## Measures of Nonclassical Correlations and Quantum-Enhanced Interferometry

Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/30398

##### View/Open

Title

Measures of Nonclassical Correlations and Quantum-Enhanced Interferometry

Author(s)

Lang, Matthias Dominik

Advisor(s)

Caves, Carlton M.

Committee Member(s)

Miyake, Akimasa

Dunlap, David

Somma, Rolando

Dunlap, David

Somma, Rolando

Department

University of New Mexico. Dept. of Physics & Astronomy

Degree Level

Doctoral

Abstract

In the first part of this dissertation a framework for categorizing entropic measures of nonclassical correlations in bipartite quantum states is presented. The measures are based on the difference between a quantum
entropic quantity and the corresponding classical quantity obtained from measurements on
the two systems. Three types of entropic quantities are used, and three different measurement
strategies are applied to these quantities. Many of the resulting measures of nonclassical
correlations have been proposed previously. Properties of the various measures are explored,
and results of evaluating the measures for two-qubit quantum states are presented.
To demonstrate how these measures differ from entanglement we move to the set of Bell-diagonal states for two qubits, which can be depicted as a tetrahedron in three dimensions. We consider the level surfaces of entanglement and of the correlation measures from our framework for Bell-diagonal states. This
provides a complete picture of the structure of entanglement and discord for this simple case and, in
particular, of their nonanalytic behavior under decoherence. The pictorial approach also indicates
how to show that all of the proposed correlation measures are neither convex nor concave.
In the second part we look at two practical interferometric setups that use nonclassical states of light to enhance their performance. First we consider an interferometer powered by laser light (a coherent state) into one input port and ask
the following question: what is the best state to inject into the second input port, given a constraint
on the mean number of photons this state can carry, in order to optimize the interferometer's phase
sensitivity? This question is the practical question for high-sensitivity interferometry. We answer the
question by considering the quantum Cram\'er-Rao bound for such a setup. The answer is squeezed
vacuum.
Then we analyze the ultimate bounds on the phase sensitivity of an interferometer, given the constraint
that the state input to the interferometer's initial 50:50 beam splitter B is a product state of the
two input modes. Requiring a product state is a natural restriction: if one were allowed to input
an arbitrary, entangled two-mode state $|\Xi \rangle$ to the beam splitter, one could generally just as easily
input the state $B|\Xi \rangle$ directly into the two modes after the beam splitter, thus rendering the beam
splitter unnecessary. We find optimal states for a fixed photon number and for a fixed mean photon
number. Our results indicate that entanglement is not a crucial resource for quantum-enhanced interferometry. Initially the analysis for both of these setups is performed for the idealized case of a lossless interferometer. Then the analysis is extended to the more realistic scenario where the interferometer suffers from photon losses.

Date

July 2015

Subject(s)

quantum correlations

discord

interferometry

quantum metrology

discord

interferometry

quantum metrology

##### Collections

- Physics [69]