Quantum entanglement equation
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Quantum Entanglement Equation: Insights and Developments
Evolution Equation for Quantum Entanglement
Quantum entanglement is a cornerstone of quantum information technology, enabling phenomena such as quantum teleportation and dense coding. A significant challenge in this field is understanding how entanglement evolves over time, especially under the influence of environmental decoherence. Recent research has established a general factorization law for quantum systems shared by two parties, which describes the time evolution of entanglement when either component passes through a noisy channel. This factorization law simplifies the characterization of the robustness of entanglement-based protocols by focusing on a single quantity1.
Quantum Master Equation and Entanglement in Nanocavity Arrays
In the context of nanocavity arrays, quantum interference between linearly coupled modes with weak local nonlinearity can generate continuous variable entanglement. By solving the quantum master equation for the density matrix, researchers have demonstrated that this entanglement can survive realistic levels of pure dephasing. This mechanism provides a new paradigm for entanglement generation in arrays of coupled quantum modes2.
Dynamics of Quantum Entanglement
The dynamics of quantum entanglement in bipartite systems involve complex interactions between global unitary dynamics and local bistochastic or decaying channels. For initially pure states, the decay of entanglement is accompanied by an increase in von Neumann entropy. Interestingly, revivals of entanglement can occur due to unitary interactions between subsystems. Additionally, for mixed states with different marginal entropies, there is an observed asymmetry in the speed of entanglement decay, with faster decay occurring when the depolarizing channel acts on the subsystem with smaller marginal entropy4.
Real-Space Entanglement and Analytical Methods
A novel method has been introduced to analytically determine entanglement entropy and related quantities between configurations of a quantum field at distinct spatial locations. This approach models the system as a bipartite, continuous Gaussian system, allowing for explicit and exact formulas for entanglement entropy, mutual information, and quantum discord. This method contrasts with previous numerical studies and provides exact results for massless fields in flat space, showing that mutual information decays as the fourth power of the distance ratio at large distances5.
Continuous-Variable Quantum Networks
In continuous-variable quantum networks, entanglement dynamics can be mapped to a random-walk process on a graph, allowing for exact solutions. Squeezing is identified as the source of entanglement generation, leading to a diffusive spread of entanglement characterized by a "parabolic light cone." Despite the nonlinear nature of entanglement dynamics, a surprising linear superposition law in entanglement growth has been predicted and numerically verified. The equilibrium entanglement distribution, or Page curves, varies depending on the average squeezing density and strength6.
Variational Algorithms for Entanglement Detection and Quantification
In the Noisy Intermediate-Scale Quantum (NISQ) era, detecting and quantifying entanglement is crucial. Two variational quantum algorithms, Variational Entanglement Detection (VED) and Variational Logarithmic Negativity Estimation (VLNE), have been proposed. VED uses the positive map criterion and decomposes a positive map into quantum operations implementable on near-term devices, while VLNE estimates the logarithmic negativity entanglement measure. These methods have been validated through experimental and numerical results on various quantum states7.
Conclusion
The study of quantum entanglement equations and their dynamics is a rapidly evolving field with significant implications for quantum information technology. From the development of general factorization laws and quantum master equations to novel analytical methods and variational algorithms, researchers are making strides in understanding and harnessing this fundamental quantum resource. These advancements not only deepen our theoretical understanding but also pave the way for practical applications in quantum computing, communication, and beyond.
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Most relevant research papers on this topic
Evolution equation for quantum entanglement
This paper presents a simple factorization law for quantum systems shared by two parties, describing the time evolution of entanglement on passage of either component through an arbitrary noisy channel, improving the robustness of entanglement-based quantum information processing protocols.
Highly CitedQuantum entanglement in nanocavity arrays
Quantum entanglement can be generated in nanocavity arrays through weak local nonlinearity, surviving realistic levels of pure dephasing.
Entanglement: quantum or classical?
Entanglement is fundamentally different from classical phenomena, challenging classical hidden variables theories and revealing exciting manifestations like N00N states and non-separable single particle states.
Dynamics of quantum entanglement
Quantum entanglement decays with increasing von Neumann entropy in initially pure states, and can be revived by unitary interaction of subsystems.
Highly CitedReal-space entanglement of quantum fields
Our method allows for the analytical determination of entanglement entropy, mutual information, and quantum discord in quantum fields, with exact formulas for arbitrary distances.
Entanglement formation in continuous-variable random quantum networks
Squeezing is the source of entanglement generation in continuous-variable quantum networks, leading to a linear superposition law and various shapes of equilibrium entanglement distributions.
Detecting and quantifying entanglement on near-term quantum devices
Variational Entanglement Detection (VED) and Variational Logarithmic Negativity Estimation (VLNE) effectively detect and quantify entanglement on near-term quantum devices.
Quantum Entanglement
Quantum entanglement allows for new communication methods like quantum teleportation and dense coding, and is essential for quantum cryptographic protocols and algorithms.
Highly CitedAdvances in high-dimensional quantum entanglement
High-dimensional quantum entanglement advances enable future technologies like quantum teleportation and quantum internet, revolutionizing computation, communication, metrology, and imaging.
Highly CitedMeasuring entanglement entropy in a quantum many-body system
This study successfully measures entanglement in a quantum many-body system using quantum interference of many-body twins, enabling the study of quantum phases and dynamics in strongly correlated systems.
Rigorous JournalHighly Cited