This series consists of talks in the area of Quantum Information Theory.
I will describe some of the recent progress in quantum query complexity, including super-quadratic separations between classical and quantum measures for total functions, a better understanding of the power of some lower bound techniques, and insight into when we should expect exponential quantum speedups for partial functions.
We use powerful concentration of measure techniques to study how many states are useful for quantum metrology, i.e., give a precision in parameter estimation surpassing fundamental limits in the classical case. First, we show that random pure multiparticle states do not lead to quantum enhancement. Conversely, we prove that typical pure states on the symmetric (bosonic) subspace achieve Heisenberg scaling with probability approaching unity for any fixed Hamiltonian encoding. We generalize our results to random mixed states having the fixed spectrum and study the impact of particle losses.
Topological quantum computation is a fault tolerant protocol for quantum computing using non-abelian topological phases of matter. Information is encoded in states of multi-quasiparticle excitations(anyons), and quantum gates are realized by braiding of anyons. The mathematical foundation of anyon systems is described by unitary modular tensor categories.
An essential component of scalable quantum computing is the ability to reliably protect quantum information from decoherence. Such protection can in principle be achieved via the use of quantum error correcting codes.
We discuss a construction to obtain families of quantum codes based on regular tilings of surfaces with constant negative curvature. This construction results in two-dimensional quantum codes whose tradeoff between encoding rate and protection is more favorable than for the standard surface code.
Quantum key distribution protocols can be based on
quantum error correcting codes, where the structure of the code determines the
post processing protocol applied to a raw key produced by BB84 or a similar
scheme. Luo and Devetak showed that
basing a similar protocol on entanglement-assisted quantum error-correcting
codes (EAQECCs) leads to quantum key expansion (QKE) protocols, where some
amount of previously shared secret key is used as a seed in the post-processing
In
quantum information theory, random techniques have proven to be very useful.
For example, many questions related to the problem of the additivity of
entropies of quantum channels rely on fine properties of concentration of
measure.
In this talk I will sketch a project which aims at the
design of systematic and efficient procedures to infer quantum models from
measured data. Progress in experimental control have enabled an increasingly
fine tuned probing of the quantum nature of matter, e.g., in superconducting
qubits. Such experiments have shown that we not always have a good
understanding of how to model the experimentally performed measurements via
POVMs. It turns out that the ad hoc postulation of POVMs can lead to
It is widely known in the
quantum information community that the states that satisfy strong subadditivity
of entropy with equality have the form of quantum Markov chain. Based on a
recent strengthening of strong subadditivity of entropy, I will describe how
such structure can be exploited in the studies of gapped quantum many-body
system. In particular, I will describe a diagrammatic trick to i) give a
quantitative statement about the locality of entanglement spectrum ii)
A "one-time program" for a channel C is a
hypothetical cryptographic primitive by which a user may evaluate C on only one
input state of her choice. (Think Mission Impossible: "this tape
will self-destruct in five seconds.") One-time programs cannot be
achieved without extra assumptions such as secure hardware; it is known that
one-time programs can be constructed for classical channels using a very basic
hypothetical hardware device called a "one-time memory".