Universal separability criterion for arbitrary density matrices from
causal properties of separable and entangled quantum states
- URL: http://arxiv.org/abs/2012.09428v2
- Date: Wed, 7 Jul 2021 09:18:59 GMT
- Title: Universal separability criterion for arbitrary density matrices from
causal properties of separable and entangled quantum states
- Authors: Gleb A. Skorobagatko
- Abstract summary: General physical background of Peres-Horodecki positive partial transpose (ppt-) separability criterion is revealed.
C causal separability criterion has been proposed for arbitrary $ DN times DN$ density matrices acting in $ mathcalH_Dotimes N $ Hilbert spaces.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: General physical background of Peres-Horodecki positive partial transpose
(ppt-) separability criterion is revealed. Especially, the physical sense of
partial transpose operation is shown to be equivalent to the "local causality
reversal" (LCR-) procedure for all separable quantum systems or to the
uncertainty in a global time arrow direction in all entangled cases. Using
these universal causal considerations the heuristic causal separability
criterion has been proposed for arbitrary $ D^{N} \times D^{N}$ density
matrices acting in $ \mathcal{H}_{D}^{\otimes N} $ Hilbert spaces which
describe the ensembles of $ N $ quantum systems of $ D $ eigenstates each.
Resulting general formulas have been then analyzed for the widest special type
of one-parametric density matrices of arbitrary dimensionality, which model
equivalent quantum subsystems being equally connected (EC-) with each other by
means of a single entnaglement parameter $ p $. In particular, for the family
of such EC-density matrices it has been found that there exists a number of $ N
$- and $ D $-dependent separability (or entanglement) thresholds $ p_{th}(N,D)
$ which in the case of a qubit-pair density matrix in $ \mathcal{H}_{2} \otimes
\mathcal{H}_{2} $ Hilbert space are shown to reduce to well-known results
obtained earlier by Peres [5] and Horodecki [6]. As the result, a number of
remarkable features of the entanglement thresholds for EC-density matrices has
been described for the first time. All novel results being obtained for the
family of arbitrary EC-density matrices are shown to be applicable for a wide
range of both interacting and non-interacting multi-partite quantum systems,
such as arrays of qubits, spin chains, ensembles of quantum oscillators,
strongly correlated quantum many-body systems with the possibility of many-body
localization, etc.
Related papers
- Quantum Chaos on Edge [36.136619420474766]
We identify two different classes: the near edge physics of sparse'' and the near edge of dense'' chaotic systems.
The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension.
While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different.
arXiv Detail & Related papers (2024-03-20T11:31:51Z) - Krylov complexity of density matrix operators [0.0]
Krylov-based measures such as Krylov complexity ($C_K$) and Spread complexity ($C_S$) are gaining prominence.
We investigate their interplay by considering the complexity of states represented by density matrix operators.
arXiv Detail & Related papers (2024-02-14T19:01:02Z) - Covariance-based method for eigenstate factorization and generalized singlets [0.0]
We derive a general method for determining the necessary and sufficient conditions for exact factorization $|Psirangle=otimes_p |psi_prangle$ of an eigenstate of a many-body Hamiltonian $H$.
The formalism is then used to derive exact dimerization and clusterization conditions in spin systems.
arXiv Detail & Related papers (2023-11-08T01:43:33Z) - Quantum tomography of helicity states for general scattering processes [55.2480439325792]
Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics.
We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
arXiv Detail & Related papers (2023-10-16T21:23:42Z) - Renormalization group and spectra of the generalized P\"oschl-Teller
potential [0.0]
We study the P"oschl-Teller potential $V(x) = alpha2 g_s sinh-2(alpha x) + alpha2 g_c cosh-2(alpha x)$, for every value of the dimensionless parameters $g_s$ and $g_c singularity.
We show that supersymmetry of the potential, when present, is also spontaneously broken, along with conformal symmetry.
arXiv Detail & Related papers (2023-08-08T21:44:55Z) - Vectorization of the density matrix and quantum simulation of the von
Neumann equation of time-dependent Hamiltonians [65.268245109828]
We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations.
We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix.
A quantum algorithm to simulate the dynamics of the density matrix is proposed.
arXiv Detail & Related papers (2023-06-14T23:08:51Z) - Annihilating Entanglement Between Cones [77.34726150561087]
We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied.
Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
arXiv Detail & Related papers (2021-10-22T15:02:39Z) - Reachable sets for two-level open quantum systems driven by coherent and
incoherent controls [77.34726150561087]
We study controllability in the set of all density matrices for a two-level open quantum system driven by coherent and incoherent controls.
For two coherent controls, the system is shown to be completely controllable in the set of all density matrices.
arXiv Detail & Related papers (2021-09-09T16:14:23Z) - Quantum interpolating ensemble: Biorthogonal polynomials and average
entropies [3.8265321702445267]
The average of quantum purity and von Neumann entropy for an ensemble interpolates between the Hilbert-Schmidt and Bures-Hall ensembles.
The proposed interpolating ensemble is a specialization of the $theta$-deformed Cauchy-Laguerre two-matrix model.
arXiv Detail & Related papers (2021-03-07T01:56:08Z) - Complete entropic inequalities for quantum Markov chains [17.21921346541951]
We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality.
We also establish the first general approximateization property of relative entropy.
arXiv Detail & Related papers (2021-02-08T11:47:37Z) - SU$(3)_1$ Chiral Spin Liquid on the Square Lattice: a View from
Symmetric PEPS [55.41644538483948]
Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projectedangled Pair States (PEPS)
Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder.
Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence.
arXiv Detail & Related papers (2019-12-31T16:30:25Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.