Every Rank-Two Entangled State is Projectively Steerable

• URL: http://arxiv.org/abs/2606.08189v1
• Date: Sat, 06 Jun 2026 14:20:05 GMT
• Title: Every Rank-Two Entangled State is Projectively Steerable
• Abstract summary: rank two is the first genuinely mixed rank at which entanglement and Einstein--Podolsky--Rosen steering could bifurcate.<n>We prove that every rank-two bipartite entangled state in arbitrary finite local dimensions is projectively steerable in at least one direction.
• Score: 5.478582839093083
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Pure entangled states are already steerable by suitable projective measurements within their Schmidt supports, whereas rank two is the first genuinely mixed rank at which entanglement and Einstein--Podolsky--Rosen steering could bifurcate. We prove that this bifurcation does not occur even under the restricted measurement class of projective measurements: every rank-two bipartite entangled state in arbitrary finite local dimensions is projectively steerable in at least one direction, and is two-way projectively steerable when the effective local dimensions are equal. The proof is a boundary theorem rather than a steering-inequality optimization or a two-qubit reduction. A dimension--rank obstruction forces a projective outcome on the larger effective party to hit a pure boundary point of the trusted state cone. At such a contact, a nonzero support--kernel tangent block is simultaneously an NPT minor and a projective-steering certificate; if the first contact is degenerate, the rank-two constraint closes that branch and forces a second, active contact. Thus the entire first mixed-state stratum is a complete projective-steering sector, and the same support--kernel geometry gives a practical low-rank certificate whenever the relevant boundary contact is nondegenerate.

Related papers

• CyclOT: Learning Quadratic Optimal Transport Maps via Synchronized Forward-Backward Interpolants [20.064386074670605]
  We introduce a bidirectional neural framework in which the learned maps induce forward and backward displacement interpolants.<n>Experiments on Swiss roll, MNIST, CelebA, single-cell data, and chest X-ray images evaluate endpoint fidelity, transport cost inverse, consistency, and the geometry of the induced inverts.
  arXiv  Detail & Related papers  (2026-09-12T11:31:53Z)
• Chiral Color Ice: Exact Local Handedness Constraints and Möbius Zero Modes in Frustrated Magnets [0.0]
  We show that handedness can be imposed as an exact local quantum constraint without selecting an axis in spin space.<n> Connecting the same local constraint in different ways produces qualitatively different collective regimes.<n>Results establish a tractable setting in which local handedness, nonlinear constraint geometry, and quantum degeneracy can be disentangled.
  arXiv  Detail & Related papers  (2026-08-31T13:54:02Z)
• Restricted Dynamic Geometric Complexity: Path-Space Reduction and Möbius--Jacobi Response [0.0]
  We study restricted dynamic geometric complexity as a path-space value problem.<n>The main response result is global on a Hadamard state space.
  arXiv  Detail & Related papers  (2026-07-08T09:36:45Z)
• Fundamental limits on state preparation for an open qubit [0.0]
  We analytically determine the ultimate limits of state preparation in two-level open quantum systems driven by coherent control.<n>For a dissipative qubit governed by a GKSL master equation, we give an exact characterization of the reachable set in the Bloch ball.
  arXiv  Detail & Related papers  (2026-07-05T14:09:53Z)
• Boundary Geometry Turns Entanglement into Steering [5.478582839093083]
  Quantum entanglement does not necessarily imply Einstein-Podolsky-Rosen steering.<n>We identify a emphboundary mechanism that closes this gap when an entangled state meets the boundary of the trusted state space.<n>We provide a filtered standard form, an explicit rank-three Cholesky parametrization, and a compact boundary certificate.
  arXiv  Detail & Related papers  (2026-05-20T14:33:16Z)
• A Measure-Theoretic Analysis of Reasoning: Structural Generalization and Approximation Limits [17.425526755350948]
  We project discrete trajectories into a metric space to quantify domain shifts.<n>Invoking Kantorovich duality, we bound OOD generalization via architectural Lipschitz continuity and functional approximation limits.
  arXiv  Detail & Related papers  (2026-05-19T15:00:51Z)
• Enabling Deterministic Passive Quantum State Transfer with Giant Atoms [30.634025315483466]
  Achieving quantum state transfer in passive ways can become a powerful asset for scalable quantum networks.<n>We show that giant atoms coupled to 1D waveguides provide a platform for such a passive, deterministic transfer.<n>Our results establish giant atoms as a powerful platform for realizing high-fidelity quantum state transfer in a setting without time-dependent control.
  arXiv  Detail & Related papers  (2026-05-12T12:06:28Z)
• Scale-Dependent Radial Geometry and Metric Mismatch in Wasserstein Propagation for Reverse Diffusion [20.064604732340037]
  We formalize a metric mismatch between the geometry that contracts early and the geometry in which the terminal error is measured.<n>We exploit this mismatch through an explicit radial lower profile for the learned reverse drift.<n>For discretizations of the learned reverse SDE under (L2) score-error control, we obtain explicit non-asymptotic end-to-end (Wtwo) guarantees.
  arXiv  Detail & Related papers  (2026-03-20T06:08:29Z)
• Strict area law entanglement versus chirality [19.441221681703468]
  Chirality is a gapped phase of matter in two spatial dimensions that can be manifested through non-zero thermal or electrical Hall conductance.<n>We prove two no-go theorems that forbid such chirality for a quantum state in a finite dimensional local Hilbert space with strict area law entanglement entropies.
  arXiv  Detail & Related papers  (2024-08-19T18:00:01Z)
• Witnessing network steerability of every bipartite entangled state without inputs [0.0]
  We consider quantum networks and focus on the swap-steering scenario without inputs. We find linear witnesses of network steerability corresponding to any negative partial transpose (NPT) bipartite state. We construct linear inequalities to witness swap-steerability of every bipartite entangled state.
  arXiv  Detail & Related papers  (2024-06-17T18:08:00Z)
• Generating magnon Bell states via parity measurement [0.0]
  We propose a scheme to entangle two magnon modes based on parity measurement. In particular, we consider a system that two yttrium-iron-garnet spheres are coupled to a $V$-type superconducting qutrit.
  arXiv  Detail & Related papers  (2024-01-22T04:36:39Z)
• Triggering Boundary Phase Transitions through Bulk Measurements in 2D Cluster States [20.295517930821084]
  We investigate the phase diagram at the boundary of an infinite two-dimensional cluster state subject to bulk measurements. Our results show that the boundary of the system exhibits volume-law entanglement at the measurement angle. These findings demonstrate that the phase diagram of the boundary of a two-dimensional system can be more intricate than that of a standard one-dimensional system.
  arXiv  Detail & Related papers  (2023-05-23T16:46:32Z)

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.