1,960 research outputs found
Macroscopicity of quantum superpositions on a one-parameter unitary path in Hilbert space
We analyze quantum states formed as superpositions of an initial pure product
state and its image under local unitary evolution, using two measurement-based
measures of superposition size: one based on the optimal quantum binary
distinguishability of the branches of the superposition and another based on
the ratio of the maximal quantum Fisher information of the superposition to
that of its branches, i.e., the relative metrological usefulness of the
superposition. A general formula for the effective sizes of these states
according to the branch distinguishability measure is obtained and applied to
superposition states of quantum harmonic oscillators composed of Gaussian
branches. Considering optimal distinguishability of pure states on a
time-evolution path leads naturally to a notion of distinguishability time that
generalizes the well known orthogonalization times of Mandelstam and Tamm and
Margolus and Levitin. We further show that the distinguishability time provides
a compact operational expression for the superposition size measure based on
the relative quantum Fisher information. By restricting the maximization
procedure in the definition of this measure to an appropriate algebra of
observables, we show that the superposition size of, e.g., N00N states and
hierarchical cat states, can scale linearly with the number of elementary
particles comprising the superposition state, implying precision scaling
inversely with the total number of photons when these states are employed as
probes in quantum parameter estimation of a 1-local Hamiltonian in this
algebra
Geometric information in eight dimensions vs. quantum information
Complementary idempotent paravectors and their ordered compositions, are used
to represent multivector basis elements of geometric Clifford algebra for 3D
Euclidean space as the states of a geometric byte in a given frame of
reference. Two layers of information, available in real numbers, are
distinguished. The first layer is a continuous one. It is used to identify
spatial orientations of similar geometric objects in the same computational
basis. The second layer is a binary one. It is used to manipulate with 8D
structure elements inside the computational basis itself. An oriented unit cube
representation, rather than a matrix one, is used to visualize an inner
structure of basis multivectors. Both layers of information are used to
describe unitary operations -- reflections and rotations -- in Euclidian and
Hilbert spaces. The results are compared with ones for quantum gates. Some
consequences for quantum and classical information technologies are discussed.Comment: 14 pages, presented at International Symposium "Quantum Informatics
2007", October 3rd - 5th, 2007, Moscow Zvenigorod, Russi
Macroscopic superpositions require tremendous measurement devices
We consider fundamental limits on the detectable size of macroscopic quantum
superpositions. We argue that a full quantum mechanical treatment of system
plus measurement device is required, and that a (classical) reference frame for
phase or direction needs to be established to certify the quantum state. When
taking the size of such a classical reference frame into account, we show that
to reliably distinguish a quantum superposition state from an incoherent
mixture requires a measurement device that is quadratically bigger than the
superposition state. Whereas for moderate system sizes such as generated in
previous experiments this is not a stringent restriction, for macroscopic
superpositions of the size of a cat the required effort quickly becomes
intractable, requiring measurement devices of the size of the Earth. We
illustrate our results using macroscopic superposition states of photons,
spins, and position. Finally, we also show how this limitation can be
circumvented by dealing with superpositions in relative degrees of freedom.Comment: 20 pages (including appendices), 1 Figur
Quantum many-body simulations using Gaussian phase-space representations
Phase-space representations are of increasing importance as a viable and
successful means to study exponentially complex quantum many-body systems from
first principles. This review traces the background of these methods, starting
from the early work of Wigner, Glauber and Sudarshan. We focus on modern
phase-space approaches using non-classical phase-space representations. These
lead to the Gaussian representation, which unifies bosonic and fermionic
phase-space. Examples treated include quantum solitons in optical fibers,
colliding Bose-Einstein condensates, and strongly correlated fermions on
lattices.Comment: Short Review (10 pages); Corrected typo in eq (14); Added a few more
reference
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