Contextuality with Pauli observables in cycle scenarios

• URL: http://arxiv.org/abs/2502.03451v1
• Date: Wed, 05 Feb 2025 18:51:32 GMT
• Title: Contextuality with Pauli observables in cycle scenarios
• Authors: Raman Choudhary, Rui Soares Barbosa,
• Abstract summary: Contextuality is a fundamental marker of quantum non-classicality. We focus on cycle measurement scenarios, the simplest scenarios capable of exhibiting contextual behaviour.
• Score: 0.0
• License:
• Abstract: Contextuality is a fundamental marker of quantum non-classicality, which has emerged as a key resource for quantum computational advantage in multiple settings. Many such results hinge specifically on contextuality witnessed through Pauli measurements. In this work, we initiate a systematic study of (state-dependent) Pauli contextuality, focusing on cycle measurement scenarios, the simplest scenarios capable of exhibiting contextual behaviour. First, we study realizability of cycle scenarios with multi-qubit Pauli observables: we show that the maximum size of a cycle faithfully realizable by $m$-qubit Paulis is upper bounded by $3m$, while we construct explicit realizations of cycles of size $2m-1$ or $2m$, depending on whether $m \not\equiv 1 \pmod{3}$ or $m \equiv 1 \pmod{3}$. Then, we investigate the presence of contextuality: we prove that no $n$-cycle Pauli realization for $n > 4$ can witness contextuality (on any quantum state), whereas for $n = 4$ every Pauli realization exhibits contextuality, attaining the quantum bound for all noncontextuality inequalities on some pure state. Finally, we discuss arbitrary Pauli scenarios in light of Vorob'ev's theorem, and show that, contrary to what our cycle characterization might suggest, the presence of $4$-cycles is not necessary for witnessing contextuality in general Pauli scenarios.

Related papers

• Coherence in Property Testing: Quantum-Classical Collapses and Separations [42.44394412033434]
  We show that no tester can distinguish subset states of size $2n/8$ from $2n/4$ with probability better than $2-Theta(n)$. We also show connections to disentangler and quantum-to-quantum transformation lower bounds.
  arXiv  Detail & Related papers  (2024-11-06T19:52:15Z)
• Optimal tradeoffs for estimating Pauli observables [13.070874080455862]
  We revisit the problem of Pauli shadow tomography: given copies of an unknown $n$-qubit quantum state $rho$, estimate $texttr(Prho)$ for some set of Pauli operators $P$ to within additive error $epsilon$. We show any protocol that makes $textpoly(n)$-copy measurements must make $Omega (1/epsilon4)$ measurements. The protocols we propose can also estimate the actual values $texttr(Prho)$, rather than just their absolute values
  arXiv  Detail & Related papers  (2024-04-29T20:57:05Z)
• The Power of Unentangled Quantum Proofs with Non-negative Amplitudes [55.90795112399611]
  We study the power of unentangled quantum proofs with non-negative amplitudes, a class which we denote $textQMA+(2)$. In particular, we design global protocols for small set expansion, unique games, and PCP verification. We show that QMA(2) is equal to $textQMA+(2)$ provided the gap of the latter is a sufficiently large constant.
  arXiv  Detail & Related papers  (2024-02-29T01:35:46Z)
• Tight bounds on Pauli channel learning without entanglement [2.2845597309741157]
  We consider learning algorithms without entanglement to be those that only utilize states, measurements, and operations that are separable between the main system of interest and an ancillary system. We show that these algorithms are equivalent to those that apply quantum circuits on the main system interleaved with mid-circuit measurements and classical feedforward.
  arXiv  Detail & Related papers  (2023-09-23T19:12:29Z)
• Beyond the mixture of generalized Pauli dephasing channels [3.4521402245831583]
  We show that non-invertibility of mixed channels is not a prerequisite for the resulting mapping to constitute a Markovian semigroup. We demonstrate that every Pauli channel can be represented as a mixture of $(d+1)$ Pauli dephasing channels, but this generalization doesn't apply to higher dimensions.
  arXiv  Detail & Related papers  (2023-09-10T00:50:38Z)
• Context-lumpable stochastic bandits [49.024050919419366]
  We consider a contextual bandit problem with $S$ contexts and $K$ actions. We give an algorithm that outputs an $epsilon$-optimal policy after using at most $widetilde O(r (S +K )/epsilon2)$ samples. In the regret setting, we give an algorithm whose cumulative regret up to time $T$ is bounded by $widetilde O(sqrtr3(S+K)T)$.
  arXiv  Detail & Related papers  (2023-06-22T17:20:30Z)
• Classical shadows based on locally-entangled measurements [0.03922370499388702]
  We study classical shadows protocols based on randomized measurements in $n$-qubit entangled bases. We show that entangled measurements enable nontrivial and potentially advantageous trade-offs in the sample complexity of learning Pauli expectation values.
  arXiv  Detail & Related papers  (2023-05-18T05:48:59Z)
• Towards Theoretical Understanding of Inverse Reinforcement Learning [45.3190496371625]
  Inverse reinforcement learning (IRL) denotes a powerful family of algorithms for recovering a reward function justifying the behavior demonstrated by an expert agent. In this paper, we make a step towards closing the theory gap of IRL in the case of finite-horizon problems with a generative model.
  arXiv  Detail & Related papers  (2023-04-25T16:21:10Z)
• Lower Bounds for Learning in Revealing POMDPs [88.23337313766355]
  This paper studies the fundamental limits of reinforcement learning (RL) in the challenging emphpartially observable setting. For emphmulti-step revealing POMDPs, we show that the latent state-space dependence is at least $Omega(S1.5)$ in the sample complexity.
  arXiv  Detail & Related papers  (2023-02-02T18:59:30Z)
• Tractable Optimality in Episodic Latent MABs [75.17357040707347]
  We consider a multi-armed bandit problem with $M$ latent contexts, where an agent interacts with the environment for an episode of $H$ time steps. Depending on the length of the episode, the learner may not be able to estimate accurately the latent context. We design a procedure that provably learns a near-optimal policy with $O(textttpoly(A) + texttttpoly(M,H)min(M,H))$ interactions.
  arXiv  Detail & Related papers  (2022-10-05T22:53:46Z)
• Sample optimal Quantum identity testing via Pauli Measurements [11.98034899127065]
  We show that $Theta(mathrmpoly(n)cdotfrac4nepsilon2)$ is the sample complexity of testing whether two $n$-qubit quantum states $rho$ and $sigma$ are identical or $epsilon$-far in trace distance using two-outcome Pauli measurements.
  arXiv  Detail & Related papers  (2020-09-24T06:54:09Z)

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.