Semidefinite programming relaxations for quantum correlations

Reviews of Modern Physics, Journal Year: 2024, Volume and Issue: 96(4)

Published: Dec. 4, 2024

Semidefinite programs are convex optimisation problems involving a linear objective function and domain of positive-semidefinite matrices.Over the past two decades, they have become an indispensable tool in quantum information science.Many otherwise intractable fundamental applied can be successfully approached by means relaxation to semidefinite program.Here, we review such methodology context correlations.We discuss how core idea relaxations adapted for variety research topics correlations, including nonlocality, communication, networks, entanglement, cryptography. CONTENTSI. Introduction 2 II.Background 3 A. Primals duals B. Correlation scenarios theory 1.Entanglement-based 4 2. Communication-based 7 C. Overview hierarchies 9 III.Semidefinite polynomial Commutative 1.Moment matrix approach Sum squares 11 Noncommutative 12 13 IV.Entanglement 14 Doherty-Parrilo-Spedalieri hierarchy Bipartite entanglement 15 1.Quantifying Detecting dimension 17 Multipartite 18 1.Entanglement detection 2.Quantum marginal 19 V.Quantum nonlocality 20 The Navascués-Pironio-Acín 1. Macroscopic Locality & Almost-Quantum Correlations 21 Tsirelson bounds 22 Device-independent certification 23 1.Self-testing Entanglement 24 3. 25 4. Joint measurability 26 VI.Quantum communication 27 Channel capacities 1.Classical 28 Quantum 30 Dimension constraints Bounding set 31 Applications 32 Entanglement-assisted Teleportation Distinguishability 1.Distinguishability Discrimination tasks VII.Randomness key distribution min-entropy von Neumann entropy Beyond optimisations Device-dependent Semi-device-independent VIII.Correlations networks Inflation methods Classical inflation No-signaling independence Other SDP network correlations Relaxations factorisation Tests topology IX.Further models Generalised Bell ground-state energies D. Rank-constrained E. contextuality F. Symmetrisation X. Conclusions Table abbreviations Implementation guide Strict feasibility optimal value Eq. (12) is nonnegative.As before, it also interesting consider dual LP, min {c abxy } a,b,x,y c p(a, b|x, y) s.t.λ,a,b,x,y D(a|x, λ)D(b|y, λ) = 1, ≥ 0 ∀ λ.

Language: Английский

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Information capacity of quantum communication under natural physical assumptions

Quantum, Journal Year: 2025, Volume and Issue: 9, P. 1637 - 1637

Published: Feb. 18, 2025

The quantum prepare-and-measure scenario has been studied under various physical assumptions on the emitted states. Here, we first discuss how different are conceptually and formally related. We then identify one that can serve as a relaxation of all others, corresponding to limitation one-shot accessible information state ensemble. This motivates us study optimal discrimination probability source subject these assumptions. derive general tight bounds for states restricted by their dimension, vacuum component, an arbitrary uniform overlap, magnitude higher-dimensional signals experimenter's trust in device. Our results constitute step towards more unified picture semi-device-independent processing.

Language: Английский

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Exact Steering Bound for Two-Qubit Werner States

Physical Review Letters, Journal Year: 2024, Volume and Issue: 132(25)

Published: June 17, 2024

Two independent papers answer an important open question by showing that generalized measurements are not more powerful than projection-valued in quantum steering with two-qubit Werner states.

Language: Английский

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Classical Cost of Transmitting a Qubit

Physical Review Letters, Journal Year: 2023, Volume and Issue: 130(12)

Published: March 22, 2023

We consider general prepare-and-measure scenarios in which Alice can transmit qubit states to Bob, who perform measurements the form of positive operator-valued measures (POVMs). show that statistics obtained any such quantum protocol be simulated by purely classical means shared randomness and two bits communication. Furthermore, we prove communication is minimal cost a perfect simulation. In addition, apply our methods Bell scenarios, extends well-known Toner Bacon protocol. particular, are enough simulate all correlations associated arbitrary local POVMs applied entangled two-qubit state.

Language: Английский

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Quantum Steering with Imprecise Measurements

Physical Review Letters, Journal Year: 2024, Volume and Issue: 132(7)

Published: Feb. 16, 2024

We study quantum steering experiments without assuming that the trusted party can perfectly control their measurement device. Instead, we introduce a scenario in which these measurements are subject to small imprecision. show imprecision have large detrimental influence terms of false positives for inequalities, and this effect become even more relevant high-dimensional systems. then method taking generic into account tests bipartite inequalities. The revised bounds returned by analytical, easily computable, optimal well-known families arbitrary-dimensional tests. Furthermore, it applies equally well generalized scenarios, where shared state does not need be separable, but is instead limited some other entanglement property. Published American Physical Society 2024

Language: Английский

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Robust Classical and Quantum Polarimetry with a Single Nanostructured Metagrating

ACS Photonics, Journal Year: 2024, Volume and Issue: 11(3), P. 1060 - 1067

Published: Feb. 15, 2024

We formulate a new conceptual approach for one-shot complete polarization state measurement with nanostructured metasurfaces applicable to classical light and multi-photon quantum states, by drawing on the principles of generalized measurements based positive operator-valued measures (POVMs). Accurate reconstruction from combination photon counts or correlations several diffraction orders is robust respect even strong fabrication inaccuracies, requiring only single calibration metasurface transmission. Furthermore, this operates metagrating without interleaving, allowing size reduction while preserving high transmission efficiency output beam quality. theoretically obtained original designs, fabricated amorphous silicon nanostructures deposited glass, experimentally confirmed accurate laser beams. also anticipate operation under changes in environmental conditions, opening possibilities space-based imaging satellite optics.

Language: Английский

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Non-Markovianity in High-Dimensional Open Quantum Systems using Next-generation Multicore Optical Fibers

Quantum, Journal Year: 2024, Volume and Issue: 8, P. 1436 - 1436

Published: Aug. 12, 2024

With the advent of quantum technology, interest in communication tasks assisted by systems has increased both academia and industry. Nonetheless, transmission a state real-world scenarios is bounded environmental noise, so that channel an open system. In this work, we study high-dimensional system multicore optical fiber characterizing interaction as operations corresponding to probabilistic phase-flips. The experimental platform currently state-of-the-art for information processing with fibers. At given evolution stage observe non-Markovian behaviour system, which demonstrated through proof-of-principle implementation Quantum Vault protocol. A better understanding phase-noise fibers will improve several protocols, since they are prime candidate be adopted future telecom networks.

Language: Английский

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Experimental demonstration of the equivalence of entropic uncertainty with wave-particle duality

Science Advances, Journal Year: 2024, Volume and Issue: 10(49)

Published: Dec. 6, 2024

Wave-particle duality is one of the most notable and counterintuitive features quantum mechanics, illustrating that two incompatible observables cannot be measured simultaneously with arbitrary precision. In this work, we experimentally demonstrate equivalence wave-particle entropic uncertainty relations using orbital angular momentum (OAM) states light. Our experiment uses an innovative reconfigurable platform composed few-mode optical fibers photonic lanterns, showcasing versatility technology for information processing. results provide fundamental insights into complementarity principle from informational perspective, implications broader field technologies.

Language: Английский

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Minimal orthonormal bases for pure quantum state estimation

Quantum, Journal Year: 2024, Volume and Issue: 8, P. 1244 - 1244

Published: Feb. 8, 2024

We present an analytical method to estimate pure quantum states using a minimum of three measurement bases in any finite-dimensional Hilbert space. This is optimal as two are insufficient construct informationally complete positive operator-valued (IC-POVM) for states. demonstrate our binary tree structure, providing algorithmic path implementation. The performance the evaluated through numerical simulations, showcasing its effectiveness state estimation.

Language: Английский

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Multiparameter Estimation with Two-Qubit Probes in Noisy Channels

Entropy, Journal Year: 2023, Volume and Issue: 25(8), P. 1122 - 1122

Published: July 26, 2023

This work compares the performance of single and two qubit probes for estimating several phase rotations simultaneously under action different noisy channels. We compute quantum limits this simultaneous estimation using collective individual measurements by evaluating Holevo Nagaoka-Hayashi Cram\'er-Rao bounds respectively. Several noise channels are considered, namely decohering channel, amplitude damping channel channel. For each we find optimal probes. Where possible demonstrate an explicit measurement strategy which saturates appropriate bound investigate how closely can be approached through on multiple copies same probe. that considered channels, show enhanced parameter capabilities over almost all non-identity i.e. achievable precision with a probe degrades faster increasing exposure to environment than However, in sufficiently it is outperform maximally entangled shows that, order reach ultimate allowed mechanics, entanglement required both state preparation stages. It hoped tutorial-style nature paper will make easily accessible.

Language: Английский

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