Strong entanglement criteria for mixed states, based on uncertainty relations

• URL: http://arxiv.org/abs/2210.16551v1
• Date: Sat, 29 Oct 2022 10:00:41 GMT
• Title: Strong entanglement criteria for mixed states, based on uncertainty relations
• Abstract summary: We show that any mixed entangled state can be characterized by our criterion. The proposed criterion reduces to the Schrodinger-Robertson inequality for pure states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner-Yanase skew information. The variances in this uncertainty relation does not involve any classical mixing uncertainty, and thus turns out to be purely of quantum mechanical nature. We show that any mixed entangled state can be characterized by our criterion. We demonstrate its utility for several generalized mixed entangled state including Werner states and it turns out to be stronger than any other known criterion in identifying the correct domain of relevant parameters for entanglement. The proposed criterion reduces to the Schrodinger-Robertson inequality for pure states.

Related papers

• Quantum state determinability from local marginals is universally robust [22.159831673341287]
  We show that deviations of local marginals propagate to global states strictly bounded by a power law with exponent $in(0,1]$.<n>We apply our theory to construct a scalable two-local genuine multipartite entanglement witness.
  arXiv  Detail & Related papers  (2026-04-07T07:02:22Z)
• Tighter entropic uncertainty relations in the presence of quantum memories for complete sets of mutually unbiased bases [25.094962102120178]
  We propose more stringent quantum-memory-assisted entropic uncertainty relations for complete sets of mutually unbiased bases in multipartite scenarios.<n>We present lower and upper bounds of the quantum uncertainties based on the complementarity of the observables, the purity of the measured state, the (conditional) von-Neumann entropies, the Holevo quantities and mutual information.
  arXiv  Detail & Related papers  (2026-04-05T06:23:10Z)
• Spin minimum uncertainty states for refined uncertainty relations [10.018030428478928]
  We investigate the minimum uncertainty states associated with an information-theoretic refinement of the Heisenberg uncertainty relation in general spin systems.<n>We show that spin coherent states indeed achieve minimum uncertainty, consistent with their conventional identification as the classical states of spin systems.<n>We also identify additional classes of minimum uncertainty states beyond the coherent family.
  arXiv  Detail & Related papers  (2025-12-19T07:45:06Z)
• Identifying the $3$-qubit $W$ state with quantum uncertainty relation [14.803730343784439]
  The $W$ state is a canonical representative of multipartite quantum entanglement.<n>This paper introduces a novel approach to identifying tripartite $W$ states by leveraging tripartite quantum uncertainty relations.
  arXiv  Detail & Related papers  (2025-11-20T14:59:48Z)
• Uncertainty Principle from Operator Asymmetry [0.0]
  We introduce a new class of uncertainty relations grounded in the resource theory of asymmetry.<n>This framework resolves a long-standing open problem in quantum information theory.<n>We demonstrate the practical power of our framework by deriving tighter quantum speed limits for the dynamics of nearly conserved quantities.
  arXiv  Detail & Related papers  (2025-09-08T14:50:32Z)
• Tight upper bound and monogamy relation for the maximum quantum value of the parity-CHSH inequality and applied to device-independent randomness [15.959534674111326]
  We derive the maximum quantum value of the parity-CHSH inequality for a three-qubit system.<n>We present necessary and sufficient conditions for certain states to violate the parity-CHSH inequality.
  arXiv  Detail & Related papers  (2025-04-18T02:58:59Z)
• Closer look at sum uncertainty relations and related relations [0.0]
  We analyze the weak and critical points of various uncertainty relations that follow from the inequalities for the norms of vectors in the Hilbert space of states of a quantum system. We show that there exists an upper bound on the product of standard deviations that appears in the Heisenberg-Robertson uncertainty relation.
  arXiv  Detail & Related papers  (2025-04-12T08:11:00Z)
• Experimental investigation of the uncertainty relation in pre- and postselected systems [28.111582622994597]
  Uncertainty principle is one of the fundamental principles of quantum mechanics. We experimentally investigate the Robertson-Heisenberg-type uncertainty relation for two incompatible observables in a PPS system.
  arXiv  Detail & Related papers  (2024-12-18T00:29:23Z)
• State-dependent and state-independent uncertainty relations for skew information and standard deviation [0.0]
  We derive uncertainty equality based on standard deviation for incompatible operators with mixed states. We show that for pure states, the Wigner-Yanase skew information based state-independent uncertainty relations become standard deviation based state-independent uncertainty relations.
  arXiv  Detail & Related papers  (2024-02-05T16:28:29Z)
• Hoeffding's Inequality for Markov Chains under Generalized Concentrability Condition [15.228649445346473]
  This paper studies Hoeffding's inequality for Markov chains under the generalized concentrability condition defined via integral probability metric (IPM) The flexibility of our framework allows Hoeffding's inequality to be applied beyond the ergodic Markov chains in the traditional sense.
  arXiv  Detail & Related papers  (2023-10-04T16:21:23Z)
• Unified Uncertainty Calibration [43.733911707842005]
  We introduce emphunified uncertainty calibration (U2C), a holistic framework to combine aleatoric and uncertainty uncertainties. U2C enables a clean learning-theoretical analysis of uncertainty estimation, and outperforms reject-or-classify across a variety of ImageNet benchmarks.
  arXiv  Detail & Related papers  (2023-10-02T13:42:36Z)
• Measurement incompatibility is strictly stronger than disturbance [44.99833362998488]
  Heisenberg argued that measurements irreversibly alter the state of the system on which they are acting, causing an irreducible disturbance on subsequent measurements. This article shows that measurement incompatibility is indeed a sufficient condition for irreversibility of measurement disturbance. However, we exhibit a toy theory, termed the minimal classical theory (MCT), that is a counterexample for the converse implication.
  arXiv  Detail & Related papers  (2023-05-26T13:47:00Z)
• Rosenthal-type inequalities for linear statistics of Markov chains [20.606986885851573]
  We establish novel deviation bounds for additive functionals of geometrically ergodic Markov chains. We pay special attention to the dependence of our bounds on the mixing time of the corresponding chain.
  arXiv  Detail & Related papers  (2023-03-10T10:24:46Z)
• Simulating Entanglement beyond Quantum Steering [15.808504285017948]
  We quantify the resource content of such states in terms of how much shared randomness is needed to simulate their behavior. We rigorously show that the shared randomness cost is unbounded even for some two-qubit unsteerable states.
  arXiv  Detail & Related papers  (2023-02-17T18:52:33Z)
• Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices [0.0]
  We present several inequalities related to the Robertson-Schr"odinger uncertainty relation. By considering a concave roof of the bound, we obtain an improvement of the Robertson-Schr"odinger uncertainty relation. We present further uncertainty relations that provide lower bounds on the metrological usefulness of bipartite quantum states.
  arXiv  Detail & Related papers  (2021-09-14T18:00:07Z)
• Experimental test of the majorization uncertainty relation with mixed states [6.613272059966484]
  The uncertainty relation lies at the heart of quantum theory and behaves as a non-classical constraint on the indeterminacies of incompatible observables in a system. In this work we test the novel majorization uncertainty relations of three incompatible observables using a series of mixed states with adjustable mixing degrees.
  arXiv  Detail & Related papers  (2021-04-07T01:18:32Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Estimating means of bounded random variables by betting [39.98103047898974]
  This paper derives confidence intervals (CI) and time-uniform confidence sequences (CS) for the classical problem of estimating an unknown mean from bounded observations. We present a general approach for deriving concentration bounds, that can be seen as a generalization and improvement of the celebrated Chernoff method. We show how to extend these ideas to sampling without replacement, another heavily studied problem.
  arXiv  Detail & Related papers  (2020-10-19T17:22:03Z)
• A Universal Formulation of Uncertainty Relation for Error and Disturbance [0.9479435599284545]
  We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement. Owing to its simplicity and operational tangibility, our general relation is also experimentally verifiable.
  arXiv  Detail & Related papers  (2020-04-13T17:57:41Z)
• Mean Value of the Quantum Potential and Uncertainty Relations [0.0]
  In this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. We derive a generalized uncertainty relation that is stronger than the Robertson-Schr"odinger inequality and hence also stronger than the Heisenberg uncertainty principle.
  arXiv  Detail & Related papers  (2020-02-04T19:25:01Z)

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.