1 = A
... J2 is the Casimir operator, which commutes with unit operator. In general case several Casimir operators may be constructed from group generators. Usually Casimir operators explicitly enter the Hamiltonian. In particular, one may use J2 instead of Δ . In some special cases Casimir operators do not e ...
... J2 is the Casimir operator, which commutes with unit operator. In general case several Casimir operators may be constructed from group generators. Usually Casimir operators explicitly enter the Hamiltonian. In particular, one may use J2 instead of Δ . In some special cases Casimir operators do not e ...
Atom InterferometryPrecision D. E. Pritchard
... diffraction grating. In this case, loss of contrast still occurs, but less abruptly as a function of separation, and this de-phasing arises from a qualitatively different reason. The atom’s own longitudinal momentum plays the role of the environment. This mechanism may not qualify as quantum decoher ...
... diffraction grating. In this case, loss of contrast still occurs, but less abruptly as a function of separation, and this de-phasing arises from a qualitatively different reason. The atom’s own longitudinal momentum plays the role of the environment. This mechanism may not qualify as quantum decoher ...
The Meaning of Elements of Reality and Quantum Counterfactuals
... particles have opposite values,’’ in the example discussed above. Priorities ( 1) and ( 3) are not relevant because violations of physical laws are not considered. The counterfactual worlds are different from the actual world not because of ``miracles,’’ i.e., violations of physical laws, but becaus ...
... particles have opposite values,’’ in the example discussed above. Priorities ( 1) and ( 3) are not relevant because violations of physical laws are not considered. The counterfactual worlds are different from the actual world not because of ``miracles,’’ i.e., violations of physical laws, but becaus ...
Quantum Entanglements and Hauntological Relations of Inheritance
... emit photons when their electrons ‘jump’ from one level to another. In particular, when an electron jumps from a higher energy state to a lower one it emits a photon whose colour/frequency is determined by the size of the jump, i.e., the change in energy. In this way, there is no continuous draining ...
... emit photons when their electrons ‘jump’ from one level to another. In particular, when an electron jumps from a higher energy state to a lower one it emits a photon whose colour/frequency is determined by the size of the jump, i.e., the change in energy. In this way, there is no continuous draining ...
Precision spectroscopy using quantum superposition of atomic levels
... superposition of two states, and in this way memory and processing capabilities of quantum computers exponentially increase with the number of qubits. Quantum entanglement is also important for quantum computation and quantum cryptography. Such states in quantum metrology significantly improve the si ...
... superposition of two states, and in this way memory and processing capabilities of quantum computers exponentially increase with the number of qubits. Quantum entanglement is also important for quantum computation and quantum cryptography. Such states in quantum metrology significantly improve the si ...
Realization of the Cirac–Zoller controlled
... using NMR techniques, complex quantum algorithms such as Shor’s factorizing algorithm10 employing seven qubits have been demonstrated11. In NMR systems qubits are encoded in mixed states and ensemble measurements reveal the computational output. Thus, NMR implementations of a QC are not scalable in ...
... using NMR techniques, complex quantum algorithms such as Shor’s factorizing algorithm10 employing seven qubits have been demonstrated11. In NMR systems qubits are encoded in mixed states and ensemble measurements reveal the computational output. Thus, NMR implementations of a QC are not scalable in ...
Quantum Chaos
... the energy levels and eigenstates of the (bound) system? For an open system, in the decay rates, in the Smatrix, in the transport properties? (lectures 1 and 2) What kind of semiclassical approximations can be used? (lecture 2) What is the longtime behaviour of a quantum system? (lecture 3) For a ...
... the energy levels and eigenstates of the (bound) system? For an open system, in the decay rates, in the Smatrix, in the transport properties? (lectures 1 and 2) What kind of semiclassical approximations can be used? (lecture 2) What is the longtime behaviour of a quantum system? (lecture 3) For a ...
while (M) P
... • Branching programs are composed measurements A program if (M) P can be interpreted as the experiment measuring M and then executing the program P if M yielded the outcome true. This experiment can be expressed as a measurement in a straightforward manner: if Mi denotes the superoperator describing ...
... • Branching programs are composed measurements A program if (M) P can be interpreted as the experiment measuring M and then executing the program P if M yielded the outcome true. This experiment can be expressed as a measurement in a straightforward manner: if Mi denotes the superoperator describing ...
Theory and simulations of quantum glass forming liquids
... slowdown of dynamics when a liquid transforms into a glass is still a subject of great debate.1–4 Essentially all discussion of the glass transition has focused on the strictly classical regime of liquid state behavior, namely where the de Broglie wavelength is significantly smaller than the particl ...
... slowdown of dynamics when a liquid transforms into a glass is still a subject of great debate.1–4 Essentially all discussion of the glass transition has focused on the strictly classical regime of liquid state behavior, namely where the de Broglie wavelength is significantly smaller than the particl ...
"Liquid-State NMR Quantum Computing" in
... required resources grow with the problem size. A particularly important criterion is whether the required resources increase exponentially or polynomially with the problem size. Exponentially difficult problems are considered intractable – they become simply impossible to solve when the problem size ...
... required resources grow with the problem size. A particularly important criterion is whether the required resources increase exponentially or polynomially with the problem size. Exponentially difficult problems are considered intractable – they become simply impossible to solve when the problem size ...
- Natural Sciences Publishing
... vanishes in the asymptotic limit, this means that in this region (N(ρ ) = 0) the entanglement between the atom and the field is completely destroyed, and the total state of the system disentangled in a finite time and goes to a vacuum state. Finally, Fig. 2(c) presents the von Neumman entropy S(ρ ) ...
... vanishes in the asymptotic limit, this means that in this region (N(ρ ) = 0) the entanglement between the atom and the field is completely destroyed, and the total state of the system disentangled in a finite time and goes to a vacuum state. Finally, Fig. 2(c) presents the von Neumman entropy S(ρ ) ...
56 COPYRIGHT 2006 SCIENTIFIC AMERICAN, INC.
... great real-world importance. For example, certain widely used encryption methods could be cracked given a computer capable of breaking a large number into its component factors within a reasonable length of time. Virtually all encryption methods used for highly sensitive data are vulnerable to one q ...
... great real-world importance. For example, certain widely used encryption methods could be cracked given a computer capable of breaking a large number into its component factors within a reasonable length of time. Virtually all encryption methods used for highly sensitive data are vulnerable to one q ...
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... have a similarly intricate structure and that the Universe is trapped forever in this subset of all possible states. This might help to explain why the Universe at the quantum level seems so bizarre. For example, it may point to a natural explanation for one of the biggest puzzles of Quantum Physics ...
... have a similarly intricate structure and that the Universe is trapped forever in this subset of all possible states. This might help to explain why the Universe at the quantum level seems so bizarre. For example, it may point to a natural explanation for one of the biggest puzzles of Quantum Physics ...
Quantum numbers for relative ground states of antiferromagnetic
... Rigorous results on spin systems like the MarshallPeierls sign rule1 and the famous theorems of Lieb, Schultz, and Mattis2,3 have sharpened our understanding of magnetic phenomena. They also serve as a theoretical input for quantum computing with spin systems.4–6 Exact diagonalization methods yield ...
... Rigorous results on spin systems like the MarshallPeierls sign rule1 and the famous theorems of Lieb, Schultz, and Mattis2,3 have sharpened our understanding of magnetic phenomena. They also serve as a theoretical input for quantum computing with spin systems.4–6 Exact diagonalization methods yield ...
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.