Hi all,
Sorry for the terribly late notice --- today Philipp Höhn will continue his
talk on reference frames. Here's the link: https://ethz.zoom.us/j/362994444.
We will also record and post the talk.
Best,
Joe
Hi all,
Tomorrow Oliver Knapp will present his semester project, entitled
"Relativity from relational quantum mechanics: the emergence of Lorentz
transformations in rotational invariant qubit systems." See the abstract
below. The zoom link is https://ethz.zoom.us/j/362994444.
Best
Joe
Abstract: We show how Lorentz transformations emerge as a natural
consequence of rotational symmetry in qubit systems. To this end, we first
review relational quantum mechanics and subsequently propose a framework to
integrate the relational principle in multi- qubit systems. This principle
inevitably requires every multi-qubit system to be SU(2) symmetric, that is
one may rotate the qubits without changing the dynamics. We then examine
the properties of such SU(2) symmetric qubit systems and prove that time
evolution must consist only of permutations of the qubits, similar to the
SWAP gate. As a direct consequence, SU(2) symmetric systems are then
necessarily GL(2, C) symmetric. To deal with such non-unitary symmetry
transformations, we first consider a thought experiment exhibiting GL(2,C)
symmetry and then propose to generalize the postulates of quantum
mechanics. By regarding states as rays in a projective space the relevant
symmetry group reduces to PGL(2, C), which as a group is isomorphic to the
proper orthochronous Lorentz transformations SO+(1, 3). At last we show
that the action of PGL(2,C) on the Bloch sphere yields exactly the group of
all orientation- preserving conformal maps of the sphere S2, also known as
Möbius transformations.
Hi all,
Tomorrow Thomas Hahn will present his master's thesis project, carried out
with Ernest, on "Fidelity Bounds for Device-Independent Advantage
Distillation". See below for the abstract. The zoom link is
https://ethz.zoom.us/j/362994444.
Best
Joe
Abstract: Low noise tolerances for current device-independent quantum key
distribution protocols and the existence of fidelity-related security
conditions in device-independent advantage distillation motivate the need
for strong lower bounds on the fidelity. This thesis shows that a reduction
to qubits does not deliver optimal bounds. An algorithm is derived that can
in principle bound the fidelity for our device-independent setup to an
arbitrary precision. This algorithm is computable with a semi-definite
program and a constraint optimization. We conclude with a conjecture for a
necessary security condition against collective attacks, where a
repetition-code protocol that applies advantage distillation is considered.
Dear all,
Marco Tomamichel is hiring PhD students and postdocs in Singapore. This
is an open call. He works mostly on single-shot quantum information theory.
https://marcotom.info
Best,
Lídia
Hi all,
Tomorrow Philipp Höhn from the Okinawa Institute of Science and Technology
will tell us about "A Perspective-neutral approach to quantum frame
covariance". See below for the abstract. The talk starts, as usual, at 2pm
on zoom: https://ethz.zoom.us/j/362994444.
Best,
-joe
Title: Perspective-neutral approach to quantum frame covariance
Abstract:
General covariance posits that “all the laws of physics are the same in
every reference frame.” While this is an established pillar of general
relativity, its fate in the quantum realm remains an open question, both in
quantum gravity and the foundations of quantum theory. I will summarize a
perspective-neutral approach to quantum reference frames aimed at
addressing this question. This approach permits one to switch from the
description of physics relative to one quantum frame (a perspective) to
that relative to another. Such perspective changes work in analogy to
coordinate changes on a manifold, except that these “quantum coordinate
changes” proceed between different Hilbert spaces. In particular, they lead
to a "quantum relativity" of physical notions such as entanglement,
superposition, temporal locality or comparing clock readings. I will
explain how this approach resolves a puzzle known as the 'paradox of the
third particle' and how it has revealed a previously unknown equivalence
between three different approaches to the problem of time (relational
observables, Page-Wootters formalism and deparametrizations).
Hi all,
Tomorrow Timon Knigge will tell us about his semester project, which was
supervised by Niels Gleinig in the CS group of Prof. Torsten Hoefler. The
talk will start at 2pm on zoom: https://ethz.zoom.us/j/362994444
Title: Approximation of Classical Functions using Quantum Circuits
Abstract: We discuss the problem of approximating classical boolean
functions using quantum circuits. We specifically focus on bounding the
circuit length for general classes of boolean functions and discuss some
proof techniques for providing lower bounds on the length.
Best,
-joe
Hi all,
Tomorrow Yuxiang will give a more detailed look at his recent research. See
below for title and abstract. The zoom link is
https://ethz.zoom.us/j/362994444.
Best,
-joe
Title:
Optimal universal programming of unitary gates
Abstract:
A universal quantum processor is a device that takes as input a (quantum)
program, containing an encoding of an arbitrary unitary gate, and a
(quantum) data register, on which the encoded gate is applied. While no
perfect universal quantum processor can exist, approximate processors have
been proposed in the past two decades. A fundamental open question is how
the size of the smallest quantum program scales with the approximation
error. Here we answer the question, by proving a bound on the size of the
program and designing a concrete protocol that attains the bound in the
asymptotic limit. Our result is based on a connection between optimal
programming and the Heisenberg limit of quantum metrology, and establishes
an asymptotic equivalence between the tasks of programming, learning, and
estimating unitary gates.
This talk will be based on https://arxiv.org/abs/2007.10363.