Platonic entanglement

2021 ◽  
Vol 21 (13&14) ◽  
pp. 1081-1090
Author(s):  
Jose I. Latorre ◽  
German Sierra
Keyword(s):  
Prime Number ◽  
Quantum State ◽  
Entangled States ◽  
Platonic Solid ◽  
Platonic Solids ◽  
Reed Solomon Codes ◽  
Tensor Networks

We present a construction of highly entangled states defined on the topology of a platonic solid using tensor networks based on ancillary Absolute Maximally Entangled (AME) states. We illustrate the idea using the example of a quantum state based on AME(5,2) over a dodecahedron. We analyze the entropy of such states on many different partitions, and observe that they come on integer numbers and are almost maximal. We also observe that all platonic solids accept the construction of AME states based on Reed-Solomon codes since their number of facets, vertices and edges are always a prime number plus one.

MULTIPARTY REMOTELY PREPARING MULTIPARTITE EQUATORIAL ENTANGLED STATES IN HIGH DIMENSIONS

2011 ◽  
Vol 09 (06) ◽  
pp. 1437-1448
Author(s):  
YI-BAO LI ◽  
KUI HOU ◽  
SHOU-HUA SHI
Keyword(s):  
Quantum State ◽  
Quantum Channel ◽  
Success Probability ◽  
Quantum States ◽  
Remote State Preparation ◽  
Entangled States ◽  
Entangled State ◽  
High Dimensions ◽  
Original State ◽  
State Preparation

We propose two kinds of schemes for multiparty remote state preparation (MRSP) of the multiparticle d-dimensional equatorial quantum states by using partial entangled state as the quantum channel. Unlike more remote state preparation scheme which only one sender knows the original state to be remotely prepared, the quantum state is shared by two-party or multiparty in this scheme. We show that if and only if all the senders agree to collaborate with each other, the receiver can recover the original state with certain probability. It is found that the total success probability of MRSP is only by means of the smaller coefficients of the quantum channel and the dimension d.

The Periodic System

2019 ◽  
Author(s):  
Eric Scerri
Keyword(s):  
Middle Ages ◽  
Point Of View ◽  
Platonic Solid ◽  
Ancient Greek ◽  
Platonic Solids ◽  
System P ◽  
Chemical Inertness ◽  
Dimensional Shape ◽  
The Many

In ancient Greek times, philosophers recognized just four elements—earth, water, air, and fire—all of which survive in the astrological classification of the 12 signs of the zodiac. At least some of these philosophers believed that these different elements consisted of microscopic components with differing shapes and that this explained the various properties of the elements. These shapes or structures were believed to be in the form of Platonic solids (figure 1.1) made up entirely of the same two-dimensional shape. The Greeks believed that earth consisted of microscopic cubic particles, which explained why it was difficult to move earth. Meanwhile, the liquidity of water was explained by an appeal to the smoother shape possessed by the icosahedron, while fire was said to be painful to the touch because it consisted of the sharp particles in the form of tetrahedra. Air was thought to consist of octahedra since that was the only remaining Platonic solid. A little later, a fifth Platonic solid, the dodecahedron, was discovered, and this led to the proposal that there might be a fifth element or “quintessence,” which also became known as ether. Although the notion that elements are made up of Platonic solids is regarded as incorrect from a modern point of view, it is the origin of the very fruitful notion that macroscopic properties of substances are governed by the structures of the microscopic components of which they are comprised. These “elements” survived well into the Middle Ages and beyond, augmented with a few others discovered by the alchemists, the precursors of modern-day chemists. One of the many goals of the alchemists seems to have been the transmutation of elements. Not surprisingly, perhaps, the particular transmutation that most enticed them was the attempt to change the base metal lead into the noble metal gold, whose unusual color, rarity, and chemical inertness have made it one of the most treasured substances since the dawn of civilization.

scholarly journals Theory of Packaged Entangled States

2017 ◽  
Vol 01 (03) ◽  
pp. 1750005
Author(s):  
Rongchao Ma
Keyword(s):  
Physical Properties ◽  
Quantum Entanglement ◽  
Quantum State ◽  
Large Distance ◽  
Entangled States ◽  
Applied Physics ◽  
Observable Universe ◽  
Particle Pair ◽  
New Interpretation ◽  
Physical Quantities

The quantum entanglement that include every physical properties of particles would be important for both theoretical and applied physics. Here, we theoretically show that a particle–antiparticle pair can form the so-called packaged entangled states which encapsulate all the necessary physical quantities for completely identifying the particles. The particles in the packaged entangled states exhibit unusual properties. Thereafter, we proposed the possible protocol for teleporting the entire quantum state of a particle (or an antiparticle) to an arbitrarily large distance and the transfer of new entangled states from a particle pair to another particle pair. Finally, we presented a new interpretation to the matter–antimatter asymmetry of the observable universe.

Teleportation of an Unknown Quantum State via Partly Entangled States

2000 ◽  
Vol 17 (10) ◽  
pp. 703-704 ◽  
Author(s):  
Feng Xun-Li ◽  
Gong Shang-Qing ◽  
Wang Zhong-Yang ◽  
Xu Zhi-Zhan
Keyword(s):  
Quantum State ◽  
Entangled States ◽  
Unknown Quantum State

Quantum state sharing with mixing state from six-qubit entangled pure one

2020 ◽  
Vol 35 (32) ◽  
pp. 2050264
Author(s):  
Zhanjun Zhang ◽  
Hao Yuan ◽  
Chuanmei Xie ◽  
Biaoliang Ye
Keyword(s):  
Quantum State ◽  
Quantum Channel ◽  
Pure State ◽  
Essential Role ◽  
Entangled States ◽  
Entangled State ◽  
Quantum State Sharing ◽  
Mixing State ◽  
Preliminary Study

In this paper the possibility of using mixing entangled states as quantum channel to accomplish quantum state sharing (QSTS) is considered. As a preliminary study, an efficient tripartite QSTS scheme is put forward by utilizing a mixing entangled state, which is a derivative of a six-qubit entangled pure state under a two-qubit confusion. Some specific discussions about the QSTS scheme are made, including the issues of the scheme determinacy, the sharer symmetry, the scheme security and the essential role of quantum channel as well as the current experimental feasibility.

scholarly journals Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 886
Author(s):  
Jun-Yi Wu
Keyword(s):  
Quantum State ◽  
Adaptive Method ◽  
Upper Bounds ◽  
The State ◽  
Entangled States ◽  
Lower And Upper Bounds ◽  
Bipartite Entanglement ◽  
Higher Dimensional ◽  
Computational Basis

An adaptive method for quantum state fidelity estimation in bipartite higher dimensional systems is established. This method employs state verifier operators which are constructed by local POVM operators and adapted to the measurement statistics in the computational basis. Employing this method, the state verifier operators that stabilize Bell-type entangled states are constructed explicitly. Together with an error operator in the computational basis, one can estimate the lower and upper bounds on the state fidelity for Bell-type entangled states in few measurement configurations. These bounds can be tighter than the fidelity bounds derived in [Bavaresco et al., Nature Physics (2018), 14, 1032–1037], if one constructs more than one local POVM measurements additional to the measurement in the computational basis.

scholarly journals Quantum Universe, Horizon, and Antimatter

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 337
Author(s):  
Alexey V. Melkikh
Keyword(s):  
Quantum State ◽  
Mixed State ◽  
Transition Time ◽  
Entangled States ◽  
Speed Of Light ◽  
Quantum Universe ◽  
The Creation ◽  
The Universe ◽  
Different Parts

If the isolated system of bosons and fermions was initially in a pure maximally entangled quantum state, then, as a result of decoherence caused by the creation and annihilation of particles, this system not only enters a mixed state but also achieves equilibrium. The time of such a transition does not depend on the size of the system but is determined only by the properties of the particles. This phenomenon allows the problem of the horizon (the homogeneity of the universe) to be solved, since the transition time of different parts of the universe (if they were originally entangled with each other) to equilibrium will not depend on their sizes, and the speed of the interaction may be greater than the speed of light. Based on the decay of entangled states, the problem of the predominance of matter over antimatter in the universe can also be solved.

scholarly journals Tensor network representations from the geometry of entangled states

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Matthias Christandl ◽  
Angelo Lucia ◽  
Peter Vrana ◽  
Albert H. Werner
Keyword(s):  
General Setting ◽  
Entangled States ◽  
Strongly Correlated ◽  
Effective Dimension ◽  
Tensor Networks ◽  
Tensor Network ◽  
Correlated Quantum Systems ◽  
Network States ◽  
Tensor Network States ◽  
Entanglement Structure

Tensor networks provide descriptions of strongly correlated quantum systems based on an underlying entanglement structure given by a graph of entangled states along the edges that identify the indices of the local tensors to be contracted. Considering a more general setting, where entangled states on edges are replaced by multipartite entangled states on faces, allows us to employ the geometric properties of multipartite entanglement in order to obtain representations in terms of superpositions of tensor network states with smaller effective dimension, leading to computational savings.

scholarly journals QUANTUM CIRCUITS FOR SINGLE-QUBIT MEASUREMENTS CORRESPONDING TO PLATONIC SOLIDS

2004 ◽  
Vol 02 (03) ◽  
pp. 353-377 ◽  
Author(s):  
THOMAS DECKER ◽  
DOMINIK JANZING ◽  
THOMAS BETH
Keyword(s):  
Fourier Transform ◽  
Quantum Circuits ◽  
Platonic Solid ◽  
Bloch Sphere ◽  
Platonic Solids ◽  
Quantum Operations ◽  
Single Qubit ◽  
Orthogonal Measurement ◽  
Computational Basis ◽  
Positive Operator Valued Measure

Each platonic solid defines a single-qubit positive operator-valued measure (POVM) by interpreting its vertices as points on the Bloch sphere. We construct simple circuits for implementing these kinds of measurements and other simple types of symmetric POVMs on one qubit. Each implementation consists of a discrete Fourier transform and some elementary quantum operations followed by an orthogonal measurement in the computational basis.

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