Sequential sharing of two-qudit entanglement based on the entropic uncertainty relation

• URL: http://arxiv.org/abs/2304.05791v2
• Date: Mon, 24 Jul 2023 12:57:19 GMT
• Title: Sequential sharing of two-qudit entanglement based on the entropic uncertainty relation
• Authors: Ming-Liang Hu, Heng Fan
• Abstract summary: Entanglement and uncertainty relation are two focuses of quantum theory. We relate entanglement sharing to the entropic uncertainty relation in a $(dtimes d)$-dimensional system via weak measurements with different pointers.
• Score: 15.907303576427644
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Entanglement and uncertainty relation are two focuses of quantum theory. We relate entanglement sharing to the entropic uncertainty relation in a $(d\times d)$-dimensional system via weak measurements with different pointers. We consider both the scenarios of one-sided sequential measurements in which the entangled pair is distributed to multiple Alices and one Bob and two-sided sequential measurements in which the entangled pair is distributed to multiple Alices and Bobs. It is found that the maximum number of observers sharing the entanglement strongly depends on the measurement scenarios, the pointer states of the apparatus, and the local dimension $d$ of each subsystem, while the required minimum measurement precision to achieve entanglement sharing decreases to its asymptotic value with the increase of $d$. The maximum number of observers remain unaltered even when the state is not maximally entangled but has strong-enough entanglement.

Related papers

• Entropic uncertainty relations with quantum memory in a multipartite scenario [2.1320960069210484]
  We propose two complementary multipartite quantum-memory-assisted entropic uncertainty relations. Our lower bounds depend on values of complementarity of the observables,conditional von-Neumann entropies, Holevo quantities, and mutual information.
  arXiv  Detail & Related papers  (2023-07-25T01:42:15Z)
• Entropic Uncertainty for Biased Measurements [1.827510863075184]
  We derive a new entropic uncertainty relation for certain quantum states and for instances where the two measurement bases are no longer mutually unbiased. We show that our new bound can produce higher key-rates under several scenarios when compared with prior work using standard entropic uncertainty relations.
  arXiv  Detail & Related papers  (2023-05-16T19:01:16Z)
• Observing super-quantum correlations across the exceptional point in a single, two-level trapped ion [48.7576911714538]
  In two-level quantum systems - qubits - unitary dynamics theoretically limit these quantum correlations to $2qrt2$ or 1.5 respectively. Here, using a dissipative, trapped $40$Ca$+$ ion governed by a two-level, non-Hermitian Hamiltonian, we observe correlation values up to 1.703(4) for the Leggett-Garg parameter $K_3$. These excesses occur across the exceptional point of the parity-time symmetric Hamiltonian responsible for the qubit's non-unitary, coherent dynamics.
  arXiv  Detail & Related papers  (2023-04-24T19:44:41Z)
• Evolution of many-body systems under ancilla quantum measurements [58.720142291102135]
  We study the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom. We find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models.
  arXiv  Detail & Related papers  (2023-03-13T13:06:40Z)
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware [62.997667081978825]
  We observe partial and infinite-temperature thermalization on a quantum superconducting processor. We show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis.
  arXiv  Detail & Related papers  (2022-11-14T15:18:11Z)
• Multipartite entanglement detection based on generalized state-dependent entropic uncertainty relation for multiple measurements [15.907303576427644]
  We present the generalized state-dependent entropic uncertainty relations for multiple measurement settings. We give the experimentally accessible lower bounds on both bipartite and tripartite entanglements.
  arXiv  Detail & Related papers  (2022-11-02T06:26:07Z)
• High-dimensional entanglement certification: bounding relative entropy of entanglement in $2d+1$ experiment-friendly measurements [77.34726150561087]
  Entanglement -- the coherent correlations between parties in a quantum system -- is well-understood and quantifiable. Despite the utility of such systems, methods for quantifying high-dimensional entanglement are more limited and experimentally challenging. We present a novel certification method whose measurement requirements scale linearly with dimension subsystem.
  arXiv  Detail & Related papers  (2022-10-19T16:52:21Z)
• Simultaneous Transport Evolution for Minimax Equilibria on Measures [48.82838283786807]
  Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling. In this work we focus instead in finding mixed equilibria, and consider the associated lifted problem in the space of probability measures. By adding entropic regularization, our main result establishes global convergence towards the global equilibrium.
  arXiv  Detail & Related papers  (2022-02-14T02:23:16Z)
• Limits on sequential sharing of nonlocal advantage of quantum coherence [13.46516066673]
  We show how many observers can share the nonlocal advantage of quantum coherence (NAQC) in a $(dtimes d)$-dimensional state. Results may shed light on the interplay between nonlocal correlations and quantum measurements on high-dimensional systems.
  arXiv  Detail & Related papers  (2022-01-31T07:08:13Z)
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification [56.61325554836984]
  The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. We derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance.
  arXiv  Detail & Related papers  (2021-11-01T16:35:41Z)
• Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts [0.0]
  In a $d$ dimensional system and two mutually unbiased measurements, the sum of two information entropies is lower bounded by $ln d$. It has recently been shown that projective measurements subject to operational mutual unbiasedness can also be constructed in a continuous domain. Here we consider the whole family of R'enyi entropies applied to these discretized observables and prove that such a scheme does also admit the uncertainty relation mentioned above.
  arXiv  Detail & Related papers  (2021-07-26T18:48:26Z)

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.