HOW MANY QUESTIONS DO YOU NEED TO PROVE THAT UNASKED QUESTIONS HAVE NO ANSWERS?

2006 ◽  
Vol 04 (01) ◽  
pp. 55-61 ◽  
Author(s):  
ADÁN CABELLO
Keyword(s):  
Quantum System ◽  
Quantum State ◽  
Minimum Number ◽  
Arbitrary Quantum

Suppose a quantum system is prepared in an arbitrary quantum state. How many yes-no questions about that system would you have to consider to prove that such questions have no predefined answers? Peres conjectured that the minimum number was 18, as in the case of the set found in 1995. Asher's conjecture has recently been proven correct: there are no sets with fewer than 18 questions. This is the end of a long story which began in 1967, when Kochen and Specker found a similar set requiring 117 questions.

scholarly journals Reading a Qubit Quantum State with a Quantum Meter: Time Unfolding of Quantum Darwinism and Quantum Information Flux

2019 ◽  
Vol 26 (04) ◽  
pp. 1950023
Author(s):  
Salvatore Lorenzo ◽  
Mauro Paternostro ◽  
G. Massimo Palma
Keyword(s):  
Quantum Information ◽  
Harmonic Oscillator ◽  
Quantum System ◽  
Quantum State ◽  
Common Theme ◽  
Quantum Harmonic Oscillator ◽  
Collision Model ◽  
Single Qubit ◽  
Quantum Darwinism

Quantum non-Markovianity and quantum Darwinism are two phenomena linked by a common theme: the flux of quantum information between a quantum system and the quantum environment it interacts with. In this work, making use of a quantum collision model, a formalism initiated by Sudarshan and his school, we will analyse the efficiency with which the information about a single qubit gained by a quantum harmonic oscillator, acting as a meter, is transferred to a bosonic environment. We will show how, in some regimes, such quantum information flux is inefficient, leading to the simultaneous emergence of non-Markovian and non-darwinistic behaviours.

scholarly journals High-Efficiency Arbitrary Quantum Operation on a High-Dimensional Quantum System

2021 ◽  
Vol 127 (9) ◽  
Author(s):  
W. Cai ◽  
J. Han ◽  
L. Hu ◽  
Y. Ma ◽  
X. Mu ◽  
...  
Keyword(s):  
Quantum System ◽  
High Efficiency ◽  
High Dimensional ◽  
Quantum Operation ◽  
Arbitrary Quantum

Reconstructing a quantum state with a variational autoencoder

2021 ◽  
Author(s):  
Chuangtao Chen ◽  
Zhimin He ◽  
Zhiming Huang ◽  
Haozhen Situ
Keyword(s):  
Quantum State ◽  
Circuit Simulation ◽  
Entanglement Entropy ◽  
Ghz State ◽  
High Fidelity ◽  
Training Samples ◽  
Variational Autoencoder ◽  
Minimum Number ◽  
Number Formula ◽  
State Tomography

Quantum state tomography (QST) is an important and challenging task in the field of quantum information, which has attracted a lot of attentions in recent years. Machine learning models can provide a classical representation of the quantum state after trained on the measurement outcomes, which are part of effective techniques to solve QST problem. In this work, we use a variational autoencoder (VAE) to learn the measurement distribution of two quantum states generated by MPS circuits. We first consider the Greenberger–Horne–Zeilinger (GHZ) state which can be generated by a simple MPS circuit. Simulation results show that a VAE can reconstruct 3- to 8-qubit GHZ states with a high fidelity, i.e., 0.99, and is robust to depolarizing noise. The minimum number ([Formula: see text]) of training samples required to reconstruct the GHZ state up to 0.99 fidelity scales approximately linearly with the number of qubits ([Formula: see text]). However, for the quantum state generated by a complex MPS circuit, [Formula: see text] increases exponentially with [Formula: see text], especially for the quantum state with high entanglement entropy.

Proposal for dimensionality testing in QPQ

2018 ◽  
Vol 18 (13&14) ◽  
pp. 1125-1142
Author(s):  
Arpita Maitra ◽  
Bibhas Adhikari ◽  
Satyabrata Adhikari
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum System ◽  
Quantum State ◽  
Quantum Information Processing ◽  
Quantum States ◽  
Quantum Private Query ◽  
Unfair Advantage ◽  
Security Proofs

Recently, dimensionality testing of a quantum state has received extensive attention (Ac{\'i}n et al. Phys. Rev. Letts. 2006, Scarani et al. Phys. Rev. Letts. 2006). Security proofs of existing quantum information processing protocols rely on the assumption about the dimension of quantum states in which logical bits are encoded. However, removing such assumption may cause security loophole. In the present paper, we show that this is indeed the case. We choose two players' quantum private query protocol by Yang et al. (Quant. Inf. Process. 2014) as an example and show how one player can gain an unfair advantage by changing the dimension of subsystem of a shared quantum system. To resist such attack we propose dimensionality testing in a different way. Our proposal is based on CHSH like game. As we exploit CHSH like game, it can be used to test if the states are product states for which the protocol becomes completely vulnerable.

No-cloning Theorem and Quantum Copying

2020 ◽  
pp. 172-181
Author(s):  
M. Suhail Zubairy
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Uncertainty Relation ◽  
Foundations Of Quantum Mechanics ◽  
Quantum Cloning ◽  
Foundation Of Quantum Mechanics ◽  
Quantum Copying ◽  
Arbitrary Quantum ◽  
Principle Of Complementarity

Heisenberg’s uncertainty relation and Bohr’s principle of complementarity form the foundations of quantum mechanics. If these are violated then the edifice of quantum mechanics can come crashing down. In this chapter, it is shown how cloning or perfect copying of a quantum state can potentially lead to a violation of these sacred principles. A no-cloning theorem is proven showing that the cloning of an arbitrary quantum state is not allowed. The foundation of quantum mechanics is therefore protected. It is also shown how quantum cloning can lead to superluminal communication. It is also discussed that, if making a perfect copy of a quantum state is forbidden, how best a copy of a state can be made.

scholarly journals Probing Rényi entanglement entropy via randomized measurements

Science ◽  
2019 ◽  
Vol 364 (6437) ◽  
pp. 260-263 ◽  
Author(s):  
Tiff Brydges ◽  
Andreas Elben ◽  
Petar Jurcevic ◽  
Benoît Vermersch ◽  
Christine Maier ◽  
...  
Keyword(s):  
Quantum System ◽  
Entanglement Entropy ◽  
Quantum Systems ◽  
Quantum States ◽  
Many Body ◽  
Trapped Ion ◽  
Statistical Correlations ◽  
Quantum Simulator ◽  
Entanglement Structure ◽  
Arbitrary Quantum

Entanglement is a key feature of many-body quantum systems. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a protocol for measuring the second-order Rényi entropy based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator with partition sizes of up to 10 qubits, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts, in both the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, which is applicable to arbitrary quantum states of up to several tens of qubits.

Efficient implementation of arbitrary quantum state engineering in four-state system by counterdiabatic driving

2018 ◽  
Vol 15 (7) ◽  
pp. 075201
Author(s):  
Song-Bai Wang ◽  
Ye-Hong Chen ◽  
Qi-Cheng Wu ◽  
Zhi-Cheng Shi ◽  
Bi-Hua Huang ◽  
...  
Keyword(s):  
Quantum State ◽  
Efficient Implementation ◽  
State System ◽  
Quantum State Engineering ◽  
Arbitrary Quantum

scholarly journals COHERENT AND GENERALIZED INTELLIGENT STATES FOR INFINITE SQUARE WELL POTENTIAL AND NONLINEAR OSCILLATORS

2002 ◽  
Vol 16 (26) ◽  
pp. 3915-3937 ◽  
Author(s):  
A. H. EL KINANI ◽  
M. DAOUD
Keyword(s):  
Quantum System ◽  
Coherent States ◽  
Nonlinear Oscillators ◽  
Analytical Representation ◽  
Square Well ◽  
Arbitrary Quantum

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system.1 We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states à la Gazeau–Klauder and those à la Klauder–Perelomov, we derive the generalized intelligent states in analytical ways.

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