One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

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The classical-quantum boundary for correlations: Discord and related measures

Physics 1 Mr. Bigler Conservation of Momentum Unit: Momentum MA Curriculum Frameworks (2016): HS-PS2-2 MA Curriculum Frameworks (2006): 2.5 Mastery Objective(s): (Students will be able to...)  Solve problems involving collisions in which momentum is conserved, with or without an external impulse. Success Criteria:  Masses and velocities are correctly identified for each object, both before and after the collision.  Variables are correctly identified and substituted correctly into the correct part of the equation.  Algebra is correct and rounding to appropriate number of significant figures is reasonable. Tier 2 Vocabulary: momentum, collision Language Objectives:  Explain what happens before, during, and after a collision from the point of view of one of the objects participating in the collision.

Physics I.1

Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced performance of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations in composite states. We focus on various approaches to define and quantify general quantum correlations, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role.

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Measures and applications of quantum correlations

We review concepts and methods associated with quantum discord and related topics. We also describe their possible connections with other aspects of quantum information and beyond, including quantum communication, quantum computation, many-body physics, and open quantum dynamics. Quantum discord in the multiparty regime and its applications are also discussed.

/pdf/quantum-discord-and-its-allies-a-review-of-recent-progress-351wvpgsuq.pdf

Quantum discord and its allies: a review of recent progress.

In the system with superconducting quantum interference devices (SQUIDs) in a cavity, we propose a scheme for simultaneous implementing n phase gates and one step preparing the highly entangled cluster states based on the two-channel Raman interaction. In our scheme, the system is independent to the photon number of the cavity field, the cavity field can be initially in an arbitrary state, which is convenient for the experimental operation. The n phase gates operation and the cluster state generation are realized by using only the two lower flux states of the SQUID and the excited state would not be excited so that the influence of the decoherence due to spontaneous emission of the SQUID’s levels is possible to minimize. More importantly, the operation time of the phase gates is independent of the number n of the qubits. Finally, the experimental feasibility is also discussed in detail.

Scheme for n phase gates operation and one-step preparation of highly entangled cluster state

We propose two schemes for the generation of cluster states. One is based on cavity quantum electrodynamics (QED) techniques. The scheme only requires resonant interactions between two atoms and a single-mode cavity. The interaction time is very short, which is important in view of decoherence. Furthermore, we also discuss the cavity decay and atomic spontaneous emission case. The other is based on atomic ensembles. The scheme has an inherent fault tolerance function and is robust to realistic noise and imperfections. All the facilities used in our schemes are well within the current technology.

https://arxiv.org/pdf/quant-ph/0511138.pdf

Generation of cluster states

A scheme for teleporting an unknown two-particle entangled state via W class states is proposed. In this scheme, the W class entangled states are considered as quantum channels. It is shown that by means of optimal discrimination between two nonorthogonal quantum states, probabilistic teleportation of the two-particle entangled state can be achieved.

Teleportation of a two-particle entangled state via W class states

An entanglement concentration scheme for unknown atomic entanglement states is proposed via entanglement swapping in cavity QED. Because the interaction used here is a large-detuned one between two driven atoms and a quantized cavity mode, the effects of the cavity decay and thermal field have been eliminated. These advantages can warrant the experimental feasibility of the current scheme.

https://arxiv.org/pdf/quant-ph/0411157.pdf

Entanglement concentration for unknown atomic entangled states via entanglement swapping

The thermal entanglement is investigated in a two-qubit Heisenberg XXZ system with Dzyaloshinskii–Moriya (DM) interaction. It is shown that the entanglement can be efficiently controlled by the DM interaction parameter and coupling coefficient Jz. Dx (the x-component parameter of the DM interaction) has a more remarkable influence on the entanglement and the critical temperature than Dz (the z-component parameter of the DM interaction). Thus, by changing the DM interaction direction, we can get a more efficient control parameter to increase the entanglement and the critical temperature.

http://iopscience.iop.org/article/10.1088/0953-8984/20/32/325229/pdf

Thermal entanglement in the anisotropic Heisenberg XXZ model with the Dzyaloshinskii–Moriya interaction

In this paper, we propose two physical schemes, which can teleport unknown atomic state from user A (Alice) to user B (Bob) using the W class state as quantum channel. The two schemes are all based on Cavity QED techniques. The fidelity of the teleported state in the two schemes is equal to 1.0, and the successful probability of the schemes is decided by the smaller superposition coefficient of the state used as quantum channel. Each of the schemes has its own advantages.

Zhuo-Liang Cao

Papers

Generation of cluster states

Teleportation of a two-particle entangled state via W class states

Entanglement concentration for unknown atomic entangled states via entanglement swapping

Thermal entanglement in the anisotropic Heisenberg XXZ model with the Dzyaloshinskii–Moriya interaction

Probabilistic teleportation of unknown atomic state using W class states