# Memory cost for simulating all quantum correlations from the Peres–Mermin scenario

@article{Fagundes2017MemoryCF, title={Memory cost for simulating all quantum correlations from the Peres–Mermin scenario}, author={Gabriel Fagundes and Matthias Kleinmann}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2017}, volume={50} }

Sequences of compatible quantum measurements can be contextual and any simulation with a classical model conforming with the quantum predictions needs to use internal memory. Kleinmann et al (2011 New J. Phys. 13 113011) showed that simulating sequences from the Peres–Mermin scenario requires at least three different internal states in order not to contradict the deterministic predictions of quantum theory. We extend this analysis to probabilistic quantum predictions and ask how much memory is…

## 18 Citations

### Optimal Classical Simulation of State-Independent Quantum Contextuality.

- PhysicsPhysical review letters
- 2018

The notion of classically simulating quantum state-independent contextuality (QSIC) in the case of a single quantum system submitted to an infinite sequence of measurements randomly chosen from a finite QSIC set is made rigorous.

### Pre- and post-selection paradoxes in quantum walks

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- 2019

Many features of single-partite quantum walks can be simulated by classical waves. However, it was recently experimentally shown that some temporal sequences of measurements on a quantum walker do…

### Temporal correlations in the simplest measurement sequences

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- 2022

The minimum memory requirements for sequences to be obtained deterministically, and the probabilistic behavior below this memory threshold are characterized, which suggests a nontrivial universal upper-bound for the classical probability of realization of any sequence below thisMemory threshold.

### Contextuality bounds the efficiency of classical simulation of quantum processes

- Computer Science
- 2018

It is found that the presence of contextuality demands that the minimum number of classical bits of memory required to simulate a multi-qubit system must scale quadratically in the number of qubits; notably, this is the same scaling as the Gottesman-Knill algorithm.

### Structure of temporal correlations of a qubit

- PhysicsNew Journal of Physics
- 2018

In quantum mechanics, spatial correlations arising from measurements at separated particles are well studied. This is not the case, however, for the temporal correlations arising from a single…

### Memory cost of temporal correlations

- PhilosophyNew Journal of Physics
- 2019

A possible notion of nonclassicality for single systems can be defined on the basis of the notion of memory cost of classically simulating probabilities observed in a temporal sequence of…

### Simulating extremal temporal correlations

- Mathematics
- 2020

The correlations arising from sequential measurements on a single quantum system form a polytope. This is defined by the arrow-of-time (AoT) constraints, meaning that future choices of measurement…

### Quantum resource theories

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- 2019

Quantum resource theories (QRTs) offer a highly versatile and powerful framework for studying different phenomena in quantum physics. From quantum entanglement to quantum computation, resource…

### Contextuality, memory cost and non-classicality for sequential measurements

- Computer SciencePhilosophical Transactions of the Royal Society A
- 2019

This work will discuss a generalization of the notion of non-classical temporal correlations that goes beyond the contextuality approach and related ones based on Leggett and Garg's notion of macrorealism, and it is based on the idea of memory cost of generating correlations.

### Local certification of programmable quantum devices of arbitrary high dimensionality

- Computer Science, PhysicsArXiv
- 2019

This work shows that the quantum self-testing paradigm can be employed to an individual quantum computer that is modelled as a programmable black box by introducing a noise-tolerant certification scheme and substantiates the applicability of the scheme by providing a family of outcome statistics whose observation certifies that the computer is producing specific high-dimensional quantum states and implementing specific measurements.

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