69,891 research outputs found
Geometry of quantum correlations in space-time
The traditional formalism of non-relativistic quantum theory allows the state
of a quantum system to extend across space, but only restricts it to a single
instant in time, leading to distinction between theoretical treatments of
spatial and temporal quantum correlations. Here we unify the geometrical
description of two-point quantum correlations in space-time. Our study presents
the geometry of correlations between two sequential Pauli measurements on a
single qubit undergoing an arbitrary quantum channel evolution together with
two-qubit spatial correlations under a common framework. We establish a
symmetric structure between quantum correlations in space and time. This
symmetry is broken in the presence of non-unital channels, which further
reveals a set of temporal correlations that are indistinguishable from
correlations found in bipartite entangled states.Comment: 5 pages, 3 figure
Quantum Information Geometry in the Space of Measurements
We introduce a new approach to evaluating entangled quantum networks using
information geometry. Quantum computing is powerful because of the enhanced
correlations from quantum entanglement. For example, larger entangled networks
can enhance quantum key distribution (QKD). Each network we examine is an
n-photon quantum state with a degree of entanglement. We analyze such a state
within the space of measured data from repeated experiments made by n observers
over a set of identically-prepared quantum states -- a quantum state
interrogation in the space of measurements. Each observer records a 1 if their
detector triggers, otherwise they record a 0. This generates a string of 1's
and 0's at each detector, and each observer can define a binary random variable
from this sequence. We use a well-known information geometry-based measure of
distance that applies to these binary strings of measurement outcomes, and we
introduce a generalization of this length to area, volume and
higher-dimensional volumes. These geometric equations are defined using the
familiar Shannon expression for joint and mutual entropy. We apply our approach
to three distinct tripartite quantum states: the GHZ state, the W state, and a
separable state P. We generalize a well-known information geometry analysis of
a bipartite state to a tripartite state. This approach provides a novel way to
characterize quantum states, and it may have favorable scaling with increased
number of photons.Comment: 21 pages, 7 figure
Geometric aspects of uncertainty and correlation
The fact that the metric induced on the quantum evolution submanifold of the protective Hilbert space describes the uncertainties and correlations of the operators generating the quantum-state evolution and exhibits the inherently-quantized geometry is discussed
Loop Quantum Gravity and Quantum Information
We summarize recent developments at the interface of quantum gravity and
quantum information, and discuss applications to the quantum geometry of space
in loop quantum gravity. In particular, we describe the notions of link
entanglement, intertwiner entanglement, and boundary spin entanglement in a
spin-network state. We discuss how these notions encode the gluing of quanta of
space and their relevance for the reconstruction of a quantum geometry from a
network of entanglement structures. We then focus on the geometric entanglement
entropy of spin-network states at fixed spins, treated as a many-body system of
quantum polyhedra, and discuss the hierarchy of volume-law, area-law and
zero-law states. Using information theoretic bounds on the uncertainty of
geometric observables and on their correlations, we identify area-law states as
the corner of the Hilbert space that encodes a semiclassical geometry, and the
geometric entanglement entropy as a probe of semiclassicality.Comment: 17 pages, Invited chapter for the "Handbook of Quantum Gravity" (Eds.
C. Bambi, L. Modesto and I.L. Shapiro, Springer Singapore, expected in 2023
Composite Geometric Phase for Multipartite Entangled States
When an entangled state evolves under local unitaries, the entanglement in
the state remains fixed. Here we show the dynamical phase acquired by an
entangled state in such a scenario can always be understood as the sum of the
dynamical phases of its subsystems. In contrast, the equivalent statement for
the geometric phase is not generally true unless the state is separable. For an
entangled state an additional term is present, the mutual geometric phase, that
measures the change the additional correlations present in the entangled state
make to the geometry of the state space. For qubit states we find this
change can be explained solely by classical correlations for states with a
Schmidt decomposition and solely by quantum correlations for W states.Comment: 4 pages, 1 figure, improved presentation, results and conclusions
unchanged from v1. Accepted for publication in PR
State-space Correlations and Stabilities
The state-space pair correlation functions and notion of stability of
extremal and non-extremal black holes in string theory and M-theory are
considered from the viewpoints of thermodynamic Ruppeiner geometry. From the
perspective of intrinsic Riemannian geometry, the stability properties of these
black branes are divulged from the positivity of principle minors of the
space-state metric tensor. We have explicitly analyzed the state-space
configurations for (i) the two and three charge extremal black holes, (ii) the
four and six charge non-extremal black branes, which both arise from the string
theory solutions. An extension is considered for the ---
multi-centered black branes, fractional small black branes and two charge
rotating fuzzy rings in the setup of Mathur's fuzzball configurations. The
state-space pair correlations and nature of stabilities have been investigated
for three charged bubbling black brane foams, and thereby the M-theory
solutions are brought into the present consideration. In the case of extremal
black brane configurations, we have pointed out that the ratio of diagonal
space-state correlations varies as inverse square of the chosen parameters,
while the off diagonal components vary as inverse of the chosen parameters. We
discuss the significance of this observation for the non-extremal black brane
configurations, and find similar conclusion that the state-space correlations
extenuate as the chosen parameters are increased.Comment: 35 pages, Keywords: Black Hole Physics, Higher-dimensional Black
Branes, State-space Correlations and Statistical Configurations. PACS
numbers: 04.70.-s Physics of black holes; 04.70.Bw Classical black holes;
04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics;
04.50.Gh Higher-dimensional black holes, black strings, and related object
Quantum Correlations are Weaved by the Spinors of the Euclidean Primitives
The exceptional Lie group E_8 plays a prominent role both in mathematics and theoretical physics. It is the largest symmetry group connected to the most general possible normed division algebra, that of the non-associative real octonions, which — thanks to their non-associativity — form the only possible closed set of spinors that can parallelize the 7-sphere. By contrast, here we show how a similar 7-sphere also arises naturally from the algebraic interplay of the graded Euclidean primitives, such as points, lines, planes and volumes, characterizing the three-dimensional conformal geometry of the physical space, set within its eight-dimensional Clifford-algebraic representation. Remarkably, the resulting algebra remains associative, and allows us to understand the origins and strengths of all quantum correlations locally, in terms of the geometry of the compactified physical space, namely that of a quaternionic 3-sphere, S^3, with S^7 being the corresponding algebraic representation space. Every quantum correlation can thus be understood as a correlation among a set of points of this S^7, computed using manifestly local spinors in S^3 , thereby setting the geometrical upper bound of 2√2 on the strengths of all quantifiable correlations. We demonstrate this by first proving a comprehensive theorem about the geometrical origins of the correlations predicted by any arbitrary quantum state, and then explicitly reproducing the strong correlations predicted by the EPR-Bohm and GHZ states. The raison d'etre of strong correlations turns out to be the twist in the Hopf bundle of S^3 within S^7
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