53 research outputs found
Quantum Zeno effect as a topological phase transition in full counting statistics and spin noise spectroscopy
When the interaction of a quantum system with a detector is changing from
weak to strong coupling limits, the system experiences a transition from the
regime with quantum mechanical coherent oscillations to the regime with a
frozen dynamics. In addition to this quantum Zeno transition, we show that the
full counting statistics of detector signal events experiences a topological
phase transition at the boundary between two phases at intermediate coupling of
a quantum system to the detector. We demonstrate that this transition belongs
to the class of topological phase transitions that can be classified by
elements of the braid group. We predict that this transition can be explored
experimentally by means of the optical spin noise spectroscopy.Comment: 5 pages, 2 figure
Topologically protected Grover's oracle for the partition problem
The Number Partitioning Problem (NPP) is one of the NP-complete computational
problems. Its definite exact solution generally requires a check of all
solution candidates, which is exponentially large. Here we describe a path to
the fast solution of this problem in quasi-adiabatic quantum
annealing steps. We argue that the errors due to the finite duration of the
quantum annealing can be suppressed if the annealing time scales with only
logarithmically. Moreover, our adiabatic oracle is topologically protected, in
the sense that it is robust against small uncertainty and slow time-dependence
of the physical parameters or the choice of the annealing protocol.Comment: v2: final version; to appear in Physical Review
Randomized channel-state duality
Channel-state duality is a central result in quantum information science. It
refers to the correspondence between a dynamical process (quantum channel) and
a static quantum state in an enlarged Hilbert space. Since the corresponding
dual state is generally mixed, it is described by a Hermitian matrix. In this
article, we present a randomized channel-state duality. In other words, a
quantum channel is represented by a collection of pure quantum states that
are produced from a random source. The accuracy of this randomized duality
relation is given by , with regard to an appropriate distance measure. For
large systems, is much smaller than the dimension of the exact dual matrix
of the quantum channel. This provides a highly accurate low-rank approximation
of any quantum channel, and, as a consequence of the duality relation, an
efficient data compression scheme for mixed quantum states. We demonstrate
these two immediate applications of the randomized channel-state duality with a
chaotic -dimensional spin system
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