#### DMCA

## Contents (2010)

### Cached

### Download Links

- [quantum.phys.cmu.edu]
- [quantum.phys.cmu.edu]
- [quantum.phys.cmu.edu]
- [quantum.phys.cmu.edu]
- [quantum.phys.cmu.edu]
- [quantum.phys.cmu.edu]
- [quantum.phys.cmu.edu]
- [quantum.phys.cmu.edu]
- [quantum.phys.cmu.edu]
- [quantum.phys.cmu.edu]
- [arxiv.org]
- [arxiv.org]
- [arxiv.org]
- [arxiv.org]
- [quantum.phys.cmu.edu]
- [www.ece.usu.edu]
- [www.mcl.hu]
- [quantum.phys.cmu.edu]
- [quantum.phys.cmu.edu]
- [arxiv.org]

### Citations

10431 | Introduction to Algorithms
- Cormen, Leiserson, et al.
- 2001
(Show Context)
Citation Context ...tional power of this model is equivalent to that of other general purpose models of quantum computation, such as quantum Turing machines [7]. For an introduction to algorithms and their analysis, see =-=[8]-=-. A useful textbook on computational complexity with an introduction to classical computation and computational machine models is [9]. 2 Quantum Information The foundations of an information processin... |

2792 | Computational complexity
- Papadimitriou
- 1994
(Show Context)
Citation Context ...nes [7]. For an introduction to algorithms and their analysis, see [8]. A useful textbook on computational complexity with an introduction to classical computation and computational machine models is =-=[9]-=-. 2 Quantum Information The foundations of an information processing theory can be constructed by the procedure we followed in the previous section: 1. Define the basic unit of information. 2. Give th... |

2369 |
Quantum Computation and Quantum Information
- Nielsen, Chuang
- 2000
(Show Context)
Citation Context ...we currently know about applications of quantum information processing. A useful reference text on 36quantum computation and information with historical notes is the book by M. Nielsen and I. Chuang =-=[38]-=-. 3.1 Quantum Algorithms Shor’s factoring algorithm, which precipitated much of the current work in quantum information processing, is based on a quantum realization of the fast Fourier transform. The... |

1254 | Polynomial-time algorithms for prime factorization and discretelogarithms on a quantum computer
- Shor
- 1997
(Show Context)
Citation Context ...of quantum physics [3], a task for which general purpose, efficient, classical algorithms are not known to exist. Quantum information also leads to efficient algorithms for factoring of large numbers =-=[4, 5]-=-, which is believed to be difficult for classical computers. An efficient factoring algorithm would break the security of commonly used public key cryptographic codes used for authenticating and secur... |

1250 |
An introduction to the theory of numbers
- Hardy, Wright
- 1979
(Show Context)
Citation Context ... an algorithm is considered efficient if it uses resources bounded by a polynomial in the number of digits of N. For more information on the requisite number theory, see any textbook on number theory =-=[18, 19]-=-. We begin by showing that factoring reduces to order finding. The first observation is that to factor a whole number it is sufficient to solve the factor-finding problem, whose statement is: Given a ... |

1153 | Can quantum-mechanical description of physical reality be considered complete? Phys - Einstein, Podolsky, et al. - 1935 |

1115 | A fast quantum mechanical algorithm for database search
- Grover
- 1996
(Show Context)
Citation Context ...tographic codes used for authenticating and securing internet communications. A fourth application of quantum information improves the efficiency with which unstructured search problems can be solved =-=[6]-=-. Quantum unstructured search may make it possible to solve significantly larger instances of optimization problems such as the scheduling and traveling salesman problems. As a result of the capabilit... |

1089 | Algorithms for quantum computation: Discrete logarithms and factoring
- Shor
- 1994
(Show Context)
Citation Context ...of quantum physics [3], a task for which general purpose, efficient, classical algorithms are not known to exist. Quantum information also leads to efficient algorithms for factoring of large numbers =-=[4, 5]-=-, which is believed to be difficult for classical computers. An efficient factoring algorithm would break the security of commonly used public key cryptographic codes used for authenticating and secur... |

982 |
On the Einstein-Podolsky-Rosen paradox
- Bell
- 1964
(Show Context)
Citation Context ...etermining the physical limitations placed on classical information processing. The fact that pairs of two-level systems can have correlations not possible for classical systems was proven by J. Bell =-=[30]-=- in 1964. Subsequently, indications that quantum mechanics offers advantages to information processing came from S. Wiesner’s studies of cryptographic applications [1] in the late 1960s. S. Wiesner’s ... |

852 | Fast and robust fixed-point algorithms for independent component analysis
- Hyvärinen
- 1999
(Show Context)
Citation Context ...nsors and resolutions as with remote sensing [10, 12–14] and medical applications [15–17]. It has also been used in the photography field to combine images with multiple depths-of-field and exposures =-=[18,19]-=-. In surveillance and military operations, as well as remote sensing, fusion has been used to combine images from visual and thermal infrared sensors [20–22]. Image fusion can be performed at three pr... |

845 | Quantum theory, the Church-Turing principle and the universal quantum computer
- Deutsch
- 1985
(Show Context)
Citation Context ...ntum mechanics on a classical computer might be overcome if we could use a computer that is itself based on quantum mechanics. A formal model of quantum Turing machines was soon defined by D. Deutsch =-=[33]-=-, who later also introduced quantum networks [34]. D. Deutsch and R. Jozsa [35] were the first to introduce a black box problem that can be solved deterministically on a quantum computer in fewer step... |

748 | Mathematical foundations of quantum mechanics - Neumann - 1996 |

632 |
Logical reversibility of computation
- Bennett
- 1973
(Show Context)
Citation Context ...2]. Beginning in the 1960s, R. Landauer studied the thermodynamic cost of irreversible operations in computation [23]. C. Bennett showed that by using reversible computation, this cost can be avoided =-=[24]-=-. Limitations of measurement in quantum mechanics were investigated early by researchers such as J. von Neumann [25, 26], and later by A. Holevo [27] and C. Helstrom [28]. A. Holevo introduced the ide... |

590 |
Simulating physics with computers
- Feynman
- 1982
(Show Context)
Citation Context ... attempts necessarily disturb the exchanged quantum information without revealing the content of the communication. In computation, quantum information enables efficient simulation of quantum physics =-=[3]-=-, a task for which general purpose, efficient, classical algorithms are not known to exist. Quantum information also leads to efficient algorithms for factoring of large numbers [4, 5], which is belie... |

570 | Quantum complexity theory
- Bernstein, Vazirani
- 1997
(Show Context)
Citation Context ...as we are about to do. In fact, black box problems played a crucial role in the development of quantum algorithms by providing the first and most convincing examples of the power of quantum computers =-=[13, 14]-=-. Some of these examples involve generalizations of the parity problem. Another purpose of black box problems is to enable us to focus on what can be learned from the “input/output” behavior of an ope... |

568 |
Quantum Detection and Estimation Theory
- Helstrom
- 1976
(Show Context)
Citation Context ...ion, this cost can be avoided [24]. Limitations of measurement in quantum mechanics were investigated early by researchers such as J. von Neumann [25, 26], and later by A. Holevo [27] and C. Helstrom =-=[28]-=-. A. Holevo introduced the idea of quantum communication channels and found bounds on their capacity for transmitting classical information [29]. Initially, most work focused on determining the physic... |

439 | Rapid solution of problems by quantum computation
- Deutsch
- 1992
(Show Context)
Citation Context ...uter that is itself based on quantum mechanics. A formal model of quantum Turing machines was soon defined by D. Deutsch [33], who later also introduced quantum networks [34]. D. Deutsch and R. Jozsa =-=[35]-=- were the first to introduce a black box problem that can be solved deterministically on a quantum computer in fewer steps than on a classical computer. In spite of suggestions that it could lead to l... |

427 | On the power of quantum computation
- Simon
- 1994
(Show Context)
Citation Context ...as we are about to do. In fact, black box problems played a crucial role in the development of quantum algorithms by providing the first and most convincing examples of the power of quantum computers =-=[13, 14]-=-. Some of these examples involve generalizations of the parity problem. Another purpose of black box problems is to enable us to focus on what can be learned from the “input/output” behavior of an ope... |

419 | The logic of quantum mechanics - Birkhoff, Neumann - 1936 |

401 | Quantum Theory - Bohm - 1951 |

341 | III, Relative state formulation of quantum mechanics - Everett - 1957 |

322 |
Scheme for reducing decoherence in quantum computer memory
- Shor
- 1995
(Show Context)
Citation Context ...ring. At that point, it was still generally believed that the fragility of quantum states made it unlikely for reasonably large quantum computers to be realized in practice. But the discovery by Shor =-=[36]-=- and A. Steane [37] that quantum error-correction was possible soon changed that view, see [12] for an introductory overview. As a result of the recognition of the utility and realizability of quantum... |

303 | Quantum Error Correction Via Codes over GF(4 - Calderbank, Rains, et al. - 1998 |

291 | effects, and operations: Fundamental notions in quantum theory - States - 1983 |

286 |
Quantum computational networks
- Deutsch
- 1989
(Show Context)
Citation Context ...vercome if we could use a computer that is itself based on quantum mechanics. A formal model of quantum Turing machines was soon defined by D. Deutsch [33], who later also introduced quantum networks =-=[34]-=-. D. Deutsch and R. Jozsa [35] were the first to introduce a black box problem that can be solved deterministically on a quantum computer in fewer steps than on a classical computer. In spite of sugge... |

274 | Elementary gates for quantum computation
- Barenco, Bennett, et al.
- 1995
(Show Context)
Citation Context ...hniques from the theory of reversible classical computation. The result is an efficient network for ˆ f2l . Basic network theory can then be used to implement the controlled version of this operation =-=[21]-=-. The understand the second feature, note that we were lucky that the order of 8 modulo 15 was a power of 2, which nicely matched the measured Fourier transform we constructed on two qubits. The measu... |

264 | Fault-tolerant quantum computation - Shor - 1996 |

226 | Fault-Tolerant Quantum Computation with Constant Error - Aharonov, Ben-Or - 1997 |

191 | Quantum measurements and the abelian stabilizer problem.ECCC
- Kitaev
- 1996
(Show Context)
Citation Context ...ctoring and the powerful technique of phase estimation. This relationship helps in understanding many of the existing quantum algorithms and was first explained in [16], motivated by Kitaev’s version =-=[17]-=- of the factoring algorithm. The factoring problem requires writing a whole number N as a product of primes. (Primes are whole numbers greater than 1 that are divisible without remainder only by 1 and... |

186 | Quantum algorithms revisited
- Cleve, Ekert, et al.
- 1998
(Show Context)
Citation Context ... outline the relationship between factoring and the powerful technique of phase estimation. This relationship helps in understanding many of the existing quantum algorithms and was first explained in =-=[16]-=-, motivated by Kitaev’s version [17] of the factoring algorithm. The factoring problem requires writing a whole number N as a product of primes. (Primes are whole numbers greater than 1 that are divis... |

185 | Mixed State Entanglement and Quantum Error Correction - Bennett, DiVincenzo, et al. - 1996 |

169 | Multiple particle interference and quantum error correction
- Steane
(Show Context)
Citation Context ..., it was still generally believed that the fragility of quantum states made it unlikely for reasonably large quantum computers to be realized in practice. But the discovery by Shor [36] and A. Steane =-=[37]-=- that quantum error-correction was possible soon changed that view, see [12] for an introductory overview. As a result of the recognition of the utility and realizability of quantum information, the s... |

164 | Fault-tolerant quantum computation - Preskill - 1997 |

147 | Quantum Mechanics in the light of quantum cosmology - Gell-Mann, Hartle - 1993 |

141 | Consistent histories and the interpretation of quantum mechanics - Griffiths - 1984 |

139 |
Universal quantum simulators
- Lloyd
- 1996
(Show Context)
Citation Context ...tion using a suitable formulation of general-purpose quantum computers. After 37such computers were formalized by Deutsch, the implementation of the emulation was generalized and refined by S. Lloyd =-=[39]-=-, Wiesner [40] and C. Zalka [41]. The ability to emulate the evolution of quantum systems is actually widely used by classical “Monte-Carlo” algorithms for simulating physics, where the states amplitu... |

138 |
The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines
- Benioff
- 1980
(Show Context)
Citation Context ...ich can be used to communicate in secret. Initially, the term “quantum computation” was mostly used to refer to classical computers realized using quantum mechanical systems. In the 1980s, P. Benioff =-=[31]-=-, R. Feynman [3] and Y. I. Manin [32] introduced the idea of a quantum computer based on quantum information. They noted that the apparent exponential complexity of simulating quantum mechanics on a c... |

126 | Quantum Error Correction and Orthogonal Geometry Phys - Calderbank, Rains, et al. - 1997 |

118 | Quantum Counting
- Brassard, Hoyer, et al.
- 1998
(Show Context)
Citation Context ...tput, but an efficient algorithm that finds a satisfying input is conjectured to be impossible. This is the P ̸= NP conjecture. Generalizations of Grover’s search algorithm (“amplitude amplification” =-=[47]-=-) can be used to find satisfying inputs faster than the naive classical search, which tries each possible input in some, possibly random, order. It is worth noting, howoever, that if sufficient classi... |

116 |
Bounds for the quantity of information transmitted by a quantum communication channel
- Holevo
- 1973
(Show Context)
Citation Context ...n [25, 26], and later by A. Holevo [27] and C. Helstrom [28]. A. Holevo introduced the idea of quantum communication channels and found bounds on their capacity for transmitting classical information =-=[29]-=-. Initially, most work focused on determining the physical limitations placed on classical information processing. The fact that pairs of two-level systems can have correlations not possible for class... |

104 | Sending entanglement through noisy quantum channels - Schumacher - 1996 |

96 | Demonstrating the viability of universal quantum computation using teleportation and single- qubit operations - Gottesman, Chuang - 1999 |

94 | Resilient quantum computation - Knill, Laflamme, et al. - 1998 |

84 |
Adaptive blind signal and image processing
- Cichocki, Amari
- 2002
(Show Context)
Citation Context ... is the base image, A is the image being blended into the base, i,j indicates the pixel coordinates, and 255 is the maximum possible pixel value (8 bits). Another method used by Constable and Spencer =-=[20]-=- for medical imaging is to use the square root of the sum of the squares (rms), written Fi,j = √ ( Âi,j) 2 + ( ˆ Bi,j) 2 , (3.2) where the hat (ˆ) indicates that the mean has been removed from A and B... |

78 | Efficient simulation of quantum systems by quantum computers
- Zalka
- 1998
(Show Context)
Citation Context ...n of general-purpose quantum computers. After 37such computers were formalized by Deutsch, the implementation of the emulation was generalized and refined by S. Lloyd [39], Wiesner [40] and C. Zalka =-=[41]-=-. The ability to emulate the evolution of quantum systems is actually widely used by classical “Monte-Carlo” algorithms for simulating physics, where the states amplitudes are, in effect, represented ... |

73 | 1999]: The Quantum Mechanics of Minds and Worlds - Barrett |

72 | The physical implementation of quantum computation - DiVincenzo |

67 |
Quantum Cryptography, or Unforgeable Subway Tokens advances in cryptography
- Bennett, Brassard, et al.
- 1983
(Show Context)
Citation Context ..., or information based on quantum mechanics, has capabilities that exceed those of traditional “classical” information. For example, in communication, quantum information enables quantum cryptography =-=[1, 2]-=-, which is a method for communicating in secret. Secrecy is guaranteed because eavesdropping attempts necessarily disturb the exchanged quantum information without revealing the content of the communi... |

59 | A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
- Abrams, Lloyd
- 1999
(Show Context)
Citation Context ...istical errors. How to efficiently implement measurements of these quantities has been the topic of more recent work in this area, much of which is based on variants of the phase estimation algorithm =-=[42, 43, 44, 45, 46]-=-. Although several researchers have suggested that there are interesting quantum physics simulations that can be implemented with well below 100 qubits, one of the interesting problems in this area of... |

59 | Quantum error correction with imperfect gates - Kitaev - 1997 |

57 | Theory of fault-tolerant quantum computation - Gottesman - 1998 |

57 | Dynamical decoupling of open quantum systems - Viola, Knill, et al. - 1999 |

55 | The Interpretation of quantum mechanics and the measurement process - Mittelstaedt - 1998 |

54 | Do we really understand quantum mechanics?. Strange correlations, paradoxes, and theorems - Laloë - 2012 |

50 | Semiclassical Fourier transform for quantum computation
- Griffiths, Niu
- 1996
(Show Context)
Citation Context ...twork works with two qubits representing the binary numbers from 0 to 3. Such a network is shown in Fig. 7. |u2∗a1+a0 〉 ⎧ ⎪⎨ H Z a0 ⎪⎩ −i H 1 2 3 4 Z a1 FIG. 7: The measured quantum Fourier transform =-=[20]-=- on two qubits representing the numbers 0, 1, 2, 3. If the input is one of the Fourier states |ua〉, where the binary digits of a are determined by a = 2∗a1+a0, then the measurement outcomes are a0 and... |

48 |
On the power of one bit of quantum information
- Knill, Laflamme
- 1998
(Show Context)
Citation Context ...istical errors. How to efficiently implement measurements of these quantities has been the topic of more recent work in this area, much of which is based on variants of the phase estimation algorithm =-=[42, 43, 44, 45, 46]-=-. Although several researchers have suggested that there are interesting quantum physics simulations that can be implemented with well below 100 qubits, one of the interesting problems in this area of... |

44 | Universal quantum computation using only projective measurement, quantum memory, and preparation of the |0 - Nielsen |

35 | The Problem of Measurement - Wigner - 1963 |

32 | Show-Through Cancellation in Scans of Duplex Printed Documents
- Sharma
- 2001
(Show Context)
Citation Context ... . . . . . . . . . . . 62 7.2 Most effective matched filters for different texts, listed in order of quality. . 63viii List of Figures Figure Page 1.1 Image cube representation of multispectral data =-=[1]-=-. . . . . . . . . . . . . . 1 1.2 Oxyrhynchus papyrus fragment 1822 original color photograph [6] and 950 nm MSI image [7]. Oxyrhynchus images c○ The Oxford Imaging Papyri Multi-spectral Laboratory an... |

32 | Nonlocal character of quantum theory - Stapp - 1997 |

29 |
Problem of equilibration and the computation of correlation functions on a quantum computer, Physical Review A 61(2
- Terhal, DiVincenzo
- 2000
(Show Context)
Citation Context ...istical errors. How to efficiently implement measurements of these quantities has been the topic of more recent work in this area, much of which is based on variants of the phase estimation algorithm =-=[42, 43, 44, 45, 46]-=-. Although several researchers have suggested that there are interesting quantum physics simulations that can be implemented with well below 100 qubits, one of the interesting problems in this area of... |

28 | Against “measurement”, in Sixty-Two Years of Uncertainty - Bell - 1990 |

27 |
Statistical problems in quantum physics
- Holevo
- 1973
(Show Context)
Citation Context ...g reversible computation, this cost can be avoided [24]. Limitations of measurement in quantum mechanics were investigated early by researchers such as J. von Neumann [25, 26], and later by A. Holevo =-=[27]-=- and C. Helstrom [28]. A. Holevo introduced the idea of quantum communication channels and found bounds on their capacity for transmitting classical information [29]. Initially, most work focused on d... |

27 | Consistent Quantum Theory (Cambridge - Griffiths - 2002 |

26 | Upper bounds on the size of quantum codes - Ashikhmin, Litsyn - 1999 |

25 | On randomization in sequential and distributed algorithms
- Gupta, Smolka, et al.
- 1994
(Show Context)
Citation Context ...n whether every probabilistic algorithm can be “derandomized” efficiently. There are important communication problems that can be solved probabilistically but not deterministically. For a survey, see =-=[10]-=-. What is the difference between bits, pbits and qubits? One way to visualize the difference and see the enrichment provided by pbits and qubits is shown in Fig. 1. 6Bit 0 Pbit 0 Qubit 0 1 States: 0 ... |

25 | Efficient fault-tolerant quantum computing - Steane - 1999 |

23 | Concatenated quantum codes - Knill, Laflamme - 1996 |

21 | Matching of double-sided document images to remove interference
- Wang, Tan
- 2001
(Show Context)
Citation Context ...presentation of multispectral data [1].2 with greater contrast between ink and parchment [2]. Infrared wavelengths have also been shown to enhance ancient murals, ceramics, and papyri by Ware et al. =-=[3,4]-=-. More recently an effort has been made to utilize the full MSI data cube to read the erased Archimedes Palimpsest [5]. Figure 1.2 illustrates the improvement infrared monospectral images have on the ... |

18 | Reduction of bleed-through in scanned manuscripts documents
- Dubois, Pathak
- 2001
(Show Context)
Citation Context ...ral images taken at the Thessaloniki Archaeological Museum, Thessalonike, Greece, October 2-10, 2006, by Gene A. Ware in conjuction with the Ancient Textual Imaging Group at Brigham Young University. =-=[2]-=- B. Zuckerman, “Bringing the Dead Sea Scrolls back to Life: a new evaluation of photographic and electric imaging of the Dead Sea Scrolls,” Dead Sea Discoveries, vol. 3, no. 2, pp. 178–207, 1996. [3] ... |

17 | Insolubility of the Quantum Measurement Problem for Unsharp Observables - Busch, Shimony - 1996 |

15 | Introduction to Quantum Error Correction
- Knill, Laflamme, et al.
- 207
(Show Context)
Citation Context ...esources. However, the cost of using only reversible operations is not negligible. In particular, for ease of programming, and more importantly, when performing repetitive error-correction tasks (see =-=[12]-=-), the inability to discard or reset qubits can be very inconvenient. We therefore introduce additional operations that enable resetting and discarding. Although resetting has a so-called “thermodynam... |

14 | Quantum algorithms for Fermionic simulations
- Ortiz, Gubernatis, et al.
(Show Context)
Citation Context |

14 | Constructing qubit in physical systems - Viola, Knill, et al. |

14 |
A multispectral imaging system for mapping of pigments in works of art by the use of principal-component analysis
- Baronti, Casini, et al.
- 1998
(Show Context)
Citation Context ...nsors and resolutions as with remote sensing [10, 12–14] and medical applications [15–17]. It has also been used in the photography field to combine images with multiple depths-of-field and exposures =-=[18,19]-=-. In surveillance and military operations, as well as remote sensing, fusion has been used to combine images from visual and thermal infrared sensors [20–22]. Image fusion can be performed at three pr... |

14 | On physics and philosophy - d’Espagnat - 2006 |

12 | An introduction to consistent quantum theory - Hohenberg |

11 | Symmetrical composite pulse sequences for NMR population inversion - Levitt |

10 | Introduction to NMR quantum information processing. xxx.lanl.gov
- Laflamme, Knill, et al.
- 2002
(Show Context)
Citation Context ...o the poles. This representation of qubit states is called the “Bloch sphere”. The explicit correspondence is discussed at the end of Sect. 2.7. See also the definition and use of the Bloch sphere in =-=[11]-=-. The correspondence between the pure states and the sphere is physically motivated and comes from a way of viewing a spin-1 system as a small quantum magnet. Intuitively, a state is determined by the... |

10 | Thresholds for linear optics quantum computation - Knill, Laflamme, et al. - 2000 |

9 | Implementation of the five qubit error correction benchmark - Knill, Laflamme, et al. |

9 | Consistent Resolution of Some Relativistic Quantum Paradoxes - Griffiths - 2002 |

8 |
From quantum, code-making to quantum code-breaking
- Ekert
- 1996
(Show Context)
Citation Context ...ly used public key cryptographic protocols relies on the conjectured difficulty of factoring large numbers. An elementary overview of these protocols and the quantum algorithm for breaking them is in =-=[15]-=-. Here, we outline the relationship between factoring and the powerful technique of phase estimation. This relationship helps in understanding many of the existing quantum algorithms and was first exp... |

8 | A nonlinear blind source separation solution for removing the show-through effect in the scanned documents
- Merrikh-Bayat, Babaie-Zadeh, et al.
- 2008
(Show Context)
Citation Context ...est. Techniques utilizing pixel-level fusion include arithmetic blending, principal component analysis (PCA), wavelets, filtering, hidden Markov models (HMM) [23], multiscale geometric analysis (MGA) =-=[16]-=-, independent component analysis (ICA) [24], statistical methods [25], and many more. Often these techniques are used together and may even include fusion rules at the feature and image level as well.... |

8 | The EPR Paradox, Bell’s Inequality and the Question of Locality - Blaylock |

7 |
Interpretation of tomography and spectroscopy as dual forms of quantum computations
- Miquel, Paz, et al.
(Show Context)
Citation Context |

6 | What Bell proved: A reply to Blaylock - Maudlin |

5 |
Elementary Number Theory: An Algebraic Approach
- Bolker
- 2007
(Show Context)
Citation Context ... an algorithm is considered efficient if it uses resources bounded by a polynomial in the number of digits of N. For more information on the requisite number theory, see any textbook on number theory =-=[18, 19]-=-. We begin by showing that factoring reduces to order finding. The first observation is that to factor a whole number it is sufficient to solve the factor-finding problem, whose statement is: Given a ... |

4 |
Conjugate coding. Sigact News, (original manuscript
- Wiesner
- 1969
(Show Context)
Citation Context ..., or information based on quantum mechanics, has capabilities that exceed those of traditional “classical” information. For example, in communication, quantum information enables quantum cryptography =-=[1, 2]-=-, which is a method for communicating in secret. Secrecy is guaranteed because eavesdropping attempts necessarily disturb the exchanged quantum information without revealing the content of the communi... |

4 |
The Computable and the Not Computable. Sovetskoye Radio
- Manin
- 1980
(Show Context)
Citation Context ...ret. Initially, the term “quantum computation” was mostly used to refer to classical computers realized using quantum mechanical systems. In the 1980s, P. Benioff [31], R. Feynman [3] and Y. I. Manin =-=[32]-=- introduced the idea of a quantum computer based on quantum information. They noted that the apparent exponential complexity of simulating quantum mechanics on a classical computer might be overcome i... |

4 | Introduction to quantum information processing - Knill, Laflamme, et al. - 2001 |

4 | Correlations in separated quantum systems: a consistent history analysis of the EPR problem - Griffiths - 1987 |

3 | Unpublished analysis of the accuracy threshold - Gottesman, Preskill - 1999 |

3 | Quantum repeaters for communication. quant-ph/9803056 - Briegel, Dür, et al. - 1998 |

3 |
Multispectral document enhancement: Ancient carbonized scrolls
- Ware, Chabries, et al.
- 2000
(Show Context)
Citation Context ...-specific. Common fusion rules are absolute minimum/maximum, average, addition, subtraction, and substitution. Different fusion rules can also be used for combining the high and low frequency details =-=[17]-=-. Area-based fusion rules are used to minimize the effect of noise on the fusion process [35]. An excellent review of fusion rules and concepts is given by Zhang and Blum [36]. An image fusion toolbox... |

2 |
Information is physical. Phys. Today, 44:22–29
- Landauer
- 1991
(Show Context)
Citation Context ...te and to process information. The recognition that usable types of information need to be physically realizable was repeatedly emphasized by R. Landauer who proclaimed that “information is physical” =-=[22]-=-. Beginning in the 1960s, R. Landauer studied the thermodynamic cost of irreversible operations in computation [23]. C. Bennett showed that by using reversible computation, this cost can be avoided [2... |

2 |
Measurement and reversibility
- Neumann
- 1932
(Show Context)
Citation Context ...]. C. Bennett showed that by using reversible computation, this cost can be avoided [24]. Limitations of measurement in quantum mechanics were investigated early by researchers such as J. von Neumann =-=[25, 26]-=-, and later by A. Holevo [27] and C. Helstrom [28]. A. Holevo introduced the idea of quantum communication channels and found bounds on their capacity for transmitting classical information [29]. Init... |

2 |
The measuring process
- Neumann
- 1932
(Show Context)
Citation Context ...]. C. Bennett showed that by using reversible computation, this cost can be avoided [24]. Limitations of measurement in quantum mechanics were investigated early by researchers such as J. von Neumann =-=[25, 26]-=-, and later by A. Holevo [27] and C. Helstrom [28]. A. Holevo introduced the idea of quantum communication channels and found bounds on their capacity for transmitting classical information [29]. Init... |

2 | Linear optics quantum computation i–v. Tutorial lectures, online at http://online.itp.ucsb.edu/qinfo01/knill{,1,2,3,4,5}/, (expand curly brackets for six links - Knill - 2001 |

1 | Mermin, “What’s wrong with this pillow?,” Phys - David - 1989 |