Fully undistillable quantum states are separable

• URL: http://arxiv.org/abs/2207.05193v4
• Date: Wed, 23 Oct 2024 13:57:17 GMT
• Title: Fully undistillable quantum states are separable
• Authors: Satvik Singh, Nilanjana Datta,
• Abstract summary: We prove that Alice cannot distill entanglement with either Bob or Charlie using $|psi_ABCrangle$. We show that even though not all low rank states are 1-way distillable, a randomly sampled low rank state will almost surely be 1-way distillable.
• Score: 9.054540533394926
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Assume that Alice, Bob, and Charlie share a tripartite pure state $|\psi_{ABC}\rangle$. We prove that if Alice cannot distill entanglement with either Bob or Charlie using $|\psi_{ABC}\rangle$ and local operations with any one of the following configurations for classical communication: $(A\to B, A\leftrightarrow C), (A\leftrightarrow B, A\to C),$ and $(A\leftrightarrow B, A\leftrightarrow C)$, then the same is also true for the other two configurations. Moreover, this happens precisely when the state is such that both its reductions on systems $AB$ and $AC$ are separable, which is further equivalent to the reductions being PPT. This, in particular, implies that any NPT bipartite state is such that either the state itself or its complement is 2-way distillable. To prove these results, we first obtain an explicit lower bound on the 2-way distillable entanglement of low rank bipartite states. Furthermore, we show that even though not all low rank states are 1-way distillable, a randomly sampled low rank state will almost surely be 1-way distillable.

Related papers

• Tripartite Haar random state has no bipartite entanglement [2.8271134123622064]
  We show that no EPR-like bipartite entanglement can be distilled from a tripartite Haar random state. We derive an upper bound on the probability of sampling a state with EPR-like entanglement at a given EPR fidelity tolerance.
  arXiv  Detail & Related papers  (2025-02-06T19:00:01Z)
• 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)
• One-half reflected entropy is not a lower bound for entanglement of purification [6.578021055948705]
  We prove that the entanglement of purification $E_p(A:B)$ is bounded below by half of the $q$-R'enyi reflected entropy $S_R(q)(A:B)$ for all $qgeq2$. This result does not preclude the possibility that restricted sets of states, such as CFT states with semi-classical gravity duals, could obey the bound in question.
  arXiv  Detail & Related papers  (2023-09-05T18:00:13Z)
• 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)
• Entanglement distillation in terms of Schmidt rank and matrix rank [7.238541917115604]
  We distill non-positive-partial-transpose (NPT) bipartite states of some given Schmidt rank and matrix rank. We show that all bipartite states of Schmidt rank two are locally equivalent to classical-classical states, and all bipartite states of Schmidt rank three are 1-undistillable.
  arXiv  Detail & Related papers  (2023-04-12T01:50:21Z)
• Layered State Discovery for Incremental Autonomous Exploration [106.37656068276901]
  Layered Autonomous Exploration (LAE) is a novel algorithm for AX that attains a sample complexity of $tildemathcalO(LSrightarrow_LAln12(Srightarrow_LAln12(Srightarrow_LAln12(Srightarrow_LAln12(Srightar row_LAln12(Srightarrow_LAln12
  arXiv  Detail & Related papers  (2023-02-07T22:58:12Z)
• Entangled state distillation from single copy mixed states beyond LOCC [0.0]
  No pure entangled state can be distilled from a $2otimes 2$ or $2otimes 3$ mixed state by separable operations. In $3otimes 3$, pure entanglement can be distilled by separable operation but not by LOCC.
  arXiv  Detail & Related papers  (2022-12-20T21:46:46Z)
• Sequential Analysis of a finite number of Coherent states [0.0]
  We investigate an advantage for information processing of ordering a set of states over making a global quantum processing with a fixed number of copies of coherent states. We find that for the symmetric case $|gammarangle,|-gammarangle$ there is no advantage of taking any batch size $l$.
  arXiv  Detail & Related papers  (2022-06-09T16:50:34Z)
• Multi-Party Quantum Purity Distillation with Bounded Classical Communication [8.594140167290098]
  We consider the task of distilling local purity from a noisy quantum state $rhoABC$. We provide a protocol for three parties, Alice, Bob and Charlie, to distill local purity from many independent copies of a given quantum state $rhoABC$.
  arXiv  Detail & Related papers  (2022-03-10T18:04:33Z)
• Nearly Horizon-Free Offline Reinforcement Learning [97.36751930393245]
  We revisit offline reinforcement learning on episodic time-homogeneous Markov Decision Processes with $S$ states, $A$ actions and planning horizon $H$. We obtain the first set of nearly $H$-free sample complexity bounds for evaluation and planning using the empirical MDPs.
  arXiv  Detail & Related papers  (2021-03-25T18:52:17Z)
• 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)
• Tight Quantum Lower Bound for Approximate Counting with Quantum States [49.6558487240078]
  We prove tight lower bounds for the following variant of the counting problem considered by Aaronson, Kothari, Kretschmer, and Thaler ( 2020) The task is to distinguish whether an input set $xsubseteq [n]$ has size either $k$ or $k'=(1+varepsilon)k$.
  arXiv  Detail & Related papers  (2020-02-17T10:53:50Z)

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.