Bounds on the smallest sets of quantum states with special quantum nonlocality

• URL: http://arxiv.org/abs/2202.09034v4
• Date: Thu, 31 Aug 2023 11:31:59 GMT
• Title: Bounds on the smallest sets of quantum states with special quantum nonlocality
• Authors: Mao-Sheng Li and Yan-Ling Wang
• Abstract summary: We find that in the case of two qubits systems locally stable sets are coincide with locally indistinguishable sets. We present a characterization of locally stable sets via the dimensions of some states depended spaces.
• Score: 2.1991772588394825
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: An orthogonal set of states in multipartite systems is called to be strong quantum nonlocality if it is locally irreducible under every bipartition of the subsystems \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.040403}{Phys. Rev. Lett. \textbf{122}, 040403 (2019)}]. In this work, we study a subclass of locally irreducible sets: the only possible orthogonality preserving measurement on each subsystems are trivial measurements. We call the set with this property is locally stable. We find that in the case of two qubits systems locally stable sets are coincide with locally indistinguishable sets. Then we present a characterization of locally stable sets via the dimensions of some states depended spaces. Moreover, we construct two orthogonal sets in general multipartite quantum systems which are locally stable under every bipartition of the subsystems. As a consequence, we obtain a lower bound and an upper bound on the size of the smallest set which is locally stable for each bipartition of the subsystems. Our results provide a complete answer to an open question (that is, can we show strong quantum nonlocality in $\mathbb{C}^{d_1} \otimes \mathbb{C}^{d_1}\otimes \cdots \otimes \mathbb{C}^{d_N} $ for any $d_i \geq 2$ and $1\leq i\leq N$?) raised in a recent paper [\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.022209}{Phys. Rev. A \textbf{105}, 022209 (2022)}]. Compared with all previous relevant proofs, our proof here is quite concise.

Related papers

• Strong quantum nonlocality without entanglement in every $(n-1)$-partition [0.0]
  Rigorous proofs show that these sets are locally irreducible in every $(n-1)-partition. Our results can also enhance one understanding for the nonlocality without entanglement.
  arXiv  Detail & Related papers  (2024-07-03T13:57:10Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Small-time controllability for the nonlinear Schr\"odinger equation on $\mathbb{R}^N$ via bilinear electromagnetic fields [55.2480439325792]
  We address the small-time controllability problem for a nonlinear Schr"odinger equation (NLS) on $mathbbRN$ in the presence of magnetic and electric external fields. In detail, we study when it is possible to control the dynamics of (NLS) as fast as desired via sufficiently large control signals.
  arXiv  Detail & Related papers  (2023-07-28T21:30:44Z)
• Locally stable sets with minimum cardinality [0.0]
  Li and Wang arXiv:2202.09034 proposed the concept of a locally stable set. We focus on the constructions of locally stable sets in multipartite quantum systems.
  arXiv  Detail & Related papers  (2023-07-17T09:00:12Z)
• Constructions of $k$-uniform states in heterogeneous systems [65.63939256159891]
  We present two general methods to construct $k$-uniform states in the heterogeneous systems for general $k$. We can produce many new $k$-uniform states such that the local dimension of each subsystem can be a prime power.
  arXiv  Detail & Related papers  (2023-05-22T06:58:16Z)
• Nonlocality under Computational Assumptions [51.020610614131186]
  A set of correlations is said to be nonlocal if it cannot be reproduced by spacelike-separated parties sharing randomness and performing local operations. We show that there exist (efficient) local producing measurements that cannot be reproduced through randomness and quantum-time computation.
  arXiv  Detail & Related papers  (2023-03-03T16:53:30Z)
• Strong quantum nonlocality without entanglement in $n$-partite system with even $n$ [0.0]
  We find general construction of strongly nonlocal product sets in space. We present a local entangled state discrimination protocol for our sets. As an application, we connect our sets with local information hiding in multipartite system.
  arXiv  Detail & Related papers  (2022-08-15T07:53:55Z)
• Orthogonal product sets with strong quantum nonlocality on plane structure [0.0]
  We construct a strongly nonlocal OPS in $mathcalCd_Aotimes mathcalCd_C$ $(d_A,B,Cgeq 4)$ and generalize the structures of known OPSs to any possible three and four-partite systems. It is shown that the protocols without teleportation use less entanglement resources on average and these sets can always be discriminated locally with multiple copies of 2-qubit maximally entangled states.
  arXiv  Detail & Related papers  (2022-05-22T13:07:16Z)
• Non-standard entanglement structure of local unitary self-dual models as a saturated situation of repeatability in general probabilistic theories [61.12008553173672]
  We show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry. We also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable.
  arXiv  Detail & Related papers  (2021-11-29T23:37:58Z)
• Scattering data and bound states of a squeezed double-layer structure [77.34726150561087]
  A structure composed of two parallel homogeneous layers is studied in the limit as their widths $l_j$ and $l_j$, and the distance between them $r$ shrinks to zero simultaneously. The existence of non-trivial bound states is proven in the squeezing limit, including the particular example of the squeezed potential in the form of the derivative of Dirac's delta function. The scenario how a single bound state survives in the squeezed system from a finite number of bound states in the finite system is described in detail.
  arXiv  Detail & Related papers  (2020-11-23T14:40:27Z)
• Nonlocality of tripartite orthogonal product states [0.0]
  We construct a locally indistinguishable subset in $mathbbC2dbigotimesmathbbC2dbigotimesmathbbC2d$. We generalize our method to arbitrary tripartite quantum systems. We prove that a three-qubit GHZ state is sufficient as a resource to distinguish each of the above classes of states.
  arXiv  Detail & Related papers  (2020-11-07T18:46:24Z)

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.