curve
is a loop back in time (somewhat like the time portals in the Hollywood
film Looper). That is,
at certain "locations" in spacetime, there is a wormhole such that,
if you jump in, you'll emerge at some point in the past. To the best of our
knowledge, these time loops are not ruled out by the laws of physics.
Recent research of Todd
Brun, Andreas Winter and I shows how a time traveler can copy quantum data at
will, in violation of a fundamental principle of quantum mechanics often
referred to as the "no quantum Xerox machine" theorem. The method involves
looping a quantum particle back many times in the past and then reading out
many copies of it in such a way that you don't disturb the past.
Backtracking a little
bit, in 1991, David Deutsch, a theoretical physicist at Oxford University, came
up with a model of time travel and quantum mechanics that resolves various time
travel paradoxes that can arise (and which have often been depicted in
Hollywood films such as Terminator,
Looper, and Back
to the Future).
There are two well known
paradoxes:
1) First, the most famous
is the "grandfather paradox," in which the time traveler goes back in
time and kills her grandfather. If she is successful, how was she born in the
first place to do so?
2) Second, we have the
"Shakespeare paradox." That is, the time traveler reads the works of
Shakespeare, writes them down in a book, and sends them back in time.
Shakespeare then finds the book and writes everything down. Who wrote the works
of Shakespeare in the first place?
An interesting aspect of
Deutsch's model is that it allows for a time traveler to change the past, as
long as she does so in a self-consistent manner. That is, a time traveler could
kill her grandfather with probability one half, and then she wouldn't be born
with probability one half, but the opposite possibility (her being born) is a
fair chance with probability one half.
On the other hand, the
no-cloning (or "no quantum Xerox machine") theorem is a fundamental
tenet of quantum mechanics, the statement that it is impossible to produce a
perfect copy of the state of an unknown quantum particle. Since it's easy to
copy classical information and we do it all the time, it might seem a bit
counterintuitive at first that copying quantum information is impossible.
However, this theorem is at the heart of our understanding of quantum
information and it represents one of the main physical reasons why quantum
cryptography is secure.
What Todd Brun, Andreas
Winter, and I recently showed is that, if these time loops behave according to
Deutsch's model, then it would be possible to produce copies of quantum states
at will, which is a violation of the no-cloning theorem discussed above. We
first realized that we could create many copies of a quantum particle simply by
sending it back into the past many times. You could then attempt to read out
many copies of the particle, but if you do so, you'll disturb the past! So the
main innovation was to figure out what to do to the quantum particle before
sending it back many times into the past. After figuring that out, we realized
we could send the particle back many times into the past and then read out many
copies of it while not disturbing the past (so that no one there would notice
the difference).
This ability to copy
quantum information freely would turn quantum theory into an effectively
classical theory in which, for example, classical data thought to be secured by
quantum cryptography would no longer be safe. A malicious time looper could
take advantage of this device to break quantum secured communications,
potentially leading to catastrophic consequences.
Since the ability to
copy quantum information freely is a strong violation of our beliefs about what
should be possible in the physical world, we think our work serves as evidence
against Deutsch's model. That is, it seems as if there should be a revision to
Deutsch's model which would simultaneously resolve the various time travel
paradoxes but not lead to such striking consequences for quantum information
processing. However, no one yet has offered a model that meets these two requirements.
This is the subject of open research!
Mark Wilde is Assistant
Professor in the Physics and Astronomy Department at LSU.
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