Elementary Particle Mixing for Maximum Channel Capacity in Measured Decays
... The purification in Eq. (12) uses a ’reservoir’ {Σ0 , Λ0 } that replicates the number of basis elements in the original system. The reservoir elements interact with neither the system nor the environment. It is interesting to consider the Cabibbo rotation between weakly interacting quarks as a purif ...
... The purification in Eq. (12) uses a ’reservoir’ {Σ0 , Λ0 } that replicates the number of basis elements in the original system. The reservoir elements interact with neither the system nor the environment. It is interesting to consider the Cabibbo rotation between weakly interacting quarks as a purif ...
The fractional quantum Hall effect in wide quantum wells
... freedom. The second subband hosts another two-dimensional electron system that may interact with the one in the first subband and charge may be transferred from one to the other. Here, we have investigated the fractional quantum Hall states and in particular the 5/2-state under these conditions in a ...
... freedom. The second subband hosts another two-dimensional electron system that may interact with the one in the first subband and charge may be transferred from one to the other. Here, we have investigated the fractional quantum Hall states and in particular the 5/2-state under these conditions in a ...
Realization of the Quantum Toffoli Gate with Trapped Ions
... The factor expði 2p1 ffiffi2 Z;t Þ, with the Pauli operator Z , is a phase shift on the target qubit jti. This phase factor can either be included in a redefinition of the computational basis or compensated for by single qubit operations. In total, this unitary evolution is fully equivalent to an id ...
... The factor expði 2p1 ffiffi2 Z;t Þ, with the Pauli operator Z , is a phase shift on the target qubit jti. This phase factor can either be included in a redefinition of the computational basis or compensated for by single qubit operations. In total, this unitary evolution is fully equivalent to an id ...
How Quantum Computers Fail - Einstein Institute of Mathematics
... based on the individual qubits.) In contrast, we can regard the subspace of bosonic states as a quantum code, and the type of noise we expect amounts to having a mixed state between the intended bosonic state and other bosonic states. Such a noise does not exhibit a strong dependence on the computa ...
... based on the individual qubits.) In contrast, we can regard the subspace of bosonic states as a quantum code, and the type of noise we expect amounts to having a mixed state between the intended bosonic state and other bosonic states. Such a noise does not exhibit a strong dependence on the computa ...
Angular Momentum in Quantum Mechanics
... This means that it is possible to obtain solutions to Schrödinger equation (Equation 60) which are common eigenfunctions of Ĥ, L2 and Lz . We already know simultaneous eigenfunctions of L2 and Lz : these are of course the spherical harmonics, Ylm (θ, φ). Thus, a full solution to Schrödinger equat ...
... This means that it is possible to obtain solutions to Schrödinger equation (Equation 60) which are common eigenfunctions of Ĥ, L2 and Lz . We already know simultaneous eigenfunctions of L2 and Lz : these are of course the spherical harmonics, Ylm (θ, φ). Thus, a full solution to Schrödinger equat ...
STUDY ON THE WAVE NATURE OF THE REST MASS
... the matter wave is a real physical wave, it must either be associated with the oscillation of the EM field, or with a unified field that behaves like the EM field in long distance. Like the Standard Model, we also think that the EM, weak and strong interactions can be unified into a single field. If ...
... the matter wave is a real physical wave, it must either be associated with the oscillation of the EM field, or with a unified field that behaves like the EM field in long distance. Like the Standard Model, we also think that the EM, weak and strong interactions can be unified into a single field. If ...
Kinetic Theory - damtp - University of Cambridge
... enough then it will eventually relax down to equilibrium. (This is sometimes said to be the −1th law of thermodynamics). Of course, this begs the question of why equilibrium is special. Why do all systems eventually reach this state. How do they approach this state? How does such irreversible behavi ...
... enough then it will eventually relax down to equilibrium. (This is sometimes said to be the −1th law of thermodynamics). Of course, this begs the question of why equilibrium is special. Why do all systems eventually reach this state. How do they approach this state? How does such irreversible behavi ...
Quantum Proofs for Classical Theorems
... This tensor product of states |φ i and |ψi is also often denoted simply as |φ i|ψi. Note that this new state is a unit vector, as it should be. Not every pure state in Cmn can be expressed as a tensor product in this way; √ those that cannot are called entangled. The best-known entangled state is th ...
... This tensor product of states |φ i and |ψi is also often denoted simply as |φ i|ψi. Note that this new state is a unit vector, as it should be. Not every pure state in Cmn can be expressed as a tensor product in this way; √ those that cannot are called entangled. The best-known entangled state is th ...
Ultrafast geometric control of a single qubit using chirped pulses
... vector turns about the effective field vector Ω1 (about the x-axis); it stays in the y, z-plane all the time and points in the −z (z)-direction at the end of the pulse. Due to the second π-pulse, the population is transferred back to the initial state |0i (|1i); therefore the Bloch vector returns to ...
... vector turns about the effective field vector Ω1 (about the x-axis); it stays in the y, z-plane all the time and points in the −z (z)-direction at the end of the pulse. Due to the second π-pulse, the population is transferred back to the initial state |0i (|1i); therefore the Bloch vector returns to ...
using standard pra s
... used for the atom-field interaction Hamiltonian. Then the above expressions are valid for the diagonal matrix elements of the atom-field interaction, but in this case all the sublevels of the degenerate state should be excluded from the sum for the reduced Green function 共5兲 共see, e.g., 关14兴兲. In vi ...
... used for the atom-field interaction Hamiltonian. Then the above expressions are valid for the diagonal matrix elements of the atom-field interaction, but in this case all the sublevels of the degenerate state should be excluded from the sum for the reduced Green function 共5兲 共see, e.g., 关14兴兲. In vi ...
Excitation of an Atomic Electron to a Coherent Superposition of
... is one of the signatures of this type of coherent superposition state. Two particularly dramatic state distributions occur for the so called even and odd coherent states, jal 1 j 2 al and jal 2 j 2 al, respectively. The even coherent state contains only even eigenstates jnl, and the odd state is a s ...
... is one of the signatures of this type of coherent superposition state. Two particularly dramatic state distributions occur for the so called even and odd coherent states, jal 1 j 2 al and jal 2 j 2 al, respectively. The even coherent state contains only even eigenstates jnl, and the odd state is a s ...
Quantum Phenomena Modeled by Interactions between Many
... the guiding wave, which has no source but which occupies the entire configuration space. This makes it challenging to give an ontology for the wave function in parts of configuration space so remote from the “real” configuration that it will never affect its trajectory (a nice analogy can be found i ...
... the guiding wave, which has no source but which occupies the entire configuration space. This makes it challenging to give an ontology for the wave function in parts of configuration space so remote from the “real” configuration that it will never affect its trajectory (a nice analogy can be found i ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.