Oscillating between classically entangled state and separable state: an analogy between classical and quantum optics

2020 ◽  
Vol 37 (7) ◽  
pp. 2058
Author(s):  
Shahram Dehdashti ◽  
Firat Yasar
Keyword(s):  
Quantum Optics ◽  
Entangled State ◽  
Separable State

Entanglement witnesses of four-qubit tripartite separable quantum states

2021 ◽  
Author(s):  
Miao Xu ◽  
Wei-feng Zhou ◽  
Feng Chen ◽  
Lizhen Jiang ◽  
Xiao-yu Chen
Keyword(s):  
Necessary Conditions ◽  
Quantum Systems ◽  
Ghz State ◽  
W State ◽  
Necessary Condition ◽  
Entangled State ◽  
Separable State ◽  
Entanglement Witnesses ◽  
Qubit System ◽  
Bipartite Quantum Systems

Abstract A quantum entangled state is easily disturbed by noise and degenerates into a separable state. Comparing to the entanglement of bipartite quantum systems, less progresses have been made for the entanglement of multipartite quantum systems. For tripartite separability of a four-qubit system, we propose two entanglement witnesses, each of which corresponds to a necessary condition of tripartite separability. For the four-qubit GHZ state mixed with a W state and white noise, it is proved that the necessary conditions of tripartite separability are also sufficient at W state side.

A New Kind of Bipartite Coherent-Entangled State and Its Applications in Quantum Optics

2010 ◽  
Vol 50 (3) ◽  
pp. 906-915 ◽  
Author(s):  
Xiang-Guo Meng ◽  
Ji-Suo Wang ◽  
Bao-Long Liang
Keyword(s):  
Quantum Optics ◽  
Entangled State

ENTANGLED STATES, SQUEEZED STATES GAINED VIA THE ROUTE OF DEVELOPING DIRAC'S SYMBOLIC METHOD AND THEIR APPLICATIONS

2004 ◽  
Vol 18 (10n11) ◽  
pp. 1387-1455 ◽  
Author(s):  
HONG-YI FAN
Keyword(s):  
Quantum Optics ◽  
Fourier Optics ◽  
Entangled States ◽  
Entangled State ◽  
Squeezed States ◽  
Iwop Technique ◽  
The Iwop Technique ◽  
Operator Ordering ◽  
Symbolic Method ◽  
Interdisciplinary Study

Via the route of developing Dirac's symbolic method by virtue of the technique of integration within an ordered product (IWOP) of operators we derive various entangled state representations, squeezed states, and operator ordering formulae. We show how the entangled states can be applied to many aspects of quantum optics theory. The applications of the entangled states in the interdisciplinary study of quantum optics and Fourier optics are also introduced. All these discussions exhibit the power of Dirac's symbolic method with the aid of the IWOP technique.

scholarly journals ENTANGLEMENT IN A DIMERIZED ANTIFERROMAGNETIC HEISENBERG CHAIN

2006 ◽  
Vol 04 (06) ◽  
pp. 1037-1047 ◽  
Author(s):  
XIANG HAO ◽  
SHIQUN ZHU
Keyword(s):  
Ground State ◽  
State Energy ◽  
Characteristic Temperature ◽  
Critical Value ◽  
Entangled State ◽  
Minimal Energy ◽  
Heisenberg Chain ◽  
Separable State ◽  
Heisenberg Spin ◽  
The Difference

The entanglement properties in an antiferromagnetic dimerized Heisenberg spin-1/2 chain are investigated. The entanglement gap, which is the difference between the ground-state energy and the minimal energy that any separable state can attain, is calculated to detect the entanglement. It is found that the entanglement gap can be increased by varying the alternation parameter. Through thermal energy, the witness of the entanglement can determine a characteristic temperature below which an entangled state can be obtained. The entanglement detected by the energy can provide a lower bound for that determined by the concurrence. If the alternation parameter is smaller than a critical value, there is always no inter-dimer entanglement in the chain.

Magnetic resonance with number states versus coherent states

2018 ◽  
Vol 32 (30) ◽  
pp. 1850336
Author(s):  
Navin Khaneja
Keyword(s):  
Electromagnetic Field ◽  
Magnetic Resonance ◽  
Coupling Strength ◽  
Coherent States ◽  
Microwave Field ◽  
Transverse Magnetization ◽  
Entangled State ◽  
Separable State ◽  
Paramagnetic Resonance ◽  
Electron Paramagnetic

In this paper, we study the interaction of quantized radio-frequency (rf)/microwave-field with nuclear spin in Nuclear Magnetic Resonance (NMR) or electron spin in Electron Paramagnetic Resonance (EPR). In magnetic resonance experiments, interaction of quantized rf-field leads to entanglement of spin with the electromagnetic field. In an entangled state, the spins are depolarized with no net transverse magnetization, which cannot give a detectable signal in inductive detection (or Q detection) that detects transverse magnetization. We show that when the electromagnetic field is in coherent state, inductive detection becomes possible. We use the mathematics of quantum optics to study the evolution of a coherent rf-field with a sample of all polarized spins. We show that evolution can be solved in closed form as a separable state of rf-field and spin ensemble, where spin ensemble evolves according to Bloch equations in an rf-field. We extend the analysis and results to a spin ensemble with Boltzmann polarization. The rabi frequency and coupling strength of spins to rf-field depends on number state of the rf-field. We show that in interaction with a coherent rf-field, this variation in coupling strength introduces negligible error.

CLASSICAL OPTICAL TRANSFORMS STUDIED IN THE CONTEXT OF QUANTUM OPTICS VIA THE ROUTE OF DEVELOPING DIRAC'S SYMBOLIC METHOD

2005 ◽  
Vol 19 (05) ◽  
pp. 799-856 ◽  
Author(s):  
HONG-YI FAN ◽  
HAI-LIANG LU
Keyword(s):  
Quantum Optics ◽  
Coherent State ◽  
Fractional Fourier Transform ◽  
Entangled State ◽  
Contact Transformation ◽  
Complex Wavelet Transform ◽  
State Representation ◽  
Normal Product ◽  
Symbolic Method ◽  
Fresnel Transform

Via the route of developing Dirac's symbolic method and following Dirac's assertion: "⋯ for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory", we find the generalized Fresnel operator (GFO) corresponding to the generalized Fresnel transform (GFT) in classical optics. We derive GFO's normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in quantum optics. With the aid of entangled state representation the entangled Fresnel transform is proposed; new eigenfunctions of the complex fractional Fourier transform and fractional Hankel transform are obtained; the two-variable Hermite eigenmodes of light propagation are used in studying the Talbot effect in quadratic-index media; the complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Moreover, quantum optical version of classical z-transforms is obtained on the basis of the eigenvector of creation operator. Throughout our discussions, the coherent state, squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used.

Quantum entanglement purification assisted by classical phase noise

2020 ◽  
Vol 35 (32) ◽  
pp. 2050269
Author(s):  
Qi-Jun Zhi ◽  
Qiang Zheng
Keyword(s):  
Phase Noise ◽  
Phase Fluctuation ◽  
Entangled State ◽  
Separable State ◽  
Fractal Boundary ◽  
High Quality ◽  
Entanglement Purification ◽  
Positive Role ◽  
Maximally Entangled State ◽  
Initial States

Entanglement purification is a vital protocol to produce a high-quality entangled state from an ensemble of identical states. Based on the particular scheme of entanglement purification [Phys. Rev. A 87, 052316 (2013)], the effect of phase fluctuation is investigated. The convergence pattern of the initial states can be divided into two kinds of regions, corresponding to the purified outcomes being a maximally entangled state (MES) or a separable state. And there is the fractal-like structure near the boundary between these two regions. It is found that the phase noise plays a positive role in generating an MES for an initial states near some fractal boundary, which can only become the separable one if the noise is absent. It is also found that the minimal iteration steps to achieve the maximally entangled state with the phase noise can be decreased, which can save the resource in the protocol.

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