18 research outputs found
Qubits from Number States and Bell Inequalities for Number Measurements
Bell inequalities for number measurements are derived via the observation
that the bits of the number indexing a number state are proper qubits.
Violations of these inequalities are obtained from the output state of the
nondegenerate optical parametric amplifier.Comment: revtex4, 7 pages, v2: results identical but extended presentation,
v3: published versio
Collectibility for Mixed Quantum States
Bounds analogous to entropic uncertainty relations allow one to design
practical tests to detect quantum entanglement by a collective measurement
performed on several copies of the state analyzed. This approach, initially
worked out for pure states only [Phys. Rev. Lett. 107, 150502 (2011)], is
extended here for mixed quantum states. We define collectibility for any mixed
states of a multipartite system. Deriving bounds for collectibility for
positive partially transposed states of given purity provides a new insight
into the structure of entangled quantum states. In case of two qubits the
application of complementary measurements and coincidence based detections
leads to a new test of entanglement of pseudopure states.Comment: 13 page
Measuring the Orbital Angular Momentum of Light with Time Mapping and Using it to Probe Higher Dimensional States.
The orbital angular momentum of light (OAM) is a fundamental property of light. Beams with OAM have a helical wave front that carries quantized orbital angular momentum L hbar per photon, where L is any integer. This unbounded Hilbert space can increase information capacity of both classical and quantum communications and also improve and extend qubit and qudit quantum algorithms. Additionally, the use of the OAM modes allows for novel imaging techniques to directly observe and measure various topological properties of objects ranging from defects in semiconductors to rotating black holes and extrasolar planets. However, measuring such higher dimensional OAM states is fundamentally important, albeit challenging, in order to use this rich degree of freedom.
In the work that follows, I present two novel OAM to time mapping schemes and an application using the higher dimensionality of OAM to non-destructively probe quantum states. These are the first OAM measuring schemes to use the temporal degree of freedom to measure OAM. The use of the novel loop nature allows for high fidelity and high speed measurements of a large number of OAM states without significant increase in experimental resources. The first scheme experimentally demonstrates a compact and practical device to measure the OAM spectrum. I report a fidelity of -21.3 dB for 5 different OAM states. The second scheme extends the first, but uses non-demolition measurements to iteratively test for specific OAM values. While this increases experimental complexity, it allows for the detection of an arbitrarily large OAM value from a single photon. I also discuss details of each technique investigate the affects of misalignment on the OAM spectrum. In the remaining part, I discuss my novel generalized quantum Zeno interrogation. The original quantum Zeno interrogation is limited to the two-dimensional state of a single object; while the generalized version has the ability to non-destructively probe the quantum state a set of objects, and deterministically imprint that information onto a single photon using the OAM degree of freedom.PhDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/110481/1/paopao_1.pd
Beyond photon pairs
In this thesis we explore spatial quantum correlations of high-dimensional multi-photon states. These states are produced using the process of parametric down-conversion and are experimentally explored by measuring correlations with only two detectors. Compared to earlier investigations of multi-photon states, the correlations in this thesis are created in the spatial domain instead of the temporal domain. This has a distinct experimental advantage because it is much easier to measure the emission direction compared to a measurement of the arrival time of the photons.Quantum Matter and Optic