Related papers: Krylov complexity of purification
Two classically equivalent expressions of mutual information of probability distributions (classical bipartite states) diverge when extended to quantum systems, and this difference has been employed to define quantum discord, a quantifier…
Characterizing and quantifying quantum correlations in states of many-particle systems is at the core of a full understanding of phase transitions in matter. In this work, we continue our investigation of the notion of generalized…
We initiate an investigation into a notion of state complexity for discrete-variable quantum systems. Specifically, we propose an information-theoretic quantifier for the complexity of quantum states within the stabilizer formalism of…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random…
We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the…
Krylov complexity, as a novel measure of operator complexity under Heisenberg evolution, exhibits many interesting universal behaviors and also bounds many other complexity measures. In this work, we study Krylov complexity $\mathcal{K}(t)$…
Entanglement is a unique nature of quantum theory and has tremendous potential for application. Nevertheless, the complexity of quantum entanglement grows exponentially with an increase in the number of entangled particles. Here we…
It is not a general opinion that that a quantum system could be purified into a target eigenstate via repeated measurements on a coupled qubit rather than direct transitions in the Hamiltonian. The projective measurement on the ancillary…
Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…
Many quantum gravitational frameworks, such as DBI inflation, k-essence, and effective field theories obtained by integrating out heavy modes, can lead to a non-trivial sound speed. Meanwhile, our universe can be described as an open…
We study holographic subregion complexity, and its possible connection to purification complexity suggested recently by Ag\'on et al. In particular, we study the conjecture that subregion complexity is the purification complexity by…
We consider unitary evolution of finite bipartite quantum systems and study time dependence of purity for initial cat states -- coherent superpositions of Gaussian wave-packets. We derive explicit formula for purity in systems with nonzero…
We propose a nonlinear Schr\"odinger equation in a Hilbert space enlarged with an ancilla such that the partial trace of its solution obeys to the Lindblad equation of an open quantum system. The dynamics involved by this nonlinear…
In this work we study how entanglement of purification (EoP) and the new quantity of "complexity of purification" are related to each other using the $E_P=E_W$ conjecture. First, we consider two strips in the same side of a boundary and…
Summary. A simple derivation of finite Schmidt decomposition of pure states describing finite dimensional systems interacting with the infinite dimensional ones is presented. In particular, maximally entangled pure states in such systems…
In this work we generalize the entanglement of purification and its conjectured holographic dual to conditional and multipartite versions of the same, where the optimization defining the entanglement of purification is now optimized in…
Quantum reservoir computing algorithms recently emerged as a standout approach in the development of successful methods for the NISQ era, because of its superb performance and compatibility with current quantum devices. By harnessing the…
We present a theoretical framework based on second quantization in Liouville space to treat open quantum systems. We consider an ensemble of identical quantum emitters characterized by a discrete set of quantum states. The second…
Complexity will be more and more essential in high-energy physics. It is naturally extended into the very early universe. Considering the universe as a quantum chaotic system, the curvature perturbation of the scalar field is identified…