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OSA Trends in Optics and Photonics Series

Geometric phase for single-photon mixed polarization states

Julio T. Barreiro, Marie Ericsson, Nicholas A. Peters, Daryl Achilles, David A. Branning, Paul G. Kwiat

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

The resilience of geometric phase against errors may enable fault-tolerant quantum computation. We use an interferometric scheme to measure geometric phases of various mixed polarization states generated classically and from conditionally prepared (entangled) single photons

Related papers

Geometric phase for single-photon mixed polarization states

Julio T. Barreiro, Marie Ericsson, Nicholas A. Peters +3 more

The resilience of geometric phase against errors may enable fault-tolerant quantum computation. We use an interferometric scheme to measure geometric phases of various mixed polarization states generated classically and from conditionally prepared (entangled) single photons.

Conference on Lasers and Electro-Optics•Jan 1, 2004•0 citations

Geometric Phase for Mixed States using Single-Photon Interferometry

Marie Ericsson

The inherent resistance of geometric phase to decoherence may enable fault‐tolerant quantum computation. However, as decoherence tends to affect many implementations, we must first understand the behavior of such phases for mixed states. Here we report an experimental measurement of geometric phase for polarization mixed states.

AIP conference proceedings•Jan 1, 2004•0 citations

Measurement of Geometric Phase for Mixed States Using Single Photon Interferometry

Marie Ericsson, Daryl Achilles, Julio T. Barreiro +3 more

Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for mixed input states. We report the first experiment to measure mixed-state geometric phases in optics, using a Mach-Zehnder interferometer, and polarization mixed states that are produced in two different ways: decohering pure states with birefringent elements; and producing a nonmaximally entangled state of two photons and tracing over one of them, a form of remote state preparation.

arXiv:quant-ph/0412216•Physical Review Letters•Feb 7, 2005•92 citations

All-optical polarimetric generation of mixed-state single-photon geometric phases

Diego Barberena, Omar Ortiz, Yonny Yugra +2 more

We report robust polarimetric measurements of mixed-state geometric phases. An all-optical setup was used to generate geometric phases with great versatility, thereby extending the scope of analogous methods used in neutron polarimetry. Our method allows us to explore geometric phases generated by unitarily evolving mixed states. These are realized as partially polarized single-photon states whose degree of polarization and normalized Stokes vector can be fixed independently of one another. The geometric phases correspond to both open and closed trajectories in Poincar\'e space. By exploiting the gauge invariance of geometric phases we nullify their dynamical part, thereby making the geometric phase coincide with the total (Pancharatnam) phase, which can be directly addressed by employing standard techniques.

Physical Review A•Jan 5, 2016•5 citations

Geometric quantum computation

ARTUR K. EKERT, Marie Ericsson, Patrick M. Hayden +4 more

We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantum computation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantum computation.

arXiv:quant-ph/0004015•Journal of Modern Optics•Nov 1, 2000•273 citations

Observation of Geometric Phases for Mixed States using NMR Interferometry

Jiangfeng Du, Ping Zou, Mingjun Shi +6 more

Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires one to deal with geometric phases in the presence of noise and interactions between different physical subsystems. Despite the wealth of literature on the subject of geometric phases very little is known about this very important case. Here we report the first experimental study of geometric phases for mixed quantum states. We show how different they are from the well-understood, noiseless, pure-state case.

arXiv:quant-ph/0305054•Physical Review Letters•Sep 5, 2003•157 citations
Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for mixed input states. We report the first experiment to measure mixed-state geometric phases in optics, using a Mach-Zehnder interferometer, and polarization mixed states that are produced in two different ways: decohering pure states with birefringent elements; and producing a nonmaximally entangled state of two photons and tracing over one of them, a form of remote state preparation.
We report robust polarimetric measurements of mixed-state geometric phases. An all-optical setup was used to generate geometric phases with great versatility, thereby extending the scope of analogous methods used in neutron polarimetry. Our method allows us to explore geometric phases generated by unitarily evolving mixed states. These are realized as partially polarized single-photon states whose degree of polarization and normalized Stokes vector can be fixed independently of one another. The geometric phases correspond to both open and closed trajectories in Poincar\'e space. By exploiting the gauge invariance of geometric phases we nullify their dynamical part, thereby making the geometric phase coincide with the total (Pancharatnam) phase, which can be directly addressed by employing standard techniques.
We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantum computation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantum computation.
Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires one to deal with geometric phases in the presence of noise and interactions between different physical subsystems. Despite the wealth of literature on the subject of geometric phases very little is known about this very important case. Here we report the first experimental study of geometric phases for mixed quantum states. We show how different they are from the well-understood, noiseless, pure-state case.