This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.
A mixed state can be expressed as a sum of D tensor product matrices, where D is its operator Schmidt rank, or as the result of a purification with a purifying state of Schmidt rank D', where D' is its purification rank. The question whether D' can be upper bounded by D is important theoretically (to establish a description of mixed states with tensor networks), as well as numerically (as the first decomposition is more efficient, but the second one guarantees positive-semidefiniteness after truncation).
The problem of determining and describing the family of 1-particle reduced density operators (1-RDO) arising from N-fermion pure states (viapartial trace) is known as the fermionic quantum marginal problem. We present its solution, a multitude of constraints on the eigenvalues of the 1-RDO, generalizing the Pauli exclusion principle.
We present a family of three-dimensional local
quantum codes with pairs of fractal logical operators. It has two polynomials
over finite fields as input parameters
which generate fractal shapes of anti-commuting logical operators, and
possesses exotic topological order with quantum glassiness which is beyond
descriptions of conventional topological field theory. A necessary and
sufficient condition for being free from string-like logical operators is
Quantum process tomography is the experimental procedure
to determine the action of general transformations on quantum states. When an
external environment is interacting with the system these transformations are
called open. We show that if the state of the system and the environment is
correlated, at the beginning of the experiment, then the standard quantum
process tomography procedure fails. It produces results that are nonlinear and
non-positive (i.e., the dynamical map is not completely positive) . These
In my talk, I will discuss various families of quantum
low-density parity check
(LDPC) codes and their fault tolerance. Such codes yield finite code rates and
at the same time
simplify error correction and encoding due to low-weight stabilizer
generators. As an example, a large family of
Until fairly recently, it
was generally assumed that the initial state of a quantum system prepared for information processing was in a product state with its environment. If this is the case,
the evolution is described by a completely positive map. However, if the system and environment are initially correlated, or entangled, such that the so-called quantum discord is non-zero, then the
I will discuss two
generalizations of Kochen-Specker (KS) sets: projective KS sets and generalized
KS sets. We will see that projective KS sets can be used to characterize all
graphs for which the chromatic number is strictly larger than the quantum
chromatic number. Here, the quantum chromatic number is defined via a nonlocal
game based on graph coloring. We will further show that from any graph with
separation between these two quantities, one can construct a classical channel
We discuss the extension of the smooth entropy formalism to arbitrary physical systems with no bound on the number of degrees of freedom, comparing them with already existing notions of entropy for infinite-dimensional systems.
When two independent analog signals, $X$ and $Y$ are added together giving $Z=X+Y$, the entropy of $Z$, $H(Z)$, is not a simple function of the entropies $H(X)$ and $H(Y)$, but rather depends on the details of $X$ and $Y$'s distributions. Nevertheless, the entropy power inequality (EPI), which states that $e^{2H(Z)} \geq e^{2H(X)} + e^{2H(Y)}$, gives a very tight restriction on the entropy of $Z$.