scholarly journals Quantum Correlations and Permutation Symmetries

2018 ◽  
Author(s):  
Mrittunjoy Guha Majumdar
Keyword(s):  
Quantum System ◽  
Graphical Method ◽  
Quantum Correlations ◽  
Quantum States ◽  
Matrix Analysis ◽  
Reduced Density Matrix ◽  
Density Matrices ◽  
Quantum Non Locality ◽  
Reduced Density ◽  
Non Locality

In this paper, the connections between quantum non-locality and permutation symmetries areexplored. This includes two types of symmetries: permutation across a superposition and permutationof qubits in a quantum system. An algorithm is proposed for nding the separability class ofa quantum state using a method based on factorizing an arbitrary multipartite state into possiblepartitions, cyclically permuting qubits of the vectors in a superposition to check which separabilityclass it falls into and thereafter using a reduced density-matrix analysis of the system is proposed.For the case of mixed quantum states, conditions for separability are found in terms of the partialtransposition of the density matrices of the quantum system. One of these conditions turns out tobe the Partial Positive Transpose (PPT) condition. A graphical method for analyzing separabilityis also proposed. The concept of permutation of qubits is shown to be useful in dening a newentanglement measure in the `engle'.

scholarly journals Insights into one-body density matrices using deep learning

2020 ◽  
Vol 224 ◽  
pp. 265-291 ◽  
Author(s):  
Jack Wetherell ◽  
Andrea Costamagna ◽  
Matteo Gatti ◽  
Lucia Reining
Keyword(s):  
Deep Learning ◽  
Density Matrix ◽  
Reduced Density Matrix ◽  
Body Density ◽  
Density Matrices ◽  
Learning Constraints ◽  
The One ◽  
Reduced Density

Deep-learning constraints of the one-body reduced density matrix from its compressibility to enable efficient determination of key observables.

scholarly journals Reduced Density Matrix Cumulants: The Combinatorics of Size-Consistency and Generalized Normal Ordering

2020 ◽  
Author(s):  
Jonathon Misiewicz ◽  
Justin Turney ◽  
Henry Schaefer
Keyword(s):  
Density Matrix ◽  
Generating Function ◽  
Reduced Density Matrix ◽  
General Mechanism ◽  
Density Matrices ◽  
Reduced Density Matrices ◽  
Normal Ordering ◽  
Combinatorial Constructions ◽  
Reduced Density

Reduced density matrix cumulants play key roles in the theory of both reduced density matrices and multiconfigurational normal ordering, but the underlying formalism has remained mysterious. We present a new, simpler generating function for reduced density matrix cumulants that is formally identical to equating the coupled cluster and configuration interaction ansätze. This is shown to be a general mechanism to convert between a multiplicatively separable quantity and an additively separable quantity, as defined by a set of axioms. It is shown that both the cumulants of probability theory and reduced density matrices are entirely combinatorial constructions, where the differences can be associated to changes in the notion of "multiplicative separability'' for expectation values of random variables compared to reduced density matrices. We compare our generating function to that of previous works and criticize previous claims of probabilistic significance of the reduced density matrix cumulants. Finally, we present the simplest proof to date of the Generalized Normal Ordering formalism to explore the role of reduced density matrix cumulants therein.

scholarly journals Quantum Rayleigh Annihilation of Entangled Photons

2018 ◽  
Author(s):  
Andre Vatarescu
Keyword(s):  
Physical Reality ◽  
Quantum States ◽  
Entangled States ◽  
Entangled Photons ◽  
Dielectric Media ◽  
Quantum Phenomenon ◽  
Quantum Non Locality ◽  
Linearly Polarized ◽  
Photonic States ◽  
Non Locality

The interpretation of published experimental results intended to prove the existence of a quantum phenomenon of non-locality involving photonic entangled states did not take into consideration the existence of the quantum Rayleigh conversion of photons in dielectric media. This phenomenon leads to the existence of high levels of correlations between two independent photonic and linearly polarized quantum states generated after the entangled photons have been absorbed through the quantum Rayleigh conversion. Both pure and mixed individual states of polarization result in expressions normally associated with entangled photonic states, providing support for the view that the physical reality of quantum non-locality is highly questionable.

scholarly journals Quantum Rayleigh Annihilation of Entangled Photons

2018 ◽  
Author(s):  
Andre Vatarescu
Keyword(s):  
Physical Reality ◽  
Quantum States ◽  
Entangled States ◽  
Entangled Photons ◽  
Dielectric Media ◽  
Quantum Phenomenon ◽  
Quantum Non Locality ◽  
Linearly Polarized ◽  
Photonic States ◽  
Non Locality

The interpretation of published experimental results intended to prove the existence of a quantum phenomenon of non-locality involving photonic entangled states did not take into consideration the existence of the quantum Rayleigh conversion of photons in dielectric media. This phenomenon leads to the existence of high levels of correlations between two independent photonic and linearly polarized quantum states generated after the entangled photons have been absorbed through the quantum Rayleigh conversion. Both pure and mixed individual states of polarization result in expressions normally associated with entangled photonic states, providing support for the view that the physical reality of quantum non-locality is highly questionable.

scholarly journals Quantum Correlations and Quantum Non-Locality: A Review and a Few New Ideas

2019 ◽  
Vol 9 (24) ◽  
pp. 5406 ◽  
Author(s):  
Marco Genovese ◽  
Marco Gramegna
Keyword(s):  
Quantum Mechanics ◽  
Special Relativity ◽  
Quantum Correlations ◽  
Quantum Non Locality ◽  
Higher Dimensional ◽  
New Ideas ◽  
Non Locality

In this paper we make an extensive description of quantum non-locality, one of the most intriguing and fascinating facets of quantum mechanics. After a general presentation of several studies on this subject dealing with different but connected facets of quantum non-locality, we consider if this, and the friction it carries with special relativity, can eventually find a “solution” by considering higher dimensional spaces.

OFF-DIAGONAL LONG RANGE ORDER OF THE REDUCED DENSITY MATRICES FOR A ONE-DIMENSIONAL SOLVABLE MODEL OF FERMIONS

1988 ◽  
Vol 02 (06) ◽  
pp. 1439-1442
Author(s):  
FU-CHO PU ◽  
BAO-HENG ZHAO
Keyword(s):  
Long Range ◽  
Solvable Model ◽  
Range Order ◽  
Reduced Density Matrix ◽  
Particle State ◽  
Long Range Order ◽  
Density Matrices ◽  
One Dimensional ◽  
Ferromagnetic Chain ◽  
Reduced Density

A one-dimensional solvable model of fermions is mapped to the XXX ferromagnetic chain. At T = 0, it is shown that there is off-diagonal long range order for the reduced density matrix ρ2 in the model. In momentum space the single particle state pairs are coherently occupied. The momenta of the particles in each pair are equal but with opposite directions.

scholarly journals Reduced Density Matrix Cumulants: The Combinatorics of Size-Consistency and Generalized Normal Ordering

2020 ◽  
Author(s):  
Jonathon Misiewicz ◽  
Justin Turney ◽  
Henry Schaefer
Keyword(s):  
Density Matrix ◽  
Generating Function ◽  
Reduced Density Matrix ◽  
General Mechanism ◽  
Density Matrices ◽  
Reduced Density Matrices ◽  
Normal Ordering ◽  
Combinatorial Constructions ◽  
Reduced Density

Reduced density matrix cumulants play key roles in the theory of both reduced density matrices and multiconfigurational normal ordering, but the underlying formalism has remained mysterious. We present a new, simpler generating function for reduced density matrix cumulants that is formally identical to equating the coupled cluster and configuration interaction ansätze. This is shown to be a general mechanism to convert between a multiplicatively separable quantity and an additively separable quantity, as defined by a set of axioms. It is shown that both the cumulants of probability theory and reduced density matrices are entirely combinatorial constructions, where the differences can be associated to changes in the notion of "multiplicative separability'' for expectation values of random variables compared to reduced density matrices. We compare our generating function to that of previous works and criticize previous claims of probabilistic significance of the reduced density matrix cumulants. Finally, we present the simplest proof to date of the Generalized Normal Ordering formalism to explore the role of reduced density matrix cumulants therein.

scholarly journals An algorithm to explore entanglement in small systems

2018 ◽  
Vol 474 (2214) ◽  
pp. 20180023 ◽  
Author(s):  
R. Reuvers
Keyword(s):  
Iterative Algorithm ◽  
Entanglement Entropy ◽  
Quantum States ◽  
Entangled States ◽  
Density Matrices ◽  
Reduced Density Matrices ◽  
Output Entropy ◽  
Maximally Entangled States ◽  
Reduced Density ◽  
Minimal Output Entropy

A quantum state’s entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms. Depending on the choice of norm, the optimizing states maximize or minimize entanglement, possibly across several bipartite cuts at the same time and possibly only among states in a specified subspace. Recognizing that convergence but not success is certain, we use the algorithm to explore topics ranging from fermionic reduced density matrices and varieties of pure quantum states to absolutely maximally entangled states and minimal output entropy of channels.

scholarly journals Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 276 ◽  
Author(s):  
Zhang Jiang ◽  
Amir Kalev ◽  
Wojciech Mruczkiewicz ◽  
Hartmut Neven
Keyword(s):  
Density Matrix ◽  
Simple Structure ◽  
System Size ◽  
Quantum Circuit ◽  
Quantum States ◽  
Reduced Density Matrix ◽  
Single Quantum ◽  
Pauli Operator ◽  
Fermionic System ◽  
Reduced Density

We introduce a fermion-to-qubit mapping defined on ternary trees, where any single Majorana operator on an n-mode fermionic system is mapped to a multi-qubit Pauli operator acting nontrivially on ⌈log3⁡(2n+1)⌉ qubits. The mapping has a simple structure and is optimal in the sense that it is impossible to construct Pauli operators in any fermion-to-qubit mapping acting nontrivially on less than log3⁡(2n) qubits on average. We apply it to the problem of learning k-fermion reduced density matrix (RDM), a problem relevant in various quantum simulation applications. We show that one can determine individual elements of all k-fermion RDMs in parallel, to precision ϵ, by repeating a single quantum circuit for ≲(2n+1)kϵ−2 times. This result is based on a method we develop here that allows one to determine individual elements of all k-qubit RDMs in parallel, to precision ϵ, by repeating a single quantum circuit for ≲3kϵ−2 times, independent of the system size. This improves over existing schemes for determining qubit RDMs.

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