# By Leaps and Bounds: PhD Student Positions LSU as a Leading Contributor to Research on Quantum Key Distribution

Eneet Kaur is a doctoral student and rising star in quantum information science at
LSU. She recently presented her work on quantum key distribution, a method to secure
communications based on the physical principles of quantum mechanics, as an invited
talk at the QCrypt conference in Montreal, Canada. Her advisor Mark M. Wilde is an
associate professor in the Department of Physics & Astronomy with a joint position
at the Center for Computation & Technology; 2018 Rainmaker; and author of *Quantum Information Theory* (Cambridge University Press, Second Edition, 2017).

Kaur grew up in New Delhi, India. On her path to do a PhD in quantum information science,
she’d read Wilde’s textbook, which made her decide to come to LSU.

“I was debating on whom to work with, but once I came to LSU, that was it,” she recalls.
“Mark is a good teacher—very interactive—and that’s why I wanted to work with him.”

Kaur and Wilde have been working together on quantum key distribution, which is the
focus of Kaur’s PhD. Quantum key distribution is a central topic of research in the
field of quantum communications to secure information that’s transmitted over an insecure
quantum channel.

“There’s a regime in quantum key distribution that’s called device-independent quantum
key distribution,” Kaur explains. “Let’s say you have Alice and Bob and they do not
trust the devices in their laboratories; they do not know what the quantum states
in their devices are, and they do not know the measurements the devices are implementing—and
still, they want to extract a secure key. What Mark and I did was to find an upper
bound on the best rate of secure key that Alice and Bob can extract in this scenario.”

“... we want to make an information-theoretic evaluation of security from physical principles, and this is what quantum key distribution does. Even if you get a very powerful computer, like a classical computer, a supercomputer, or a quantum computer, it shouldn’t matter. The security of the scheme should still hold.”

Kaur describes quantum key distribution by going back to Alice and Bob, who are separated
geographically and might use optical fibers to transmit information to each other.

“Let’s say there’s an eavesdropper or malicious party who can receive the information
that’s traveling in that optical fiber, or even control the fiber, maybe replacing
it with something else, and do whatever the eavesdropper wants to do,” Kaur says.
“Now, the question is—can you still establish a secure message between Alice and Bob?
How can Alice and Bob share something that isn’t known to anyone else in the world,
something that’s just between the two of them? What I want to do is to establish the
security of their communication from an information-theoretic perspective.”

“We do not want to make statements on computational hardness like you do in existing
schemes like RSA cryptography,” Kaur continues. “Instead, we want to make an information-theoretic
evaluation of security from physical principles, and this is what quantum key distribution
does. Even if you get a very powerful computer, like a classical computer, a supercomputer,
or a quantum computer, it shouldn’t matter. The security of the scheme should still
hold.”

There are, of course, different systems to implement quantum key distribution. Part
of the challenge is in figuring out the strategies where it’s easier to implement
using current technologies. For that, Kaur relies on the regime of continuous-variable
quantum key distribution.

“We use the amplitude and phase quadrature of photons to encode the information and
then establish a security proof,” she explains. “We basically said, okay, we have
a way to deal with these photons and can get a secure key out of that.”

An eavesdropper could simply cut the cable or the fiber, and then there would be no
message at all. Or an eavesdropper could send in enough noise that there is no message
between Alice and Bob. But ultimately, what the eavesdropper wants is for there to
be a message, and to know that message. What Kaur and Wilde needed to do was to prove
mathematically that an eavesdropper cannot do this.

“In principle, an eavesdropper can have a beam splitter inside the fiber and leak
some of the information outside,” Kaur says. “We want to have a security protocol
that is secure under this type of attack and any other attacks that you can think
about. The security of the protocol has to be on mathematical terms. So, what we do
is work on security proofs. We rigorously prove that the key you obtain is secure
under any attack. There’s a whole community working on this area.”

”How you actually choose your questions, that’s really important. Can you even answer them? What tools do you have? If you’re given a certain problem, how do you approach it? What’s the first thing you need to think about?”

It is generally considered too difficult to find the exact secure key rates. What
Kaur and Wilde are doing instead is to establish lower bounds on achievable secure
key rates in continuous-variable quantum key distribution, finding the point up to
which a key is going to be secure. They’ve also established upper bounds in device-independent
quantum key distribution. By working on both lower and upper bounds, they’ve narrowed
down the possible secure key rates.

“It requires a lot of hard work to close the gap,” she says. “We have to develop new
techniques, and it’s not easy to think of what techniques can be used in this scenario.”

Last August, Kaur presented an invited talk about their work at a conference for quantum
cryptography in Montreal, Canada called QCrypt.

“It’s quite competitive—you submit and only a few people get selected,” Kaur says.
“Mark and I just got an invitation to present our work without having to submit, and
so it was quite exciting.”

Ten years from now, Kaur sees herself still doing quantum information research. She
would like to focus on quantum communications, including network designs; figuring
out new protocols that would have an advantage over classical scenarios and how they
can be implemented in the lab.

Kaur was always interested in science. At first, mostly in biology, which in India
turned out to be a crowded field. Instead, she decided to pursue physics. Biophysics
became a way for her to “covertly” do biology, but this turned out to be an overcrowded
path as well. When she expressed interest in a summer internship in biophysics at
the Indian Institute of Science Education and Research, Mohali, there was no position
open. Her supervisor, who worked in both biophysics and quantum information, encouraged
her to head in a new direction.

“My supervisor just handed me something to read on quantum information, and from that
first time, I found it to be super-interesting,” Kaur remembers. “There are counterintuitive
phenomena that you don’t expect to happen, and then you figure out why they do. When
I encountered this, that was my starting point to get involved in research. I started
reading a standard textbook and then got more and more interested.”

During her four years at LSU, Kaur has had the opportunity to learn from leading experts
in her field. She visited Stephanie Wehner, a German physicist and computer scientist
known for introducing the noisy-storage model in quantum cryptography, in her second
year.

“Every researcher has a different process of thinking and you can learn from everyone,
how they approach their problems,” Kaur says. “I saw how Wehner organized her work
and how passionate she is about science. How you actually choose your questions, that’s
really important. Can you even answer them? What tools do you have? If you’re given
a certain problem, how do you approach it? What’s the first thing you need to think
about?”

”Sometimes a new perspective helps you, just extracting the basics of the problem and getting rid of the complicated features ... You distill out the most important parts and sometimes, if you’re lucky, what’s left is a simple thing. Most things have an underlying intuition, a root, which is important to understand.”

Kaur has traveled to conferences all around the world—in Cambridge, England; Brazil;
Baiona and Barcelona, Spain, where she also visited the German mathematician and mathematical
physicist Andreas Winter; College Park, Maryland; Seattle, Washington; Boulder, Colorado;
and Urbana-Champaign, Illinois.

It was in the first summer after joining LSU that Kaur made her first significant
breakthrough. Wilde had asked her to quantify the quantum steering effect using conditional
mutual information while he was out of town, and as she was “just playing around with
some functions,” she made an observation about how to construct a function that eventually
led to the QCrypt talk and also will constitute half of her PhD thesis, which she
plans to defend in March in time for graduation in May 2020.

“I haven’t really started writing my thesis yet,” she says. “I’m trying to finish
a lot of projects before I leave LSU.”

One of these projects began this past summer, when Kaur was working with a quantum
information researcher in Tokyo, Japan—Masahiro Takeoka.

“He had been working on something for a year or two and had come up with an information
measure, a mathematical function of a quantum state,” Kaur recalls. “Let’s say that
you want to upper-bound the capacity of quantum communications, like state-distillation
in a quantum network. Suppose that Alice, Bob, and Charlie share a quantum state and
they want to distill out a particular quantum state that’s the maximally entangled
state between several parties. Our colleague in Japan was looking at the rate of secret
key distillation and had a mathematical function to address that problem, but then
I looked at it for a week—two, maybe—and realized it was too complicated of a function.
It could be simplified by a lot.”

“It was not a complicated task,” she continues. “It was a simple observation. Sometimes
a new perspective helps you, just extracting the basics of the problem and getting
rid of the complicated features. The proofs went from two to three pages long to about
half a page. This aspect ended up being nice. It was not like he couldn’t do it or
anything; it was just that I had a new perspective. I wasn’t seeking to simplify it.
But when I look at a formula, I just want to dumb it down so that I can understand
it. I want to make it as simple as possible so it’s easy for me to grasp. When I was
looking at his function, I wasn’t able to understand a couple of things—I couldn’t
understand why some parts were involved, I couldn’t understand their relevance—so
I thought, if I didn’t need them, what would be the function that I would construct?
And then I did that and saw that it could be simplified. You distill out the most
important parts and sometimes, if you’re lucky, what’s left is a simple thing. Most
things have an underlying intuition, a root, which is important to understand.”

Kaur and Wilde’s joint paper, “Amortized Entanglement of a Quantum Channel and Approximately Teleportation-simulable
Channels,” was selected as a highlight of 2018 by *Journal of Physics A*. Another paper, “Extendibility Limits the Performance of Quantum Processors,” was recently accepted into the journal *Physical Review Letters*, the premier venue for physics research.

Elsa Hahne

LSU Office of Research & Economic Development

225-578-4774

ehahne@lsu.edu