Qubits on the Poincaré (Bloch) Sphere

2008 ◽  
Keyword(s):  
Bloch Sphere

scholarly journals Geometry of the Rabi Problem and Duality of Loops

2020 ◽  
Vol 75 (5) ◽  
pp. 381-391 ◽  
Author(s):  
Heinz-Jürgen Schmidt
Keyword(s):  
Magnetic Field ◽  
Differential Geometry ◽  
Floquet Theory ◽  
Bloch Sphere ◽  
Classical Spin ◽  
Periodic Magnetic Field

AbstractWe investigate the motion of a classical spin processing around a periodic magnetic field using Floquet theory, as well as elementary differential geometry and considering a couple of examples. Under certain conditions, the role of spin and magnetic field can be interchanged, leading to the notion of “duality of loops” on the Bloch sphere.

scholarly journals Control of inhomogeneous ensembles on the Bloch sphere

2012 ◽  
Vol 86 (2) ◽  
Author(s):  
Philip Owrutsky ◽  
Navin Khaneja
Keyword(s):  
Bloch Sphere

scholarly journals Entanglement cost of generalised measurements

2003 ◽  
Vol 3 (5) ◽  
pp. 405-422
Author(s):  
R. Jozsa ◽  
M. Koashi ◽  
N. Linden ◽  
S. Popescu ◽  
S. Presnell ◽  
...  
Keyword(s):  
Quantum Measurements ◽  
Great Circle ◽  
Bloch Sphere ◽  
Numerical Techniques ◽  
Bipartite Entanglement ◽  
Von Neumann ◽  
Tensor Product Space ◽  
Large N ◽  
Dimension 2 ◽  
The Cost

Bipartite entanglement is one of the fundamental quantifiable resources of quantum information theory. We propose a new application of this resource to the theory of quantum measurements. According to Naimark's theorem any rank 1 generalised measurement (POVM) M may be represented as a von Neumann measurement in an extended (tensor product) space of the system plus ancilla. By considering a suitable average of the entanglements of these measurement directions and minimising over all Naimark extensions, we define a notion of entanglement cost E_{\min}(M) of M. We give a constructive means of characterising all Naimark extensions of a given POVM. We identify various classes of POVMs with zero and non-zero cost and explicitly characterise all POVMs in 2 dimensions having zero cost. We prove a constant upper bound on the entanglement cost of any POVM in any dimension. Hence the asymptotic entanglement cost (i.e. the large n limit of the cost of n applications of M, divided by n) is zero for all POVMs. The trine measurement is defined by three rank 1 elements, with directions symmetrically placed around a great circle on the Bloch sphere. We give an analytic expression for its entanglement cost. Defining a normalised cost of any $d$-dimensional POVM by E_{\min} (M)/\log_2 d, we show (using a combination of analytic and numerical techniques) that the trine measurement is more costly than any other POVM with d>2, or with d=2 and ancilla dimension 2. This strongly suggests that the trine measurement is the most costly of all POVMs.

scholarly journals Bloch-sphere representation of three-vertex geometric phases

2011 ◽  
Vol 84 (5) ◽  
Author(s):  
Shuhei Tamate ◽  
Kazuhisa Ogawa ◽  
Masao Kitano
Keyword(s):  
Bloch Sphere ◽  
Geometric Phases

QUANTUM GATES AND PROTOCOLS WITH SPHERICAL WIGNER FUNCTIONS

2005 ◽  
Vol 03 (03) ◽  
pp. 501-509
Author(s):  
ORSOLYA KÁLMÁN ◽  
MIHÁLY G. BENEDICT
Keyword(s):  
Information Theory ◽  
Distribution Function ◽  
Quantum Information ◽  
Wigner Function ◽  
Quantum Information Theory ◽  
Quantum Gates ◽  
Bloch Sphere ◽  
Dense Coding ◽  
Space Formulation ◽  
Quasiprobability Distribution

The fundamental concepts and operations of quantum information theory are considered in the framework of a phase space formulation of quantum mechanics, where the states of one or several qubits are represented by a specific continuous quasiprobability distribution function on the Bloch sphere or on its generalizations. The function we use is the spherical Wigner function. It is shown that the usual transformations of quantum information theory are certain rotations or more general transformations of this Wigner function. We show that the standard teleportation and dense coding protocols can be appropriately formulated in terms of the Wigner function.

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