Microsoft Research

We prove that quantum approximate Markov chains are thermal. We then use this result to show that the entanglement spectrum of 2D low temperature states of matter has a local structure.

1. Efficient quantum walk on the grid with multiple marked elements 2. Controlled quantum amplification "1.

1. Two-way assisted capacities for quantum and private communication 2. Converse bounds for private communication over quantum channels "1.

1. Overlapping qubits 2. Parallel self-testing of (tilted) EPR pairs via copies of (tilted) CHSH 3. The parallel-repeated magic square game is rigid "1.

"We present a method to show that the ground states of some quantum many-body spin Hamiltonians in one spatial dimension are nonlocal.

Microsoft Research – 2 февраля 2017, 0:43

"We show an exponentially large separation between {\em quantum communication complexity} and {\em classical information complexity} by exhibiting a Boolean function with such a property.

We address the question of whether symmetry-protected topological (SPT) order can persist at nonzero temperature. We present three results in this direction.

We prove generalizations of de Finetti theorems where the local space is not finite-dimensional but rather an infinite-dimensional Fock space.

Preparing quantum thermal states on a quantum computer is in general a difficult task.

We show a meaningful theory of classical communication over quantum channels when assisted by no-signalling (NS) and PPT-preserving (PPT) codes, for which both the optimal success probability of a

Using tools from operator algebras, such as ternary rings of operators (TRO) and the notion of independence we investigate Stinespring spaces of quantum channels obtained by perturbation.

"We consider a quantum generalization of the classical heat equation, whose associated semigroup consists of additive Gaussian classical noise channels.

"Proving security of device-independent (DI) cryptographic protocols has been regarded a complex and tedious task.

We prove that Gaussian thermal input states minimize the output von Neumann entropy of the one-mode Gaussian quantum-limited attenuator for fixed input entropy.

The Gottesman-Knill theorem asserts that a quantum circuit composed of Clifford gates can be efficiently simulated on a classical computer.

"Tsirelson's problem asks whether the commuting operator model for two-party quantum correlations is equivalent to the tensor-product model.

Demonstrating quantum supremacy, a complexity-guaranteed quantum advantage over the best classical algorithms by using less universal quantum devices, is an important near-term milestone for quantum

Highly unpredictable events appear to be abundant in life. However, when modeled rigorously, their existence in nature is far from evident.

"We introduce a simple two-player test which certifies that the players apply tensor products of Pauli $\sigma_X$ and $\sigma_Z$ observables on the tensor product of $n$ EPR pairs.

"A frustration-free local Hamiltonian has the property that its ground state minimises the energy of all terms simultaneously.

"We give a quasi-polynomial time classical algorithm for estimating the ground state energy and for computing low energy states of quantum impurity models.

"One of the central challenges in the study of quantum many-body systems is the complexity of simulating them on a classical computer.

We establish the ultimate limits to the compression of sequences of identically prepared qubits.

Semidefinite programming (SDP) is one of the most powerful general purpose methods in combinatorial optimization, and understanding its strengths and limitations is a central focus of research in

"Efficient simulation of quantum systems motivates quantum computers and is a longstanding problem.

Given a problem which is intractable for both quantum and classical algorithms, can we find a sub-problem for which quantum algorithms provide an exponential advantage?

We prove several trace inequalities that extend the Golden-Thompson and the Araki-Lieb-Thirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb's triple matrix inequality.

"The fact that the quantum relative entropy $D(\cdot \| \cdot)$ is non-increasing with respect to quantum channels lies at the core of many optimality theorems in quantum information theory.

"We introduce a new method for using reductions to construct integrality gaps for semidefinite programs (SDPs).