Partial Transpose Moments, Principal Minors and Entanglement Detection
arXiv:2305.08376 · doi:10.1007/s11128-023-03966-7
Abstract
Recently, it has been shown that locally randomized measurements can be employed to get partial transpose moments of a density matrix [Elben A., {\it et al.} Phys. Rev. Lett. {\bf 125}, 200501 (2020)]. Consequently, two general entanglement detection methods were proposed based on partial transpose moments of a density matrix [Yu X-D., {\it et al.} Phys. Rev. Lett. {\bf 127}, 060504 (2021)]. In this context, a natural question arises that how partial transpose moments are related with entanglement and with well known idea of principal minors. In this work, we analytically demonstrate that for qubit-qubit quantum systems, partial transpose moments can be expressed as simple functions of principal minors. We expect this relation to exist for every bipartite quantum systems. In addition, we have extended the idea of PT-moments for tripartite qubit systems and have shown that PT-moments can only detect the whole range of being NPT for and states mixed with white noise.
arXiv comment15 pages, no figures
References in corpus (43)
- Quantum entanglement
- Quantum Computing in the NISQ era and beyond
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Separability of Mixed States: Necessary and Sufficient Conditions
- Entanglement detection
- Quantum computational advantage using photons
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Strong quantum computational advantage using a superconducting quantum processor
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Unknown Quantum States and Operations, a Bayesian View
- Probing entanglement entropy via randomized measurements
- Advances in High Dimensional Quantum Entanglement
- From Classical to Quantum Shannon Theory
- Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
- Entanglement Certification From Theory to Experiment
- Taming multiparticle entanglement
- Separability criteria for genuine multiparticle entanglement
- Mixed-state entanglement from local randomized measurements
- Quantum walks on a programmable two-dimensional 62-qubit superconducting processor
- Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
- The power of random measurements: measuring Tr(ρ^n) on single copies of ρ
- Machine Learning Assisted Many-Body Entanglement Measurement
- Algebraic characterization of X-states in quantum information
- Single-copies estimation of entanglement negativity
- Testing the Structure of Multipartite Entanglement with Bell Inequalities
- Entanglement criteria for Dicke states
- Optimal Entanglement Certification from Moments of the Partial Transpose
- Characterizing multipartite entanglement with moments of random correlations
- Analytical characterization of the genuine multiparticle negativity
- Genuine multiparticle entanglement of permutationally invariant states
- Manipulating sudden death of entanglement of two-qubit X-states in thermal reservoirs
- Quantum entanglement from random measurements
- Bound entanglement from randomized measurements
- Multipartite Entanglement Analysis From Random Correlations
- Detecting multipartite entanglement structure with minimal resources
- Correlations between outcomes of random measurements
- Entanglement criteria and full separability of multi-qubit quantum states
- Entanglement characterization using quantum designs
- Statistically significant tests of multiparticle quantum correlations based on randomized measurements
- Quantum separability criteria based on realignment moments
- Entanglement breaking channels and entanglement sudden death
- A generic framework for genuine multipartite entanglement detection
Cited by in corpus (5)
- Genuine entanglement under squeezed generalized amplitude damping channels with memory
- A unifying separability criterion based on extended correlation tensor
- Detection of entanglement via moments of positive maps
- Detecting entanglement from few partial transpose moments and their decay via weight enumerators
- Sudden change of genuine multipartite entanglement in non-Markovian dynamics