This series consists of talks in the area of Quantum Information Theory.
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
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
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".
We study the robustness of quantum information stored in
the degenerate ground space of a local, frustration-free Hamiltonian with
commuting terms on a 2D spin lattice. On one hand, a macroscopic energy barrier
separating the distinct ground states under local transformations would protect
the information from thermal fluctuations. On the other hand, local topological
order would shield the ground space from static perturbations.
Self-testing a multipartite quantum state means verifying
the existence of the state based on the outcomes of unknown or untrusted
This concept is important in device-independent quantum
The minimal dimension of the Hilbert space that hosts states of an entangled pair of photons can be extremely high. The process of spontaneous parametric down-conversion (SPDC) is a possible way of producing highly entangled photon pairs, in both the spatial and temporal parts of the wave function. However, the most common approximations that are used in the analytical treatment of SPDC hinder the possibility of noticing further structures of the single joint modes.
Winter's measurement compression theorem stands as one of the most important, yet perhaps less well-known coding theorems in quantum information theory. Not only does it make an illuminative statement about measurement in quantum theory, but it also underlies several other general protocols used for entanglement distillation or local purity distillation.
We propose a framework to describe and simulate a class of many-body quantum states. We do so by considering joint eigenspaces of sets of monomial unitary matrices, called "M-spaces"; a unitary matrix is monomial if precisely one entry per row and column is nonzero. We show that M-spaces encompass various important state families, such as all Pauli stabilizer states and codes, the AKLT model, Kitaev's anyon models, W states and several others. We furthermore demonstrate how basic properties of M-spaces can transparently be understood by manipulating their monomial stabilizer groups.