scholarly journals Effect of Entanglement on Geometric Phase for Multi-Qubit States

2009 ◽  
Vol 16 (02n03) ◽  
pp. 305-323 ◽  
Author(s):  
Mark S. Williamson ◽  
Vlatko Vedral
Keyword(s):  
Hilbert Space ◽  
Geometric Phase ◽  
Correction Term ◽  
Entangled State ◽  
Cluster States ◽  
W States ◽  
Local Invariants ◽  
Projective Hilbert Space ◽  
Classical Correlations ◽  
Qubit States

When a multi-qubit state evolves under local unitaries it may obtain a geometric phase, a feature dependent on the geometry of the state projective Hilbert space. A correction term to this geometric phase, in addition to the local subsystem phases, may appear from correlations between the subsystems. We find that this correction term can be characterized completely either by the entanglement or by the classical correlations for several classes of entangled state. States belonging to the former set are W states and their mixtures, while members of the latter set are cluster states, GHZ states and two classes of bound entangled state. We probe the structures of these states more finely using local invariants and suggest that the cause of the entanglement correction is a recently introduced gauge field-like SL(2,ℂ)-invariant called twist.

DETECTION OF THE SPATIAL CURVATURE EFFECTS THROUGH PHYSICAL PHENOMENA: THE NONLINEAR COHERENT STATES APPROACH

2012 ◽  
Vol 09 (01) ◽  
pp. 1250009 ◽  
Author(s):  
A. MAHDIFAR ◽  
R. ROKNIZADEH ◽  
M. H. NADERI
Keyword(s):  
Hilbert Space ◽  
Geometric Phase ◽  
Coherent States ◽  
Transition Probability ◽  
Physical Space ◽  
Spatial Curvature ◽  
Curved Space ◽  
Curvature Effects ◽  
Projective Hilbert Space ◽  
Physical Phenomena

In this paper, by using the nonlinear coherent states approach, we find a relation between the geometric structure of the physical space and the geometry of the corresponding projective Hilbert space. To illustrate the approach, we explore the quantum transition probability and the geometric phase in the curved space.

scholarly journals FROZEN DISCORD IN NON-MARKOVIAN DEPHASING CHANNELS

2011 ◽  
Vol 09 (03) ◽  
pp. 981-991 ◽  
Author(s):  
LAURA MAZZOLA ◽  
JYRKI PIILO ◽  
SABRINA MANISCALCO
Keyword(s):  
Hilbert Space ◽  
Colored Noise ◽  
Geometric Interpretation ◽  
Quantum Decoherence ◽  
Initial State ◽  
Memory Kernel ◽  
Single Qubit ◽  
Classical State ◽  
Classical Correlations ◽  
Quantum And Classical Correlations

We investigate the dynamics of quantum and classical correlations in a system of two qubits under local colored-noise dephasing channels. The time evolution of a single qubit interacting with its own environment is described by a memory kernel non-Markovian master equation. The memory effects of the non-Markovian reservoirs introduce new features in the dynamics of quantum and classical correlations compared to the white noise Markovian case. Depending on the geometry of the initial state, the system can exhibit frozen discord and multiple sudden transitions between classical and quantum decoherence [L. Mazzola, J. Piilo and S. Maniscalco, Phys. Rev. Lett. 104 (2010) 200401]. We provide a geometric interpretation of those phenomena in terms of the distance of the state under investigation to its closest classical state in the Hilbert space of the system.

Symmetric and asymmetric cyclic controlled quantum teleportation via nine-qubit entangled state

2021 ◽  
pp. 2150249
Author(s):  
Vikram Verma
Keyword(s):  
Quantum Channel ◽  
Quantum Teleportation ◽  
Quantum States ◽  
Entangled State ◽  
Controlled Quantum Teleportation ◽  
Intrinsic Efficiency ◽  
Qubit States ◽  
Generalized Scheme

In this paper, by utilizing a nine-qubit entangled state as a quantum channel, we propose new schemes for symmetric and asymmetric cyclic controlled quantum teleportation (CYCQT). In our proposed schemes, four participants Alice, Bob, Charlie and David teleport their unknown quantum states cyclically among themselves with the help of a controller Eve. No participants can reconstruct the original states sent from the respective senders without the permission of the controller. Also, by considering same nine-qubit entangled state as a quantum channel, we propose a generalized scheme for CYCQT of multi-qubit states. In contrast to the previous CYCQT schemes involving three communicators and a controller, there are four communicators and a controller in the proposed schemes. Also, compared with previous CYCQT schemes, our proposed CYCQT schemes require less consumption of quantum resource and the intrinsic efficiency of the generalized scheme increases with the increase of number of qubits in the information states.

Entanglement criteria for the three-qubit states

2017 ◽  
Vol 15 (07) ◽  
pp. 1750049 ◽  
Author(s):  
Y. Akbari-Kourbolagh
Keyword(s):  
White Noise ◽  
Tensor Products ◽  
W State ◽  
Entangled States ◽  
Mean Values ◽  
W States ◽  
Pauli Matrices ◽  
The Mean ◽  
Simple Sets ◽  
Qubit States

We present sufficient criteria for the entanglement of three-qubit states. For some special families of states, the criteria are also necessary for the entanglement. They are formulated as simple sets of inequalities for the mean values of certain observables defined as tensor products of Pauli matrices. The criteria are good indicators of the entanglement in the vicinity of three-qubit GHZ and W states and enjoy the capability of detecting the entangled states with positive partial transpositions. Furthermore, they improve the best known result for the case of W state mixed with the white noise. The efficiency of the criteria is illustrated through several examples.

scholarly journals GAUSSIAN GEOMETRIC DISCORD

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1773-1786 ◽  
Author(s):  
GERARDO ADESSO ◽  
DAVIDE GIROLAMI
Keyword(s):  
Quantum Discord ◽  
Gaussian Quadrature ◽  
Continuous Variable ◽  
Upper And Lower Bounds ◽  
Gaussian States ◽  
Physical Constraints ◽  
Geometric Measure ◽  
Classical Correlations ◽  
Qubit States ◽  
Thermal States

We extend the geometric measure of quantum discord, introduced and computed for two-qubit states, to quantify non-classical correlations in composite Gaussian states of continuous variable systems. We lay the formalism for the evaluation of a Gaussian geometric discord in two-mode Gaussian states, and present explicit formulas for the class of two-mode squeezed thermal states. In such a case, under physical constraints of bounded mean energy, geometric discord is shown to admit upper and lower bounds for a fixed value of the conventional (entropic) quantum discord. We finally discuss alternative geometric approaches to quantify Gaussian quadrature correlations.

scholarly journals Geometric local invariants and pure three-qubit states

2011 ◽  
Vol 83 (6) ◽  
Author(s):  
Mark S. Williamson ◽  
Marie Ericsson ◽  
Markus Johansson ◽  
Erik Sjöqvist ◽  
Anthony Sudbery ◽  
...  
Keyword(s):  
Local Invariants ◽  
Qubit States

ENTANGLEMENT DISTRIBUTION AND STATE DISCRIMINATION IN TRIPARTITE QUBIT SYSTEMS

2008 ◽  
Vol 06 (02) ◽  
pp. 237-253 ◽  
Author(s):  
J. BATLE ◽  
M. CASAS
Keyword(s):  
Monte Carlo ◽  
Entangled States ◽  
Perfect State ◽  
Mixed States ◽  
W States ◽  
State Discrimination ◽  
Entanglement Measures ◽  
Entanglement Distribution ◽  
Maximally Entangled States ◽  
Qubit States

This work reviews and extends recent results concerning the distribution of entanglement, as well as nonlocality (in terms of inequality violations) in tripartite qubit systems. With recourse to a Monte Carlo generation of pure and mixed states of three-qubits, we explore several features related to the distribution of entanglement (expressed in the form of different measures of multiqubit entanglement based upon bipartitions). Also, special interest is paid to maximally entangled states (such as the GHZ for three-qubits) and W states. This study also sheds some light on the interesting relation existing between some entanglement measures and perfect state discrimination in LOCC measurements relevant to cryptographic protocols. We round off the results by studying the distribution of entanglement between Alice and Bob in a modified teleportation protocol toy model over three-qubit states.

scholarly journals Minimum Time for the Evolution to a Nonorthogonal Quantum State and Upper Bound of the Geometric Efficiency of Quantum Evolutions

2021 ◽  
Vol 3 (3) ◽  
pp. 444-457
Author(s):  
Carlo Cafaro ◽  
Paul M. Alsing
Keyword(s):  
Hilbert Space ◽  
Maximum Energy ◽  
Quantum States ◽  
Minimum Time ◽  
Quantum Evolution ◽  
Efficiency Measure ◽  
Geometric Framework ◽  
Constant Energy ◽  
Projective Hilbert Space ◽  
Arbitrary Quantum

We present a simple proof of the fact that the minimum time TAB for quantum evolution between two arbitrary states A and B equals TAB=ℏcos−1A|B/ΔE with ΔE being the constant energy uncertainty of the system. This proof is performed in the absence of any geometrical arguments. Then, being in the geometric framework of quantum evolutions based upon the geometry of the projective Hilbert space, we discuss the roles played by either minimum-time or maximum-energy uncertainty concepts in defining a geometric efficiency measure ε of quantum evolutions between two arbitrary quantum states. Finally, we provide a quantitative justification of the validity of the inequality ε≤1 even when the system only passes through nonorthogonal quantum states.

Symmetry and topology

Quantum 20/20 ◽  
2019 ◽  
pp. 225-242
Author(s):  
Ian R. Kenyon
Keyword(s):  
Hilbert Space ◽  
Conservation Laws ◽  
Geometric Phase ◽  
Electromagnetic Coupling ◽  
Charge Symmetry ◽  
Gauge Transformations ◽  
Local Charge ◽  
Classical World ◽  
Bohm Effect ◽  
Aharonov Bohm

Space-time symmetries, conservation laws and Nöther’s theorem are discussed. The Poincaré group, generators and Casimir invariants are outlined. Local charge conservation and the corresponding U(1) charge symmetry underlying electromagnetism are presented, showing the roles of minimal electromagnetic coupling and gauge transformations. Experimental demonstrations of the Aharonov–Bohm effect are described and the topological interpretation is recounted. How the Aharonov–Casher effect survives in the classical world is mentioned. Berry’s revelation of geometric phase is presented. The Bitter–Dubbers experiment confirming this analysis is presented. Some comments are given on a Hilbert space with a simple topology.

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