State transformations within entanglement classes containing permutation-symmetric states

Abstract

The study of state transformations under local operations and classical communication (LOCC) plays a crucial role in entanglement theory. While this has been long ago characterized for pure bipartite states, the situation is drastically different for systems of more parties: generic pure qudit states cannot be obtained from nor transformed to any state (i.e., they are isolated), which contains a different amount of entanglement. We consider here the question of LOCC convertibility for permutation-symmetric pure states of an arbitrary number of parties and local dimension, a class of clear interest both for physical and mathematical reasons and for which the aforementioned result does not apply given that it is a zero-measure subset in the state space. While it turns out that generic $n$-qubit symmetric states are also isolated, we consider particular families for which we can determine to be, on the contrary, endowed with a rich local stabilizer, a necessary requirement for LOCC convertibility to be possible. This allows us to identify classes in which LOCC transformations among permutation-symmetric states are possible. Notwithstanding, we provide several results that indicate severe obstructions to LOCC convertibility in general even within these highly symmetrical classes. In the course of the study of LOCC transformations, we also characterize the local symmetries of symmetric states.

arXiv commentMinor updates in Lemma 6, the paragraph containing Eq. (63), and Sec. VIII A 2d. Added Appendix K. 38 pages, 1 figure

References in corpus (49)

• Quantum entanglement
• Three qubits can be entangled in two inequivalent ways
• Area laws for the entanglement entropy - a review
• Quantum Resource Theories
• 14-qubit entanglement: creation and coherence
• Conditions for a class of entanglement transformations
• Entanglement monotones
• Four qubits can be entangled in nine different ways
• 18-qubit entanglement with photon's three degrees of freedom
• 10-qubit entanglement and parallel logic operations with a superconducting circuit
• Entanglement of pure states for a single copy
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• Experimental realization of Dicke states of up to six qubits for multiparty quantum networking
• Experimental entanglement of a six-photon symmetric Dicke state
• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• The Uniqueness Theorem for Entanglement Measures
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Operational Families of Entanglement Classes for Symmetric $N$-Qubit States
• Experimental GHZ Entanglement beyond Qubits
• Entanglement and permutational symmetry
• The maximally entangled set of multipartite quantum states
• The geometric measure of entanglement for symmetric states
• The maximally entangled symmetric state in terms of the geometric measure
• N-particle N-level singlet states: Some properties and applications
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• Four-photon orbital angular momentum entanglement
• Transformations among Pure Multipartite Entangled States via Local Operations Are Almost Never Possible
• Entanglement Equivalence of $N$-qubit Symmetric States
• Almost all multipartite qubit quantum states have trivial stabilizer
• The Lorentz singular value decomposition and its applications to pure states of 3 qubits
• Entangled pure state transformations via local operations assisted by finitely many rounds of classical communication
• Subradiance and entanglement in atoms with several independent decay channels
• Entanglement manipulation of multipartite pure states with finite rounds of classical communication
• Necessary and sufficient conditions for local manipulation of multipartite pure quantum states
• The geometric measure of entanglement for a symmetric pure state with positive amplitudes
• The moduli space of three qutrit states
• Local Transformations Requiring Infinite Rounds of Classical Communication
• Barycentric measure of quantum entanglement
• Transformations of $W$-Type Entangled States
• Classification of Entanglement in Symmetric States
• Deterministic Transformations of Multipartite Entangled States with Tensor Rank 2
• The maximally entangled set of 4-qubit states
• Entanglement classes of permutation-symmetric qudit states: symmetric operations suffice
• The MES of tripartite qutrit states and pure state separable transformations which are not possible via LOCC
• Symmetries and entanglement of stabilizer states
• Matrix Product States: Entanglement, symmetries, and state transformations
• Measurement outcomes that do not occur and their role in entanglement transformations
• Local Transformations of Multiple Multipartite States
• Symmetries and local transformations of translationally invariant Matrix Product States

Cited by in corpus (6)

• Interconversion of $W$ and Greenberger-Horne-Zeilinger states for Ising-coupled qubits with transverse global control
• Transformations in quantum networks via local operations assisted by finitely many rounds of classical communication
• Identifying families of multipartite states with non-trivial local entanglement transformations
• Entanglement Classification via Single Entanglement Measure
• Detecting genuine multipartite entanglement in multi-qubit devices with restricted measurements
• Distributed variational quantum computing with deterministic entanglement tuning