Imaging single photons in non-separable states of polarization and spatial mode
... projected the polarization before we projected the position. For projecting the position we had a large-area (20 mm diameter) fiber collimator connected to a multimode fiber. This effectively acted as a bucket detector. Before it we had an adjustable iris that was scanned in a two dimensional plane v ...
... projected the polarization before we projected the position. For projecting the position we had a large-area (20 mm diameter) fiber collimator connected to a multimode fiber. This effectively acted as a bucket detector. Before it we had an adjustable iris that was scanned in a two dimensional plane v ...
Analysis of Literature: Quantum Computer Programming
... extension quantum computing. In Dirac notation vectors are expressed using “kets”. So the vector “a” would be expressed as a . Dual vectors are expressed using “bras” so the dual vector “b” would be expressed as b . In the quantum coin toss example laid out later in this section, “heads” and “tails” ...
... extension quantum computing. In Dirac notation vectors are expressed using “kets”. So the vector “a” would be expressed as a . Dual vectors are expressed using “bras” so the dual vector “b” would be expressed as b . In the quantum coin toss example laid out later in this section, “heads” and “tails” ...
Mutually Unbiased bases: a brief survey
... be free of some statistical error. Two questions arise at this point: Given a measurement and assuming an initial probability distribution for the unknown state how can we extract an estimate for the density matrix? What are the measurements that minimize the statistical error? Complete collections ...
... be free of some statistical error. Two questions arise at this point: Given a measurement and assuming an initial probability distribution for the unknown state how can we extract an estimate for the density matrix? What are the measurements that minimize the statistical error? Complete collections ...
Basic concepts of vectors
... Figure 1. A force is a vector quantity. Applying the force in a different direction will achieve a different effect. In order to specify the force completely we must state not only its magnitude (its ‘strength’) but also the direction in which the force acts. For example we might state that ‘a force of ...
... Figure 1. A force is a vector quantity. Applying the force in a different direction will achieve a different effect. In order to specify the force completely we must state not only its magnitude (its ‘strength’) but also the direction in which the force acts. For example we might state that ‘a force of ...
Chapter 11 The Uniform Plane Wave
... these media, but it is not necessary to use a separate treatment; it is possible (and not very difficult) to solve the general problem once and for all. To consider wave motion in free space first, Maxwell's equations may be written in terms of E and H only as @E @t @H ...
... these media, but it is not necessary to use a separate treatment; it is possible (and not very difficult) to solve the general problem once and for all. To consider wave motion in free space first, Maxwell's equations may be written in terms of E and H only as @E @t @H ...
Classical vs Quantum Information - UMD Math
... A simplex has the rather special property that any state (probability distribution) can be represented in one and only one way as a mixture of extremal states, the vertices of the simplex. No other state space has this feature: if the state space is not a simplex, the representation of mixed states ...
... A simplex has the rather special property that any state (probability distribution) can be represented in one and only one way as a mixture of extremal states, the vertices of the simplex. No other state space has this feature: if the state space is not a simplex, the representation of mixed states ...
Entanglement and Quantum Cryptography
... applications. The present thesis covers several topics on quantum cryptography, such as the security analysis of quantum channels for key distribution protocols and the study of quantum cloning. First, we introduce a general formalism to characterize the cryptographic properties of quantum channels ...
... applications. The present thesis covers several topics on quantum cryptography, such as the security analysis of quantum channels for key distribution protocols and the study of quantum cloning. First, we introduce a general formalism to characterize the cryptographic properties of quantum channels ...
QUANTUM STATES, ENTANGLEMENT and CLOSED TIMELIKE
... ρ = ρS = TrA (|ΨiSA hΨ|), where |ΨiSA = k pk |ψk iS |φk iA . • There is no way to differentiate a proper mixture from improper. Given any density matrix we can always purify it in an enlarged Hilbert space (in infinite number of ways). • Purified state is independent of interaction and other extrane ...
... ρ = ρS = TrA (|ΨiSA hΨ|), where |ΨiSA = k pk |ψk iS |φk iA . • There is no way to differentiate a proper mixture from improper. Given any density matrix we can always purify it in an enlarged Hilbert space (in infinite number of ways). • Purified state is independent of interaction and other extrane ...
Certainty relations, mutual entanglement, and nondisplaceable
... with special φ (j ) -dependent internal unitaries Yj allowing for different right phase gates, but the situation described by Corollary 3 seems to be generic. We note in passing that the concept of mutual coherence is related to nonextensibility of mutually unbiased bases [51]. The set of MUBs is ca ...
... with special φ (j ) -dependent internal unitaries Yj allowing for different right phase gates, but the situation described by Corollary 3 seems to be generic. We note in passing that the concept of mutual coherence is related to nonextensibility of mutually unbiased bases [51]. The set of MUBs is ca ...
Optical probing of spin fluctuations of a single paramagnetic Mn
... curves, we compare the experimental data with a rateequation model describing the time evolution of the population of the 24 X-Mn spin levels 关Fig. 1共c兲兴 after the injection of a single exciton.14 Different spin-flip times are expected depending on whether the transitions occur with or without conse ...
... curves, we compare the experimental data with a rateequation model describing the time evolution of the population of the 24 X-Mn spin levels 关Fig. 1共c兲兴 after the injection of a single exciton.14 Different spin-flip times are expected depending on whether the transitions occur with or without conse ...
Quantum technology: the second quantum revolution
... (v) Entanglement: the superposition principle applied to certain non-local correlations. If a correlation can be realized in two or more indistinguishable ways, the state of the system is a superposition of all such correlations simultaneously. (vi) Decoherence: what happens to quantum superposition ...
... (v) Entanglement: the superposition principle applied to certain non-local correlations. If a correlation can be realized in two or more indistinguishable ways, the state of the system is a superposition of all such correlations simultaneously. (vi) Decoherence: what happens to quantum superposition ...
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.