scholarly journals Entanglement of Identical Particles

2014 ◽  
Vol 21 (01n02) ◽  
pp. 1440003 ◽  
Author(s):  
F. Benatti ◽  
R. Floreanini ◽  
K. Titimbo
Keyword(s):  
Single Particle ◽  
Entangled States ◽  
Second Quantization ◽  
Identical Particles ◽  
Nonlocal Correlation ◽  
Pure States ◽  
Bipartite States

Unlike for bipartite states consisting of distinguishable particles, in the case of identical parties the notion of entanglement is still under debate. In the following, we review two different approaches to the entanglement of systems consisting of two bosons or fermions; the first approach is based on the particle aspect typical of first quantization and identifies separable pure states as those that allow to assign two orthogonal single particle vector states to both parties. The second approach makes full use of the mode aspect of second quantization whereby separability can be formulated as absence of nonlocal correlation among two different sets of modes. While the first approach applies to pure states only, the second one is more general and characterizes generic entangled states. In the following, we shall show that the mode-based approach indeed contains the particle-based one.

Identical Particles and Second Quantization: Occupation Number Representation

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Occupation Number ◽  
Annihilation Operator ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Number Representation ◽  
Second Quantization ◽  
Identical Particles ◽  
Fundamental Properties ◽  
Minimum Uncertainty ◽  
Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

scholarly journals Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 408
Author(s):  
Matteo Villani ◽  
Guillermo Albareda ◽  
Carlos Destefani ◽  
Xavier Cartoixà ◽  
Xavier Oriols
Keyword(s):  
Single Particle ◽  
Degrees Of Freedom ◽  
Single Photon ◽  
Open Quantum Systems ◽  
Wave Functions ◽  
Practical Application ◽  
Light Matter Interaction ◽  
Pure States ◽  
Energy And Momentum ◽  
Full Quantum

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).

scholarly journals Quantum computing and second quantization

2017 ◽  
Vol 26 (03) ◽  
pp. 1741006 ◽  
Author(s):  
Hanna Makaruk
Keyword(s):  
Quantum Computing ◽  
Approximate Method ◽  
Quantum Systems ◽  
General Idea ◽  
Entangled States ◽  
Quantum Computers ◽  
Second Quantization ◽  
Particle Arrangement ◽  
The Many

Quantum computers by their nature are many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.

Most robust and fragile two-qubit entangled states under deploarizing channels

2013 ◽  
Vol 13 (7&8) ◽  
pp. 645-660
Author(s):  
Chao-Qian Pang ◽  
Fu-Lin Zhang ◽  
Yue Jiang ◽  
Mai-Lin Liang ◽  
Jing-Ling Chen
Keyword(s):  
Evolution Equation ◽  
Numerical Calculations ◽  
Entangled States ◽  
Fragile States ◽  
Qubit System ◽  
Uniform Channel ◽  
Pure States ◽  
The One ◽  
Major Factors ◽  
The Impact

For a two-qubit system under local depolarizing channels, the most robust and most fragile states are derived for a given concurrence or negativity. For the one-sided channel, the pure states are proved to be the most robust ones, with the aid of the evolution equation for entanglement given by Konrad \emph{et al.} [Nat. Phys. 4, 99 (2008)]. Based on a generalization of the evolution equation for entanglement, we classify the ansatz states in our investigation by the amount of robustness, and consequently derive the most fragile states. For the two-sided channel, the pure states are the most robust for a fixed concurrence. Under the uniform channel, the most fragile states have the minimal negativity when the concurrence is given in the region $[1/2,1]$. For a given negativity, the most robust states are the ones with the maximal concurrence, and the most fragile ones are the pure states with minimum of concurrence. When the entanglement approaches zero, the most fragile states under general nonuniform channels tend to the ones in the uniform channel. Influences on robustness by entanglement, degree of mixture, and asymmetry between the two qubits are discussed through numerical calculations. It turns out that the concurrence and negativity are major factors for the robustness. When they are fixed, the impact of the mixedness becomes obvious. In the nonuniform channels, the most fragile states are closely correlated with the asymmetry, while the most robust ones with the degree of mixture.

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.

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