Collection Number S007
Collection Type Series
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 stage to produce a larger secret key.
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 show that very different techniques of random matrix theory can complement quite efficiently more classical random techniques. I will spend some time on discussing the Weingarten calculus approach, and the operator norm approach.
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 inconsistencies.
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) perturbatively bound changes of topological entanglement entropy under generic perturbation.
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". Our main result is the construction of a one-time program for any quantum channel specified by a circuit, assuming the sam
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. Here we demonstrate that local topological order implies a constant energy barrier, thus inhibiting thermal stability.
Self-testing a multipartite quantum state means verifying the existence of the state based on the outcomes of unknown or untrusted measurements. This concept is important in device-independent quantum cryptography. There are some previously known results on self-testing which involve nonlocal binary XOR games such as the CHSH test and the GHZ paradox. In our work we expand on these results. We provide a general criterion which, when satisfied, guarantees that a given nonlocal binary XOR game is a robust self-test. The error term in this result is quadratic, which is the best possibl
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.