scholarly journals Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 928 ◽  
Author(s):  
Mladen Pavičić ◽  
Norman Megill
Keyword(s):  
Quantum Computation ◽  
Hilbert Spaces ◽  
Quantum Communication ◽  
Quantum Contextuality ◽  
Vector Component ◽  
Vector Generation ◽  
Incomplete Lists ◽  
Unified Method

Recently, quantum contextuality has been proved to be the source of quantum computation’s power. That, together with multiple recent contextual experiments, prompts improving the methods of generation of contextual sets and finding their features. The most elaborated contextual sets, which offer blueprints for contextual experiments and computational gates, are the Kochen–Specker (KS) sets. In this paper, we show a method of vector generation that supersedes previous methods. It is implemented by means of algorithms and programs that generate hypergraphs embodying the Kochen–Specker property and that are designed to be carried out on supercomputers. We show that vector component generation of KS hypergraphs exhausts all possible vectors that can be constructed from chosen vector components, in contrast to previous studies that used incomplete lists of vectors and therefore missed a majority of hypergraphs. Consequently, this unified method is far more efficient for generations of KS sets and their implementation in quantum computation and quantum communication. Several new KS classes and their features have been found and are elaborated on in the paper. Greechie diagrams are discussed.

scholarly journals Vector generation of contextual sets

2019 ◽  
Vol 198 ◽  
pp. 00009
Author(s):  
Mladen Pavičić ◽  
Norman D. Megill
Keyword(s):  
Quantum Computation ◽  
Quantum Contextuality ◽  
Large Sets ◽  
Vector Generation ◽  
Universal Quantum ◽  
General Method

As quantum contextuality proves to be a necessary resource for universal quantum computation, we present a general method for vector generation of Kochen-Specker (KS) contextual sets in the form of hypergraphs. The method supersedes all three previous methods: (i) fortuitous discoveries of smallest KS sets, (ii) exhaustive upward hypergraph-generation of sets, and (iii) random downward generation of sets from fortuitously obtained big master sets. In contrast to previous works, we can generate master sets which contain all possible KS sets starting with nothing but a few simple vector components. From them we can readily generate all KS sets obtained in the last half a century and any specified new KS sets. Herewith we can generate sufficiently large sets as well as sets with definite required features and structures to enable varieties of different implementations in quantum computation and communication.

scholarly journals Photonic entanglement as a resource in quantum computation and quantum communication

2007 ◽  
Vol 24 (2) ◽  
pp. 241 ◽  
Author(s):  
Robert Prevedel ◽  
Markus Aspelmeyer ◽  
Caslav Brukner ◽  
Anton Zeilinger ◽  
Thomas D. Jennewein
Keyword(s):  
Quantum Computation ◽  
Quantum Communication

scholarly journals ON THE POWER QUANTUM COMPUTATION OVER REAL HILBERT SPACES

2013 ◽  
Vol 11 (01) ◽  
pp. 1350001 ◽  
Author(s):  
MATTHEW McKAGUE
Keyword(s):  
Hilbert Space ◽  
Quantum Computation ◽  
Hilbert Spaces ◽  
Quantum Circuit ◽  
Complex Hilbert Space ◽  
Complexity Classes ◽  
Complex Numbers ◽  
Real Numbers ◽  
Single Qubit ◽  
Quantum Complexity

We consider the power of various quantum complexity classes with the restriction that states and operators are defined over a real, rather than complex, Hilbert space. It is well known that a quantum circuit over the complex numbers can be transformed into a quantum circuit over the real numbers with the addition of a single qubit. This implies that BQP retains its power when restricted to using states and operations over the reals. We show that the same is true for QMA (k), QIP (k), QMIP and QSZK.

scholarly journals Hyper-parallel nonlocal CNOT operation with hyperentanglement assisted by cross-Kerr nonlinearity

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Ping Zhou ◽  
Li Lv
Keyword(s):  
Quantum Computation ◽  
Channel Capacity ◽  
Quantum Channel ◽  
Quantum Communication ◽  
Kerr Nonlinearity ◽  
Spatial Mode ◽  
Cnot Gate ◽  
Long Distance ◽  
Current Technology ◽  
Cnot Operation

Abstract Implementing CNOT operation nonlocally is one of central tasks in distributed quantum computation. Most of previously protocols for implementation quantum CNOT operation only consider implement CNOT operation in one degree of freedom(DOF). In this paper, we present a scheme for nonlocal implementation of hyper-parallel CNOT operation in polarization and spatial-mode DOFs via hyperentanglement. The CNOT operations in polarization DOF and spatial-mode DOF can be remote implemented simultaneously with hyperentanglement assisited by cross-Kerr nonlinearity. Hyper-parallel nonlocal CNOT gate can enhance the quantum channel capacity for distributed quantum computation and long-distance quantum communication. We discuss the experiment feasibility for hyper-parallel nonlocal gate. It shows that the protocol for hyper-parallel nonlocal CNOT operation can be realized with current technology.

OPTICAL IMPLEMENTATION OF THE OPTIMAL UNIVERSAL AND PHASE-COVARIANT QUANTUM CLONING MACHINES

2012 ◽  
Vol 26 (16) ◽  
pp. 1250102
Author(s):  
LIU YE ◽  
XUE-KE SONG ◽  
JIE YANG ◽  
QUN YANG ◽  
YANG-CHENG MA
Keyword(s):  
Quantum Computation ◽  
Quantum Communication ◽  
Beam Splitter ◽  
Linear Optics ◽  
Quantum Cloning ◽  
Horizontal Polarization ◽  
Covariant Quantum ◽  
Experimental Technology ◽  
Symmetric Phase

Quantum cloning relates to the security of quantum computation and quantum communication. In this paper, firstly we propose a feasible unified scheme to implement optimal 1 → 2 universal, 1 → 2 asymmetric and symmetric phase-covariant cloning, and 1 → 2 economical phase-covariant quantum cloning machines only via a beam splitter. Then 1 → 3 economical phase-covariant quantum cloning machines also can be realized by adding another beam splitter in context of linear optics. The scheme is based on the interference of two photons on a beam splitter with different splitting ratios for vertical and horizontal polarization components. It is shown that under certain condition, the scheme is feasible by current experimental technology.

scholarly journals QUANTUM LOGIC BETWEEN DISTANT TRAPPED IONS

2010 ◽  
Vol 08 (01n02) ◽  
pp. 337-394 ◽  
Author(s):  
S. OLMSCHENK ◽  
D. HAYES ◽  
D. N. MATSUKEVICH ◽  
P. MAUNZ ◽  
D. L. MOEHRING ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Quantum Communication ◽  
Trapped Ions ◽  
Long Distance ◽  
Detailed Review ◽  
Atomic Ions ◽  
Experimental Implementation ◽  
Unique Path ◽  
Atomic States

Trapped atomic ions have proven to be one of the most promising candidates for the realization of quantum computation due to their long trapping times, excellent coherence properties, and exquisite control of the internal atomic states. Integrating ions (quantum memory) with photons (distance link) offers a unique path to large-scale quantum computation and long-distance quantum communication. In this article, we present a detailed review of the experimental implementation of a heralded photon-mediated quantum gate between remote ions, and the employment of this gate to perform a teleportation protocol between two ions separated by a distance of about one meter.

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