A universal framework for entanglement detection under group symmetry
- URL: http://arxiv.org/abs/2301.03849v1
- Date: Tue, 10 Jan 2023 08:43:41 GMT
- Title: A universal framework for entanglement detection under group symmetry
- Authors: Sang-Jun Park, Yeong-Gwang Jung, Jeongeun Park, Sang-Gyun Youn
- Abstract summary: We prove that all $(overlinepi_Aotimes pi_B)$-invariant quantum states are separable if and only if all extremal unital positive $(pi_A,pi_B)$-covariant maps are decomposable.
$Phi(rho)=arho+brhoT+fracctextTr(rho)dtextId_d+ (1-a-b-c)textdiag(rho)
- Score: 1.384055225262046
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: One of the most fundamental questions in quantum information theory is
PPT-entanglement of quantum states, which is an NP-hard problem in general. In
this paper, however, we prove that all PPT $(\overline{\pi}_A\otimes
\pi_B)$-invariant quantum states are separable if and only if all extremal
unital positive $(\pi_A,\pi_B)$-covariant maps are decomposable where
$\pi_A,\pi_B$ are unitary representations of a compact group and $\pi_A$ is
irreducible. Moreover, an extremal unital positive $(\pi_B,\pi_A)$-covariant
map $\mathcal{L}$ is decomposable if and only if $\mathcal{L}$ is completely
positive or completely copositive. We apply the results to prove that all PPT
quantum channels of the form
$$\Phi(\rho)=a\rho+b\rho^T+\frac{c\text{Tr}(\rho)}{d}\text{Id}_d+(1-a-b-c)\text{diag}(\rho)$$
are entanglement-breaking, and that all A-BC PPT $(U\otimes \overline{U}\otimes
U)$-invariant tripartite quantum states are A-BC separable. The former resolves
some open questions raised in [DFV08, KMS20] and the latter is a strong
contrast to the fact that there exist PPT-entangled $(U\otimes U\otimes
U)$-invariant tripartite Werner states [EW01].
Related papers
- Coherence and imaginarity of quantum states [0.32634122554914]
In BCP framework, a quantum state is called incoherent if it is diagonal in the fixed orthonormal basis.
We show that any coherence measure $C$ in BCP framework has the property $C(rho )-C($Re$rho )geq 0$ if $C$ is in quantifying under state complex conjugation.
We also establish some similar results for bosonic Gaussian states.
arXiv Detail & Related papers (2024-04-09T10:58:27Z) - Dimension Independent Disentanglers from Unentanglement and Applications [55.86191108738564]
We construct a dimension-independent k-partite disentangler (like) channel from bipartite unentangled input.
We show that to capture NEXP, it suffices to have unentangled proofs of the form $| psi rangle = sqrta | sqrt1-a | psi_+ rangle where $| psi_+ rangle has non-negative amplitudes.
arXiv Detail & Related papers (2024-02-23T12:22:03Z) - Quantum connection, charges and virtual particles [65.268245109828]
A quantum bundle $L_hbar$ is endowed with a connection $A_hbar$ and its sections are standard wave functions $psi$ obeying the Schr"odinger equation.
We will lift the bundles $L_Cpm$ and connection $A_hbar$ on them to the relativistic phase space $T*R3,1$ and couple them to the Dirac spinor bundle describing both particles and antiparticles.
arXiv Detail & Related papers (2023-10-10T10:27:09Z) - Enlarging the notion of additivity of resource quantifiers [62.997667081978825]
Given a quantum state $varrho$ and a quantifier $cal E(varrho), it is a hard task to determine $cal E(varrhootimes N)$.
We show that the one shot distillable entanglement of certain spherically symmetric states can be quantitatively approximated by such an augmented additivity.
arXiv Detail & Related papers (2022-07-31T00:23:10Z) - Beyond the Berry Phase: Extrinsic Geometry of Quantum States [77.34726150561087]
We show how all properties of a quantum manifold of states are fully described by a gauge-invariant Bargmann.
We show how our results have immediate applications to the modern theory of polarization.
arXiv Detail & Related papers (2022-05-30T18:01:34Z) - Uncertainties in Quantum Measurements: A Quantum Tomography [52.77024349608834]
The observables associated with a quantum system $S$ form a non-commutative algebra $mathcal A_S$.
It is assumed that a density matrix $rho$ can be determined from the expectation values of observables.
Abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables.
arXiv Detail & Related papers (2021-12-14T16:29:53Z) - Emergent universality in critical quantum spin chains: entanglement
Virasoro algebra [1.9336815376402714]
Entanglement entropy and entanglement spectrum have been widely used to characterize quantum entanglement in extended many-body systems.
We show that the Schmidt vectors $|v_alpharangle$ display an emergent universal structure, corresponding to a realization of the Virasoro algebra of a boundary CFT.
arXiv Detail & Related papers (2020-09-23T21:22:51Z) - An Optimal Separation of Randomized and Quantum Query Complexity [67.19751155411075]
We prove that for every decision tree, the absolute values of the Fourier coefficients of a given order $ellsqrtbinomdell (1+log n)ell-1,$ sum to at most $cellsqrtbinomdell (1+log n)ell-1,$ where $n$ is the number of variables, $d$ is the tree depth, and $c>0$ is an absolute constant.
arXiv Detail & Related papers (2020-08-24T06:50:57Z) - Completing the quantum formalism in a contextually objective framework [0.0]
In standard quantum mechanics, a state vector $| psi rangle$ may belong to infinitely many different orthogonal bases.
In an idealized case, measuring $A$ again and again will give repeatedly the same result, with the same eigenvalue.
The answer is obviously no, since $| psi rangle$ does not specify the full observable $A$ that allowed us to obtain $mu$.
arXiv Detail & Related papers (2020-03-06T10:27:10Z)
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.