Quantum Mechanics - Nanyang Technological University
... Quantum Mechanics was born in 1925 and 1926 and by the time of the famous fifth Solvay Meeting in Brussels in 1927, much of the groundwork had been done. Those two years are perhaps the most dynamic years in the history of science. When we now look back at Quantum Mechanics ninety years later, we fi ...
... Quantum Mechanics was born in 1925 and 1926 and by the time of the famous fifth Solvay Meeting in Brussels in 1927, much of the groundwork had been done. Those two years are perhaps the most dynamic years in the history of science. When we now look back at Quantum Mechanics ninety years later, we fi ...
Six easy roads to the Planck scale
... concept loses validity. Specifically the six thought experiments involve viewing a particle with a microscope, measuring a spatial distance with a light pulse, squeezing a system into a very small volume, observing the energy in a small volume, measuring the energy density of the gravitational field ...
... concept loses validity. Specifically the six thought experiments involve viewing a particle with a microscope, measuring a spatial distance with a light pulse, squeezing a system into a very small volume, observing the energy in a small volume, measuring the energy density of the gravitational field ...
Hidden Markov Model Cryptanalysis
... Sequence of hidden, probabilistic states (S) Corresponding observable outputs (O) Each state is independent of every other (memoryless) P (S1 = x1) ...
... Sequence of hidden, probabilistic states (S) Corresponding observable outputs (O) Each state is independent of every other (memoryless) P (S1 = x1) ...
PEPS, matrix product operators and the Bethe ansatz
... • Size of Hilbert space of system of N particles / modes / … scales exponentially with N. – What is the fraction of states that are physical, i.e. can be created as low-energy states of local Hamiltonians or by a quantum computer in poly time? Exponentially small !!! – Ground states (and low-energy ...
... • Size of Hilbert space of system of N particles / modes / … scales exponentially with N. – What is the fraction of states that are physical, i.e. can be created as low-energy states of local Hamiltonians or by a quantum computer in poly time? Exponentially small !!! – Ground states (and low-energy ...
Subjective Bayesian probabilities
... Subjective Bayesian answer We trust quantum over classical coin tossing because an insider attack on classical coin tossing can never be ruled out, whereas the beliefs that lead to a pure-state assignment are inconsistent with any other party’s being able to launch an insider attack. ...
... Subjective Bayesian answer We trust quantum over classical coin tossing because an insider attack on classical coin tossing can never be ruled out, whereas the beliefs that lead to a pure-state assignment are inconsistent with any other party’s being able to launch an insider attack. ...
Average-Case Quantum Query Complexity
... The above treatment of average-case complexity is the standard one used in average-case analysis of algorithms [19]. One counter-intuitive consequence of these de nitions, however, is that the average-case performance of polynomially related algorithms can be superpolynomially apart (we will see thi ...
... The above treatment of average-case complexity is the standard one used in average-case analysis of algorithms [19]. One counter-intuitive consequence of these de nitions, however, is that the average-case performance of polynomially related algorithms can be superpolynomially apart (we will see thi ...
SEGUNDO WORKSHOP INFORMACIÌN CUÊNTICA EN ESPAÑA
... in quantum information science [1]. In particular they enable to interface stationary quantum bits (encoded in atom-like systems) and flying qubits (encoded in photons). QMs are for example needed for the implementation of ultra-long distance quantum communication using quantum repeater architecture ...
... in quantum information science [1]. In particular they enable to interface stationary quantum bits (encoded in atom-like systems) and flying qubits (encoded in photons). QMs are for example needed for the implementation of ultra-long distance quantum communication using quantum repeater architecture ...
PPT2
... and duraction j = / j. This leads to an excitation probability P(q) shown right. With increasing pulse duraction the region of excitation is narrowed down. All momenta q except those with q¼0 are excited. By using Blackman pulses a more box like (inverted Fermi profile) of excitation probabiliti ...
... and duraction j = / j. This leads to an excitation probability P(q) shown right. With increasing pulse duraction the region of excitation is narrowed down. All momenta q except those with q¼0 are excited. By using Blackman pulses a more box like (inverted Fermi profile) of excitation probabiliti ...
6.1. Elliptic Curve Cryptography
... The purpose of cryptography is to transmit information in such a way that access to it is restricted entirely to the intended recipient. Originally the security of a cryptotext depended on the secrecy of the entire encrypting and decrypting procedures; however, today we use ciphers for which the alg ...
... The purpose of cryptography is to transmit information in such a way that access to it is restricted entirely to the intended recipient. Originally the security of a cryptotext depended on the secrecy of the entire encrypting and decrypting procedures; however, today we use ciphers for which the alg ...
Coherent interaction of spins induced by thermal bosonic
... the two-qubit dynamics. We do not include possible other twoqubit interactions in such comparative calculation of dynamical quantities. The overall system is described by the Hamiltonian H = HS + HB + HSB . Let us point out that such a model is quite general and it also finds applications, for instan ...
... the two-qubit dynamics. We do not include possible other twoqubit interactions in such comparative calculation of dynamical quantities. The overall system is described by the Hamiltonian H = HS + HB + HSB . Let us point out that such a model is quite general and it also finds applications, for instan ...
Experimental nonlocal and surreal Bohmian trajectories
... has no autonomous hidden variable assigned to it in standard Bohmian mechanics. [In some extensions to Bohmian mechanics, autonomous hidden variables are assigned to degrees of freedom other than position, such as spin (19). See Hiley and Callaghan (20) for a discussion in the context of the origina ...
... has no autonomous hidden variable assigned to it in standard Bohmian mechanics. [In some extensions to Bohmian mechanics, autonomous hidden variables are assigned to degrees of freedom other than position, such as spin (19). See Hiley and Callaghan (20) for a discussion in the context of the origina ...
6 Theory of the topological Anderson insulator
... We will now show that disorder can push the phase transition to positive values of m, which is the hallmark of a TAI. Qualitatively, the mechanism is as follows. Elastic scattering by a disorder potential causes states of definite momentum to decay exponentially as a function of space and time. The ...
... We will now show that disorder can push the phase transition to positive values of m, which is the hallmark of a TAI. Qualitatively, the mechanism is as follows. Elastic scattering by a disorder potential causes states of definite momentum to decay exponentially as a function of space and time. The ...
Document
... Radial part of hydrogen wave function Rnl(r) Radial part of the wave function for n=1, n=2, n=3. x-axis is in units of the Bohr radius aB. Number of radial nodes (R(r) crosses x-axis or |R(r)|2 goes to 0) is equal to n−ℓ-1 Quantum number m has no affect on the radial part of the wave function. ...
... Radial part of hydrogen wave function Rnl(r) Radial part of the wave function for n=1, n=2, n=3. x-axis is in units of the Bohr radius aB. Number of radial nodes (R(r) crosses x-axis or |R(r)|2 goes to 0) is equal to n−ℓ-1 Quantum number m has no affect on the radial part of the wave function. ...
Quantum key distribution
Quantum key distribution (QKD) uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages. It is often incorrectly called quantum cryptography, as it is the most well known example of the group of quantum cryptographic tasks.An important and unique property of quantum key distribution is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key. This results from a fundamental aspect of quantum mechanics: the process of measuring a quantum system in general disturbs the system. A third party trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies. By using quantum superpositions or quantum entanglement and transmitting information in quantum states, a communication system can be implemented which detects eavesdropping. If the level of eavesdropping is below a certain threshold, a key can be produced that is guaranteed to be secure (i.e. the eavesdropper has no information about it), otherwise no secure key is possible and communication is aborted.The security of encryption that uses quantum key distribution relies on the foundations of quantum mechanics, in contrast to traditional public key cryptography which relies on the computational difficulty of certain mathematical functions, and cannot provide any indication of eavesdropping at any point in the communication process, or any mathematical proof as to the actual complexity of reversing the one-way functions used. QKD has provable security based on information theory, and forward secrecy.Quantum key distribution is only used to produce and distribute a key, not to transmit any message data. This key can then be used with any chosen encryption algorithm to encrypt (and decrypt) a message, which can then be transmitted over a standard communication channel. The algorithm most commonly associated with QKD is the one-time pad, as it is provably secure when used with a secret, random key. In real world situations, it is often also used with encryption using symmetric key algorithms like the Advanced Encryption Standard algorithm. In the case of QKD this comparison is based on the assumption of perfect single-photon sources and detectors, that cannot be easily implemented.