scholarly journals Preparation of Entangled States through Hilbert Space Engineering

2016 ◽  
Vol 117 (14) ◽  
Author(s):  
Y. Lin ◽  
J. P. Gaebler ◽  
F. Reiter ◽  
T. R. Tan ◽  
R. Bowler ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Entangled States

Quantum Interference

2019 ◽  
pp. 66-88
Author(s):  
Jeffrey A. Barrett
Keyword(s):  
Hilbert Space ◽  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Interference ◽  
Standard Theory ◽  
Quantum Decoherence ◽  
Entangled States ◽  
Quantum Mechanical ◽  
Standard Formulation ◽  
Complex Valued

Moving to more subtle experiments, we consider how the standard formulation of quantum mechanics predicts and explains interference phenomena. Tracking the conditions under which one observes interference phenomena leads to the notion of quantum decoherence. We see why one must sharply distinguish between collapse phenomena and decoherence phenomena on the standard formulation of quantum mechanics. While collapses explain determinate measurement records, environmental decoherence just produces more complex, entangled states where the physical systems involved lack ordinary physical properties. We characterize the quantum-mechanical wave function as both an element of a Hilbert space and a complex-valued function over a configuration space. We also discuss how the wave function is interpreted in the standard theory.

Quantum secret sharing protocol based on four-dimensional three-particle entangled states

2016 ◽  
Vol 30 (02) ◽  
pp. 1550267 ◽  
Author(s):  
Yi Xiang ◽  
Zhi Wen Mo
Keyword(s):  
Hilbert Space ◽  
Secret Sharing ◽  
Single Particle ◽  
High Efficiency ◽  
Quantum Secret Sharing ◽  
Entangled States ◽  
Secret Key ◽  
Particle Measurements ◽  
Eavesdropping Attack ◽  
Dimensional Hilbert Space

In this paper, we proposed a three-party quantum secret sharing (QSS) scheme using four-dimensional three-particle entangled states. In this QSS scheme, each agent can obtain a shadow of the secret key by performing single-particle measurements. Compared with the existing QSS protocol, this scheme has high efficiency and can resist the eavesdropping attack and entangle-measuring attack, which using three-particle entangled states are based on four-dimensional Hilbert space.

scholarly journals Tsirelson's bound and supersymmetric entangled states

2014 ◽  
Vol 470 (2170) ◽  
pp. 20140253 ◽  
Author(s):  
L. Borsten ◽  
K. Brádler ◽  
M. J. Duff
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Transition Probabilities ◽  
Entangled States ◽  
Supersymmetric Extension ◽  
Standard Quantum ◽  
Local Resource ◽  
Non Local ◽  
Minimal Supersymmetric Extension ◽  
Tsirelson Bound

A superqubit, belonging to a (2|1)-dimensional super-Hilbert space, constitutes the minimal supersymmetric extension of the conventional qubit. In order to see whether superqubits are more non-local than ordinary qubits, we construct a class of two-superqubit entangled states as a non-local resource in the CHSH game. Since super Hilbert space amplitudes are Grassmann numbers, the result depends on how we extract real probabilities and we examine three choices of map: (1) DeWitt (2) Trigonometric and (3) Modified Rogers. In cases (1) and (2), the winning probability reaches the Tsirelson bound p win = cos 2 π / 8 ≃ 0.8536 of standard quantum mechanics. Case (3) crosses Tsirelson's bound with p win ≃0.9265. Although all states used in the game involve probabilities lying between 0 and 1, case (3) permits other changes of basis inducing negative transition probabilities.

NEW THERMO EXCITATION STATES AND OPERATIONS IN THERMO FIELD DYNAMICS

2009 ◽  
Vol 24 (10) ◽  
pp. 769-778
Author(s):  
XUE-FEN XU ◽  
SHIQUN ZHU
Keyword(s):  
Hilbert Space ◽  
Phase State ◽  
Optical Field ◽  
Entangled States ◽  
Squeezed State ◽  
Eigenvalue Spectrum ◽  
Thermo Field Dynamics ◽  
Excitation State ◽  
Field Excitation

According to the thermo field dynamics proposed by Takahashi–Umezawa, the Hamiltonian h = a†a - ã†ã and h|n, ñ〉 = 0 of the original optical field excitation state |n〉 and its tilde state |ñ〉 in the Hilbert space cannot embody the eigenvalue spectrum of h. To avoid the weakness, new thermo excitation states are successfully constructed by introducing appropriate thermo excitation operators. It is noted that they are entangled states. Applications of the new thermo excitation state in constructing new thermo squeezed state and phase state are also presented.

scholarly journals Creation of Greenberger-Horne-Zeilinger states with thousands of atoms by entanglement amplification

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Yajuan Zhao ◽  
Rui Zhang ◽  
Wenlan Chen ◽  
Xiang-Bin Wang ◽  
Jiazhong Hu
Keyword(s):  
Hilbert Space ◽  
Spin State ◽  
Optical Cavity ◽  
Single Frequency ◽  
Entangled States ◽  
Quantum Metrology ◽  
Atom Number ◽  
Ghz States ◽  
High Finesse ◽  
Coherent Spin

AbstractWe propose an entanglement-creation scheme in a multi-atom ensemble trapped in an optical cavity, named entanglement amplification, converting unentangled states into entangled states and amplifying less-entangled ones to maximally entangled Greenberger-Horne-Zeilinger (GHZ) states whose fidelity is logarithmically dependent on the atom number and robust against common experimental noises. The scheme starts with a multi-atom ensemble initialized in a coherent spin state. By shifting the energy of a particular Dicke state, we break the Hilbert space of the ensemble into two isolated subspaces to tear the coherent spin state into two components so that entanglement is introduced. After that, we utilize the isolated subspaces to further enhance the entanglement by coherently separating the two components. By single-particle Rabi drivings on atoms in a high-finesse optical cavity illuminated by a single-frequency light, 2000-atom GHZ states can be created with a fidelity above 80% in an experimentally achievable system, making resources of ensembles at Heisenberg limit practically available for quantum metrology.

scholarly journals A general formulation based on algebraic spinors for the quantum computation

2020 ◽  
Vol 17 (14) ◽  
pp. 2050206
Author(s):  
Marco A. S. Trindade ◽  
Sergio Floquet ◽  
J. David M. Vianna
Keyword(s):  
Information Theory ◽  
Hilbert Space ◽  
Quantum Information ◽  
Quantum Computation ◽  
Quantum Teleportation ◽  
Clifford Algebras ◽  
Quantum Information Theory ◽  
Quantum Gates ◽  
Entangled States ◽  
Space Formulation

In this work, we explore the structure of Clifford algebras and the representations of the algebraic spinors in quantum information theory. Initially, we present a general formulation through elements of minimal left ideals in tensor products of Clifford algebras. Posteriorly, we perform some applications in quantum computation: qubits, entangled states, quantum gates, representations of the braid group, quantum teleportation, Majorana operators and supersymmetry. Finally, we discuss advantages compared to standard Hilbert space formulation.

scholarly journals The Generalization of the Periodic Table. The "Periodic Table" of "Dark Matter"

2021 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Hilbert Space ◽  
Dark Matter ◽  
Periodic Table ◽  
Chemical Element ◽  
Chemical Elements ◽  
Quantum Systems ◽  
Complex Hilbert Space ◽  
Entangled States ◽  
Visible Matter ◽  
Cognitive Screen

The thesis is: the “periodic table” of “dark matter” is equivalent to the standard periodic table of the visible matter being entangled. Thus, it is to consist of all possible entangled states of the atoms of chemical elements as quantum systems. In other words, an atom of any chemical element and as a quantum system, i.e. as a wave function, should be represented as a non-orthogonal in general (i.e. entangled) subspace of the separable complex Hilbert space relevant to the system to which the atom at issue is related as a true part of it. The paper follows previous publications of mine stating that “dark matter” and “dark energy” are projections of arbitrarily entangled states on the cognitive “screen” of Einstein’s “Mach’s principle” in general relativity postulating that gravitational field can be generated only by mass or energy.

scholarly journals SEPARABILITY OF PURE N-QUBIT STATES: TWO CHARACTERIZATIONS

2003 ◽  
Vol 14 (05) ◽  
pp. 797-814 ◽  
Author(s):  
PHILIPPE JORRAND ◽  
MEHDI MHALLA
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Quantum System ◽  
Pure State ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Entangled States ◽  
Necessary And Sufficient ◽  
Qubit States

Given a pure state |ψN>∈ℋN of a quantum system composed of n qubits, where ℋN is the Hilbert space of dimension N=2n, this paper answers two questions: what conditions should the amplitudes in |ψN> satisfy for this state to be separable (i) into a tensor product of n qubit states |ψ2>0⊗ |ψ2>1 ⊗⋯⊗ |ψ2>n-1, and (ii), into a tensor product of two subsystems states |ψP> ⊗ |ψQ> with P=2p and Q=2q such that p+q=n? For both questions, necessary and sufficient conditions are proved, thus characterizing at the same time families of separable and entangled states of n qubit systems. A number of more refined questions about separability in n qubit systems can be studied on the basis of these results.

scholarly journals On the construction of charged operators inside an eternal black hole

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Monica Guica ◽  
Daniel Jafferis
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Zero Mode ◽  
Wilson Line ◽  
Point Of View ◽  
Entangled States ◽  
Object A ◽  
Boundary Currents ◽  
State Dependent ◽  
The Relationship

We revisit the holographic construction of (approximately) local bulk operators inside an eternal AdS black hole in terms of operators in the boundary CFTs. If the bulk operator carries charge, the construction must involve a qualitatively new object: a Wilson line that stretches between the two boundaries of the eternal black hole. This operator - more precisely, its zero mode - cannot be expressed in terms of the boundary currents and only exists in entangled states dual to two-sided geometries, which suggests that it is a state-dependent operator. We determine the action of the Wilson line on the relevant subspaces of the total Hilbert space, and show that it behaves as a local operator from the point of view of either CFT. For the case of three bulk dimensions, we give explicit expressions for the charged bulk field and the Wilson line. Furthermore, we show that when acting on the thermofield double state, the Wilson line may be extracted from a limit of certain standard CFT operator expressions. We also comment on the relationship between the Wilson line and previously discussed mirror operators in the eternal black hole.

Entanglement and quantum phase transition in topological insulators

2019 ◽  
Vol 33 (32) ◽  
pp. 1950394
Author(s):  
Anant Vijay Varma ◽  
Anvesh Raja Kovela ◽  
Prasanta K. Panigrahi ◽  
Bhavesh Chouhan
Keyword(s):  
Phase Transition ◽  
Hilbert Space ◽  
Quantum Phase Transition ◽  
Surface States ◽  
Dimensional Subspace ◽  
Quantum Phase ◽  
Entangled States ◽  
Spin Orbital ◽  
Orbital Space ◽  
Qubit States

Presence of entangled states is explicitly shown in a topological insulator (TI) [Formula: see text]. The surface and bulk state are found to have different structures of entanglement. The surface states live as maximally entangled states in a four-dimensional subspace of total Hilbert space (spin, orbital, space). However, bulk states are entangled in the whole Hilbert space. Bulk states are found to be entangled maximally by controlled injection of electrons with momentum only along the [Formula: see text]-direction. At quantum phase transition (QPT) point, both states become maximally entangled two qubit states.

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