scholarly journals BUILDING PARTIALLY ENTANGLED STATES WITH GROVER'S AMPLITUDE AMPLIFICATION PROCESS

2000 ◽  
Vol 11 (03) ◽  
pp. 469-484 ◽  
Author(s):  
HIROO AZUMA
Keyword(s):  
Entangled States ◽  
Entangled State ◽  
Unitary Transformations ◽  
Amplification Process ◽  
Noise Limit ◽  
Partially Entangled States ◽  
High Degree ◽  
And Inversion ◽  
State 1 ◽  
Shot Noise Limit

In the present study, we discuss how to build some partially entangled states of n two-state quantum systems (qubits). The optimal partially entangled state with a high degree of symmetry is considered to be useful for overcoming a shot noise limit of Ramsey spectroscopy under some decoherence. This state is invariant under permutation of any two qubits, and inversion between the ground state |0> and an excited state |1> for each qubit. We show that by using selective phase shifts in certain basis vectors and Grover's inversion about average operations, we can construct this high symmetric entangled state by (polynomial in n) ×2n/2 successive unitary transformations that are applied on two or three qubits.

Analysing the Efficiencies of Partially Entangled Three-Qubit States for Quantum Information Processing Under Real Conditions

2019 ◽  
Vol 74 (6) ◽  
pp. 523-537
Author(s):  
Jyoti Faujdar ◽  
Atul Kumar
Keyword(s):  
Quantum Information Processing ◽  
Weak Measurement ◽  
Entangled States ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Prepared State ◽  
Noisy Conditions ◽  
Partially Entangled States ◽  
Robust To Noise ◽  
Qubit States

AbstractIn this article, we revisit the question of analysing the efficiencies of partially entangled states in three-qubit classes under real conditions. Our results show some interesting observations regarding the efficiencies and correlations of partially entangled states. Surprisingly, we find that the efficiencies of many three-qubit partially entangled states exceed that of maximally entangled three-qubit states under real noisy conditions and applications of weak measurements. Our analysis, therefore, suggests that the efficiencies of partially entangled states are much more robust to noise than those of maximally entangled states at least for the GHZ (Greenberger–Horne–Zeilinger) class states, for certain protocols; i.e. less correlations in the initially prepared state may also lead to better efficiency and hence one need not always consider starting with a maximally entangled state with maximum correlations between the qubits. For a set of partially entangled states, we find that the efficiency is optimal, independent of the decoherence and state parameters, if the value of weak measurement parameter is very large. For other values of the weak measurement parameter, the robustness of the states depends on the decoherence and state parameters. Moreover, we further show that one can achieve higher efficiencies in a protocol by using non-optimal weak measurement strengths instead of optimal weak measurement strengths.

scholarly journals Strategies for Positive Partial Transpose (PPT) States in Quantum Metrologies with Noise

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 685
Author(s):  
Arunava Majumder ◽  
Harshank Shrotriya ◽  
Leong-Chuan Kwek
Keyword(s):  
Quantum States ◽  
Entangled States ◽  
Heisenberg Uncertainty Principle ◽  
Positive Partial Transpose ◽  
Partial Transpose ◽  
Heisenberg Uncertainty ◽  
Noise Limit ◽  
Entangled Quantum States ◽  
Standard Precision ◽  
Shot Noise Limit

Quantum metrology overcomes standard precision limits and has the potential to play a key role in quantum sensing. Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurements. Conventional bounds to the measurement precision such as the shot noise limit are not as fundamental as the Heisenberg limits, and can be beaten with quantum strategies that employ `quantum tricks’ such as squeezing and entanglement. Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered to be too weakly entangled for applications. Since no pure entanglement can be distilled from them, they are also called bound entangled states. We provide strategies, using which multipartite quantum states that have a positive partial transpose with respect to all bi-partitions of the particles can still outperform separable states in linear interferometers.

Concentration of entanglement in collective-rotating decoherence-free subspace

2020 ◽  
Vol 34 (05) ◽  
pp. 2050067
Author(s):  
Yan-Jie Zhang ◽  
Cai-Peng Shen ◽  
Zhi-Feng Pan ◽  
Ya Gao ◽  
Shi-Lei Su ◽  
...  
Keyword(s):  
Distinctive Feature ◽  
Kerr Nonlinearity ◽  
Entangled States ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Maximal Entanglement ◽  
Measurement Devices ◽  
Maximally Entangled States ◽  
Partially Entangled States ◽  
Decoherence Free Subspace

An entanglement concentration protocol in photonic collective-rotating decoherence-free subspace (CRDFS) is proposed. To accomplish the scheme, two methods to construct parity measurement devices in CRDFS are presented by exploiting the cross-Kerr nonlinearity, through which partially entangled states are converted to maximally entangled states. The performance of the protocol can be improved by iteration method. Fidelity in consideration of dissipation is discussed, which demonstrates good robustness. In contrast to the conventional protocols, the present one has distinctive feature since it can not only get maximally entangled state from less entangled state, but also maintain the maximal entanglement in collective-rotating noise environment.

scholarly journals Path identity as a source of high-dimensional entanglement

2020 ◽  
Vol 117 (42) ◽  
pp. 26118-26122
Author(s):  
Jaroslav Kysela ◽  
Manuel Erhard ◽  
Armin Hochrainer ◽  
Mario Krenn ◽  
Anton Zeilinger
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
General Scheme ◽  
Higher Dimensions ◽  
High Dimensional ◽  
Entangled States ◽  
Entangled State ◽  
Experimental Demonstration ◽  
Entanglement Generation ◽  
High Degree

We present an experimental demonstration of a general entanglement-generation framework, where the form of the entangled state is independent of the physical process used to produce the particles. It is the indistinguishability of multiple generation processes and the geometry of the setup that give rise to the entanglement. Such a framework, termed entanglement by path identity, exhibits a high degree of customizability. We employ one class of such geometries to build a modular source of photon pairs that are high-dimensionally entangled in their orbital angular momentum. We demonstrate the creation of three-dimensionally entangled states and show how to incrementally increase the dimensionality of entanglement. The generated states retain their quality even in higher dimensions. In addition, the design of our source allows for its generalization to various degrees of freedom and even for the implementation in integrated compact devices. The concept of entanglement by path identity itself is a general scheme and allows for construction of sources producing also customized states of multiple photons. We therefore expect that future quantum technologies and fundamental tests of nature in higher dimensions will benefit from this approach.

scholarly journals Surpassing the shot-noise limit by homodyne-mediated feedback

2016 ◽  
Vol 41 (17) ◽  
pp. 3932 ◽  
Author(s):  
Guofeng Zhang ◽  
Hanjie Zhu
Keyword(s):  
Shot Noise ◽  
Noise Limit ◽  
Shot Noise Limit

scholarly journals Overcoming detection loss and noise in squeezing-based optical sensing

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Gaetano Frascella ◽  
Sascha Agne ◽  
Farid Ya. Khalili ◽  
Maria V. Chekhova
Keyword(s):  
Shot Noise ◽  
Optical Sensing ◽  
Detection Efficiency ◽  
Signal To Noise Ratio ◽  
Real Life ◽  
Squeezed States ◽  
Squeezed Light ◽  
Noise Limit ◽  
Imaging And Spectroscopy ◽  
Shot Noise Limit

AbstractAmong the known resources of quantum metrology, one of the most practical and efficient is squeezing. Squeezed states of atoms and light improve the sensing of the phase, magnetic field, polarization, mechanical displacement. They promise to considerably increase signal-to-noise ratio in imaging and spectroscopy, and are already used in real-life gravitational-wave detectors. But despite being more robust than other states, they are still very fragile, which narrows the scope of their application. In particular, squeezed states are useless in measurements where the detection is inefficient or the noise is high. Here, we experimentally demonstrate a remedy against loss and noise: strong noiseless amplification before detection. This way, we achieve loss-tolerant operation of an interferometer fed with squeezed and coherent light. With only 50% detection efficiency and with noise exceeding the level of squeezed light more than 50 times, we overcome the shot-noise limit by 6 dB. Sub-shot-noise phase sensitivity survives up to 87% loss. Application of this technique to other types of optical sensing and imaging promises a full use of quantum resources in these fields.

The Construction and Simulation Analysis of Three-Qubit Hxx Chain Refrigerator Based on Quantum Entangled States

2013 ◽  
Vol 380-384 ◽  
pp. 4849-4855
Author(s):  
Xing Kui Huang
Keyword(s):  
Field Strength ◽  
Simulation Analysis ◽  
Heat Engine ◽  
State Theory ◽  
Entangled States ◽  
Entangled State ◽  
Working Process ◽  
Mapping Analysis ◽  
Quantum Entangled States ◽  
Working Efficiency

Quantum entangled state theory is combined with quantum thermodynamics theory to build quantum entangled state heat engine. The basic nature of three-qubit Hxx chain, and all parameters of the orbit are analyzed. Energy model of quantum entangled state refrigerator in working process is taken as as a theoretical basis to construct three qubits Hxx chain refrigerator based on quantum entangled states. The working nature of the new quantum entangled state refrigerator under different field strength is studied. Compaired with two-qubit Hxxx chain refrigerator based on quantum entangled states and mapping analysis, the working efficiency of three qubits Hxx chain refrigerator based on quantum entangled states is much higher when the field strength is not zero and its working state is more stable.

Optimization of Detectability in Laser-Based Polarimeters

1989 ◽  
Vol 43 (8) ◽  
pp. 1337-1341 ◽  
Author(s):  
Xiaobing Xi ◽  
Edward S. Yeung
Keyword(s):  
Shot Noise ◽  
Experimental Verification ◽  
High Frequency ◽  
Ohmic Heating ◽  
Unit Length ◽  
Power Input ◽  
Upper Limit ◽  
High Modulation ◽  
Noise Limit ◽  
Shot Noise Limit

To optimize the performance of a laser-based polarimeter, a mathematical simulation was performed. High-modulation currents allow a corresponding increase in signal. However, the effect of ohmic heating puts an upper limit on the power input to the solenoid. With this constraint, one can systematically choose the wire diameter and the number of turns per unit length. An experimental verification of the optimized parameters provided performance approaching the shot-noise limit. By using higher modulation currents, one can operate at 1 kHz to achieve detectability in the microdegree range, without the complications of high-frequency (100 kHz) modulation.

Infinitely entangled states

2003 ◽  
Vol 3 (4) ◽  
pp. 281-306
Author(s):  
M. Keyl ◽  
D. Schlingemann ◽  
R.F. Werner
Keyword(s):  
Hilbert Spaces ◽  
Degrees Of Freedom ◽  
Entangled States ◽  
Entangled State ◽  
Bounded Operators ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Density Operators ◽  
Fundamental Paper ◽  
Extended Notion

For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as a resource for tasks like the teleportation of arbitrarily many qubits. We show that appropriate states cannot be obtained by density operators in an infinite dimensional Hilbert space. However, using techniques for the description of infinitely many degrees of freedom from field theory and statistical mechanics, such states can nevertheless be constructed rigorously. We explore two related possibilities, namely an extended notion of algebras of observables, and the use of singular states on the algebra of bounded operators. As applications we construct the essentially unique infinite analogue of maximally entangled states, and the singular state used heuristically in the fundamental paper of Einstein, Rosen and Podolsky.

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