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- Qinglan Xia, Anna Vershynina
- SIAM J. Math. Analysis
- 2009

Abstract. In this article, we define the transport dimension of probability measures on Rm using ramified optimal transportation theory. We show that the transport dimension of a probability measure is bounded above by the Minkowski dimension and below by the Hausdorff dimension of the measure. Moreover, we introduce a metric, called “the dimensional… (More)

- David Gosset, Barbara M Terhal, Anna Vershynina
- Physical review letters
- 2015

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our… (More)

- Bruno Nachtergaele, Anna Vershynina, Valentin A. Zagrebnov, Valentin A.Zagrebnov
- 2011

We prove Lieb-Robinson bounds and the existence of the thermodynamic limit for a general class of irreversible dynamics for quantum lattice systems with time-dependent generators that satisfy a suitable decay condition in space.

- Elliott H. Lieb, Anna Vershynina
- Quantum Information & Computation
- 2013

We prove upper bounds on the rate, called ”mixing rate”, at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under nonlocal unitary evolution. For an ensemble consisting of two states, with probabilities of p and 1 − p, we prove that the mixing rate is bounded above by 4 √ p(1− p) for any Hamiltonian of… (More)

- Anna Vershynina, Eric A. Carlen, Elliott H. Lieb
- Scholarpedia
- 2013

We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking… (More)

- L I Hapon, O V Abaturova, +4 authors T V Alfimova
- Likars'ka sprava
- 1993

Cordipin-retard is one of the new highly effective slow-releasing hypotensive drugs from the calcium antagonists family. Single intake of the drug is equal to that of corinfar while prolonged treatment with cordipin-retard surpasses corinfar in hypotensive influence and duration of effect. No adverse effect of the drug on conductive system of the heart and… (More)

We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain convolution operation: the latter maps a classical probability distribution on phase space and a quantum state to a quantum… (More)

- Anna Vershynina, Eric A. Carlen, Elliott H. Lieb
- Scholarpedia
- 2013

- Anna Vershynina, Elliott H. Lieb
- Scholarpedia
- 2013

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