scholarly journals Informationally restricted correlations: a general framework for classical and quantum systems

Quantum ◽  
2022 ◽  
Vol 6 ◽  
pp. 620
Author(s):  
Armin Tavakoli ◽  
Emmanuel Zambrini Cruzeiro ◽  
Erik Woodhead ◽  
Stefano Pironio
Keyword(s):  
General Framework ◽  
Quantum Communication ◽  
Random Number ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Mixed States ◽  
Random Number Generators ◽  
New Methods ◽  
General Kind ◽  
Bell Nonlocality

We introduce new methods and tools to study and characterise classical and quantum correlations emerging from prepare-and-measure experiments with informationally restricted communication. We consider the most general kind of informationally restricted correlations, namely the ones formed when the sender is allowed to prepare statistical mixtures of mixed states, showing that contrary to what happens in Bell nonlocality, mixed states can outperform pure ones. We then leverage these tools to derive device-independent witnesses of the information content of quantum communication, witnesses for different quantum information resources, and demonstrate that these methods can be used to develop a new avenue for semi-device independent random number generators.

scholarly journals Bounds on Mixed State Entanglement

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 62 ◽  
Author(s):  
Bruno Leggio ◽  
Anna Napoli ◽  
Hiromichi Nakazato ◽  
Antonino Messina
Keyword(s):  
Mixed State ◽  
General Framework ◽  
Quantum Correlations ◽  
Thermal Entanglement ◽  
Mixed States ◽  
Clear Explanation ◽  
Finite Dimensionality ◽  
Partial Transpose ◽  
The Subject

In the general framework of d 1 × d 2 mixed states, we derive an explicit bound for bipartite negative partial transpose (NPT) entanglement based on the mixedness characterization of the physical system. The derived result is very general, being based only on the assumption of finite dimensionality. In addition, it turns out to be of experimental interest since some purity-measuring protocols are known. Exploiting the bound in the particular case of thermal entanglement, a way to connect thermodynamic features to the monogamy of quantum correlations is suggested, and some recent results on the subject are given a physically clear explanation.

Bell Nonlocality

2019 ◽  
Author(s):  
Valerio Scarani
Keyword(s):  
Quantum Theory ◽  
Random Number ◽  
Hidden Variables ◽  
Space Time ◽  
Applied Physics ◽  
Chronological Order ◽  
Random Number Generators ◽  
Bell Nonlocality ◽  
Future Theory

Nonlocality was discovered by John Bell in 1964, in the context of the debates about quantum theory, but is a phenomenon that can be studied in its own right. Its observation proves that measurements are not revealing pre-determined values, falsifying the idea of “local hidden variables” suggested by Einstein and others. One is then forced to make some radical choice: either nature is intrinsically statistical and individual events are unspeakable, or our familiar space-time cannot be the setting for the whole of physics. As phenomena, nonlocality and its consequences will have to be predicted by any future theory, and may possibly play the role of foundational principles in these developments. But nonlocality has found a role in applied physics too: it can be used for “device-independent” certification of the correct functioning of random number generators and other devices. After a self-contained introduction to the topic, this monograph on nonlocality presents the main tools and results following a logical, rather than a chronological, order.

scholarly journals Single-copy activation of Bell nonlocality via broadcasting of quantum states

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 499
Author(s):  
Joseph Bowles ◽  
Flavien Hirsch ◽  
Daniel Cavalcanti
Keyword(s):  
Single Copy ◽  
Quantum Correlations ◽  
The State ◽  
Mixed States ◽  
Variable Model ◽  
Variable Theory ◽  
Hidden Variable ◽  
Bell Nonlocality ◽  
Nonlocal Nature ◽  
Local Hidden Variable

Activation of Bell nonlocality refers to the phenomenon that some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. We present such a scenario that involves broadcasting the local subsystems of a single-copy of a bipartite quantum state to multiple parties, and use the scenario to study the nonlocal properties of the two-qubit isotropic state:ρα=α|Φ+⟩⟨Φ+|+(1−α)14.We present two main results, considering that Nature allows for (i) the most general no-signalling correlations, and (ii) the most general quantum correlations at the level of any hidden variable theory. We show that the state does not admit a local hidden variable description for α>0.559 and α>12, in cases (i) and (ii) respectively, which in both cases provides a device-independent certification of the entanglement of the state. These bounds are significantly lower than the previously best-known bound of 0.697 for both Bell nonlocality and device-independent entanglement certification using a single copy of the state. Our results show that strong examples of non-classicality are possible with a small number of resources.

Revival of Bell nonlocality across a quantum spin chain

2016 ◽  
Vol 14 (07) ◽  
pp. 1650037 ◽  
Author(s):  
J. Batle ◽  
M. Abutalib ◽  
S. Abdalla ◽  
Ahmed Farouk
Keyword(s):  
Sudden Death ◽  
Quantum Channel ◽  
Spin Chain ◽  
Bell Inequality ◽  
Quantum Correlations ◽  
Quantum Spin ◽  
Local Realism ◽  
Mixed States ◽  
Quantum Spin Chain ◽  
Bell Nonlocality

The transmission of pure and mixed states along a quantum spin chain is investigated. Nonlocality between two qubits will evolve as it is transmitted through the quantum channel in a way that may violate or not the Clauser–Horne–Shimony–Holt (CHSH) Bell inequality at different times. This violation of local realism is analogue to the so-called sudden death and sudden birth features of entanglement. In the quantum channel, which will turn to be a damping one, some (mixed) states will be preferred according to the nature of the quantum correlations that are preserved during the evolution along the spin chain.

scholarly journals A study of quantum correlations in open quantum systems

2011 ◽  
Vol 11 (7&8) ◽  
pp. 541-562
Author(s):  
Indranil Chakrabarty ◽  
Subhashish Banerjee ◽  
Nana Siddharth
Keyword(s):  
Open Quantum Systems ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Bell’S Inequality ◽  
Mixed States ◽  
Classical Correlation ◽  
Bell's Inequality ◽  
Qubit System ◽  
Dynamical Parameters ◽  
Potential Resource

In this work, we study quantum correlations in mixed states. The states studied are modeled by a two-qubit system interacting with its environment via a quantum non demolition (purely dephasing) as well as dissipative type of interaction. The entanglement dynamics of this two qubit system is analyzed. We make a comparative study of various measures of quantum correlations, like Concurrence, Bell's inequality, Discord and Teleportation fidelity, on these states, generated by the above evolutions. We classify these evoluted states on basis of various dynamical parameters like bath squeezing parameter $r$, inter-qubit spacing $r_{12}$, temperature $T$ and time of system-bath evolution $t$. In this study, in addition we report the existence of entangled states which do not violate Bell's inequality, but can still be useful as a potential resource for teleportation. Moreover we study the dynamics of quantum as well as classical correlation in presence of dissipative coherence.

scholarly journals TRNGs from Pre-Formed ReRAM Arrays

Cryptography ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Bertrand Cambou ◽  
Donald Telesca ◽  
Sareh Assiri ◽  
Michael Garrett ◽  
Saloni Jain ◽  
...  
Keyword(s):  
Random Number ◽  
Random Number Generator ◽  
Random Access ◽  
Random Number Generators ◽  
Cryptographic Algorithms ◽  
Cryptographic Keys ◽  
Low Levels ◽  
Stochastic Properties ◽  
Pseudo Random Number Generator ◽  
Number Of Cells

Schemes generating cryptographic keys from arrays of pre-formed Resistive Random Access (ReRAM) cells, called memristors, can also be used for the design of fast true random number generators (TRNG’s) of exceptional quality, while consuming low levels of electric power. Natural randomness is formed in the large stochastic cell-to-cell variations in resistance values at low injected currents in the pre-formed range. The proposed TRNG scheme can be designed with three interconnected blocks: (i) a pseudo-random number generator that acts as an extended output function to generate a stream of addresses pointing randomly at the array of ReRAM cells; (ii) a method to read the resistance values of these cells with a low injected current, and to convert the values into a stream of random bits; and, if needed, (iii) a method to further enhance the randomness of this stream such as mathematical, Boolean, and cryptographic algorithms. The natural stochastic properties of the ReRAM cells in the pre-forming range, at low currents, have been analyzed and demonstrated by measuring a statistically significant number of cells. Various implementations of the TRNGs with ReRAM arrays are presented in this paper.

scholarly journals Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marcin Wieśniak
Keyword(s):  
Communication Complexity ◽  
Quantum Communication ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Complexity Reduction ◽  
Main Difficulty ◽  
Quantum Communication Complexity ◽  
Number Of Particles ◽  
Dicke States

AbstractQuantum correlations, in particular those, which enable to violate a Bell inequality, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles N. In case of Dicke states, we show that persistency can reach 0.482N, significantly more than reported in previous studies.

scholarly journals Fundamental limitations on distillation of quantum channel resources

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Bartosz Regula ◽  
Ryuji Takagi
Keyword(s):  
Lower Bounds ◽  
Quantum Channel ◽  
Quantum Communication ◽  
Fault Tolerant ◽  
State Of The Art ◽  
Quantum Systems ◽  
Noisy Channels ◽  
General Transformation ◽  
Fundamental Limitations ◽  
Strong Converse

AbstractQuantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols. Focusing on the class of distillation tasks — which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels — we develop fundamental restrictions on the error incurred in such transformations, and comprehensive lower bounds for the overhead of any distillation protocol. In the asymptotic setting, our results yield broadly applicable bounds for rates of distillation. We demonstrate our results through applications to fault-tolerant quantum computation, where we obtain state-of-the-art lower bounds for the overhead cost of magic state distillation, as well as to quantum communication, where we recover a number of strong converse bounds for quantum channel capacity.

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