scholarly journals Classical and quantum fingerprinting with shared randomness and one-sided error

2005 ◽  
Vol 5 (3) ◽  
pp. 258-271
Author(s):  
R.T. Horn ◽  
A.J. Scott ◽  
J. Walgate ◽  
R. Cleve ◽  
A.I. Lvovsky ◽  
...  
Keyword(s):  
Message Passing ◽  
Error Probability ◽  
Communication Complexity ◽  
Worst Case ◽  
Error Probabilities ◽  
Quantum Fingerprinting

Within the simultaneous message passing model of communication complexity, under a public-coin assumption, we derive the minimum achievable worst-case error probability of a classical fingerprinting protocol with one-sided error. We then present entanglement-assisted quantum fingerprinting protocols attaining worst-case error probabilities that breach this bound.

scholarly journals Optimal fingerprinting strategies with one-sided error

2007 ◽  
Vol 7 (3) ◽  
pp. 243-264
Author(s):  
A.J. Scott ◽  
J. Walgate ◽  
B.C. Sanders
Keyword(s):  
Message Passing ◽  
Tight Frames ◽  
Worst Case ◽  
Classical Information ◽  
Equiangular Tight Frames ◽  
The One ◽  
Extremal Set ◽  
The Cost ◽  
Made In ◽  
Quantum Fingerprinting

Fingerprinting enables two parties to infer whether the messages they hold are the same or different when the cost of communication is high: each message is associated with a smaller fingerprint and comparisons between messages are made in terms of their fingerprints alone. In the simultaneous message passing model, it is known that fingerprints composed of quantum information can be made exponentially smaller than those composed of classical information. For small message lengths, we present constructions of optimal classical fingerprinting strategies with one-sided error, in both the one-way and simultaneous message passing models, and provide bounds on the worst-case error probability with the help of extremal set theory. The performance of these protocols is then compared to that for quantum fingerprinting strategies constructed from spherical codes, equiangular tight frames and mutually unbiased bases.

scholarly journals Efficient experimental quantum fingerprinting with channel multiplexing and simultaneous detection

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Xiaoqing Zhong ◽  
Feihu Xu ◽  
Hoi-Kwong Lo ◽  
Li Qian
Keyword(s):  
Communication Complexity ◽  
Single Photon ◽  
Simultaneous Detection ◽  
Minimum Amount ◽  
Photon Detectors ◽  
Communication Time ◽  
Quantum Communication Complexity ◽  
Detection Of Signals ◽  
Coherent Quantum ◽  
Quantum Fingerprinting

AbstractQuantum communication complexity explores the minimum amount of communication required to achieve certain tasks using quantum states. One representative example is quantum fingerprinting, in which the minimum amount of communication could be exponentially smaller than the classical fingerprinting. Here, we propose a quantum fingerprinting protocol where coherent states and channel multiplexing are used, with simultaneous detection of signals carried by multiple channels. Compared with an existing coherent quantum fingerprinting protocol, our protocol could consistently reduce communication time and the amount of communication by orders of magnitude by increasing the number of channels. Our proposed protocol can even beat the classical limit without using superconducting-nanowire single photon detectors. We also report a proof-of-concept experimental demonstration with six wavelength channels to validate the advantage of our protocol in the amount of communication. The experimental results clearly prove that our protocol not only surpasses the best-known classical protocol, but also remarkably outperforms the existing coherent quantum fingerprinting protocol.

scholarly journals Ratio-based multi-level resistive memory cells

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Miguel Angel Lastras-Montaño ◽  
Osvaldo Del Pozo-Zamudio ◽  
Lev Glebsky ◽  
Meiran Zhao ◽  
Huaqiang Wu ◽  
...  
Keyword(s):  
Error Probability ◽  
Resistance Switching ◽  
Closed Form Expression ◽  
Memory Cells ◽  
Resistive Memory ◽  
Worst Case ◽  
Information Encoding ◽  
Bit Error Probability ◽  
Multi Level ◽  
Switching Devices

AbstractRatio-based encoding has recently been proposed for single-level resistive memory cells, in which the resistance ratio of a pair of resistance-switching devices, rather than the resistance of a single device (i.e. resistance-based encoding), is used for encoding single-bit information, which significantly reduces the bit error probability. Generalizing this concept for multi-level cells, we propose a ratio-based information encoding mechanism and demonstrate its advantages over the resistance-based encoding for designing multi-level memory systems. We derive a closed-form expression for the bit error probability of ratio-based and resistance-based encodings as a function of the number of levels of the memory cell, the variance of the distribution of the resistive states, and the ON/OFF ratio of the resistive device, from which we prove that for a multi-level memory system using resistance-based encoding with bit error probability x, its corresponding bit error probability using ratio-based encoding will be reduced to $$x^2$$ x 2 at the best case and $$x^{\sqrt{2}}$$ x 2 at the worst case. We experimentally validated these findings on multiple resistance-switching devices and show that, compared to the resistance-based encoding on the same resistive devices, our approach achieves up to 3 orders of magnitude lower bit error probability, or alternatively it could reduce the cell’s programming time and programming energy by up 5–10$$\times$$ × , while achieving the same bit error probability.

scholarly journals A new algorithm for fixed point quantum search

2006 ◽  
Vol 6 (6) ◽  
pp. 483-494
Author(s):  
T. Tulsi ◽  
L.K. Grover ◽  
A. Patel
Keyword(s):  
Fixed Point ◽  
Error Probability ◽  
Search Algorithm ◽  
Quantum Search ◽  
Worst Case ◽  
Average Case ◽  
Standard Quantum ◽  
Quantum Search Algorithm ◽  
Monotonic Convergence ◽  
Worst Case Behavior

The standard quantum search lacks a feature, enjoyed by many classical algorithms, of having a fixed point, i.e. monotonic convergence towards the solution. Recently a fixed point quantum search algorithm has been discovered, referred to as the Phase-\pi/3 search algorithm, which gets around this limitation. While searching a database for a target state, this algorithm reduces the error probability from \epsilon to \epsilon^{2q+1} using q oracle queries, which has since been proved to be asymptotically optimal. A different algorithm is presented here, which has the same worst-case behavior as the Phase-\pi/3 search algorithm but much better average-case behavior. Furthermore the new algorithm gives \epsilon^{2q+1} convergence for all integral q, whereas the Phase-\pi/3 search algorithm requires q to be (3^{n}-1)/2 with n a positive integer. In the new algorithm, the operations are controlled by two ancilla qubits, and fixed point behavior is achieved by irreversible measurement operations applied to these ancillas. It is an example of how measurement can allow us to bypass some restrictions imposed by unitarity on quantum computing.

Error Probability for Coherent Modulations in Rician Fading Channel

2010 ◽  
pp. 1741-1752
Author(s):  
A. Chandra ◽  
C. Bose
Keyword(s):  
Error Rate ◽  
Fading Channel ◽  
Error Probability ◽  
Error Rates ◽  
Rician Fading ◽  
Average Error ◽  
Valuable Insight ◽  
Rician Fading Channel ◽  
Modulation Schemes ◽  
Error Probabilities

Simple closed-form solutions for the average error rate of several coherent modulation schemes including square M-QAM, DBPSK and QPSK operating over slow flat Rician fading channel are derived. Starting from a novel unified expression of conditional error probability the error rates are analysed using PDF based approach. The derived end expressions composed of infinite series summations of Gauss hypergeometric function are accurate, free from any numerical integration and general enough, as it encompasses as special situations, some cases of non-diversity and Rayleigh fading. Error probabilities are graphically displayed for the modulation schemes for different values of the Rician parameter K. In addition, to examine the dependence of error rate performance of M-QAM on the constellation size, numerical results are plotted for various values of M. The generality of the analytical results presented offers valuable insight into the performance evaluation over a fading channel in a unified manner.

scholarly journals Communication complexity of approximate maximum matching in the message-passing model

2020 ◽  
Vol 33 (6) ◽  
pp. 515-531
Author(s):  
Zengfeng Huang ◽  
Bozidar Radunovic ◽  
Milan Vojnovic ◽  
Qin Zhang
Keyword(s):  
Message Passing ◽  
Communication Complexity ◽  
Maximum Matching

scholarly journals Submodel Decomposition for Solving Limited Memory Influence Diagrams (Student Abstract)

2020 ◽  
Vol 34 (10) ◽  
pp. 13851-13852
Author(s):  
Junkyu Lee
Keyword(s):  
Message Passing ◽  
Graphical Model ◽  
Partial Evaluation ◽  
Influence Diagrams ◽  
Influence Diagram ◽  
Worst Case ◽  
Limited Memory ◽  
Worst Case Complexity ◽  
The Individual ◽  
Model Approach

This paper presents a systematic way of decomposing a limited memory influence diagram (LIMID) to a tree of single-stage decision problems, or submodels and solving it by message passing. The relevance in LIMIDs is formalized by the notion of the partial evaluation of the maximum expected utility, and the graph separation criteria for identifying submodels follow. The submodel decomposition provides a graphical model approach for updating the beliefs and propagating the conditional expected utilities for solving LIMIDs with the worst-case complexity bounded by the maximum treewidth of the individual submodels.

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