Related papers: The Marginal Problem for Density Operators
We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity…
One of the principal obstacles on the way to quantum computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set of basic operations (universal gates). A natural choice,…
We investigate the problem of the existence of a density matrix rho on the product of three Hilbert spaces with given marginals on the pair (1,2) and the pair (2,3). While we do not solve this problem completely we offer partial results in…
Via operator theoretic methods, we formalize the concentration phenomenon for a given observable `$r$' of a discrete time Markov chain with `$\mu_{\pi}$' as invariant ergodic measure, possibly having support on an unbounded state space. The…
Transversal Pauli $Z$ rotations provide a natural route to fault-tolerant logical diagonal gates in quantum CSS codes, but their capability is inherently constrained. We develop a homological framework that organizes transversal diagonal…
Many problems in robotics require reasoning over a mix of continuous dynamics and discrete events, such as making and breaking contact in manipulation and locomotion. These problems are locally well modeled by linear complementarity…
Single-shot quantum information theory is governed not only by entropy exponents, but also by the finite-resource constants that multiply them. These constants directly affect the quantitative performance of decoupling, covering,…
To implement quantum algorithms on a quantum computer, we must overcome the twin problems of fault-tolerance -- how can we realize a relatively noiseless computation by cleverly combining noisy components? -- and compilation -- how can we…
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices from indirect measurements, also known as quantum state…
Elaborating on our joint work with Abramsky in quant-ph/0402130 we further unravel the linear structure of Hilbert spaces into several constituents. Some prove to be very crucial for particular features of quantum theory while others…
I formulate an entropy-rate maximization problem at the observable level for stochastic processes observed through an information-reducing observation map. For a visible stationary law, the map determines an observational fiber of hidden…
When the wavefunction of a large quantum system unitarily evolves away from a low-entropy initial state, there is strong circumstantial evidence it develops "branches": a decomposition into orthogonal components that is indistinguishable…
Statistically interpretable axioms are formulated that define a quantum stochastic process (QSP) as a causally ordered operator field in an arbitrary space-time region T of an open quantum system under a sequential observation at a discrete…
Quantum stochastic cocycles provide a basic model for time-homogeneous Markovian evolutions in a quantum setting, and a direct counterpart in continuous time to quantum random walks, in both the Schrodinger and Heisenberg pictures. This…
In this paper we study the effect of non-trivial spatial topology on quantum entanglement by examining the degenerate ground states of a topologically ordered system on torus. Using the string-net (fixed-point) wave-function, we propose a…
We investigate whether a generic multipartite pure state can be the unique asymptotic steady state of locality-constrained purely dissipative Markovian dynamics. In the simplest tripartite setting, we show that the problem is equivalent to…
We present a unifying framework to study physical systems which exhibit topological quantum order (TQO). The guiding principle behind our approach is that of symmetries and entanglement. We introduce the concept of low-dimensional…
We derive upper and lower bounds on the convergence behavior of certain classes of one-parameter quantum dynamical semigroups. The classes we consider consist of tensor product channels and of channels with commuting Liouvillians. We…
Let $(X_i)$ be a stationary and ergodic Markov chain with kernel $Q$, $f$ an $L^2$ function on its state space. If $Q$ is a normal operator and $f = (I-Q)^{1/2}g$ (which is equivalent to the convergence of $\sum_{n=1}^\infty…
Many network datasets exhibit connectivity with variance by resolution and large-scale organization that coexists with localized departures. When vertices have observed ordering or embedding, such as geography in spatial and village…