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... and operator algebras defined over such spaces. From a current physics perspective, von Neumann’ s approach to quantum mechanics has however done much more: it has not only paved the way to expanding the role of symmetry in physics, as for example with the Wigner-Eckhart theorem and its applications ...
... and operator algebras defined over such spaces. From a current physics perspective, von Neumann’ s approach to quantum mechanics has however done much more: it has not only paved the way to expanding the role of symmetry in physics, as for example with the Wigner-Eckhart theorem and its applications ...
Topological Coherence and Decoherence
... We are interested in topological field theories because they possess ‘hidden’ topological quantum numbers which are conserved even when the system is subject to quite severe perturbations. A model of central interest is the ‘dissipative W.A.H. model’ (named after Wannier, Az’bel, & Hofstadter’). Thi ...
... We are interested in topological field theories because they possess ‘hidden’ topological quantum numbers which are conserved even when the system is subject to quite severe perturbations. A model of central interest is the ‘dissipative W.A.H. model’ (named after Wannier, Az’bel, & Hofstadter’). Thi ...
The Blind Men and the Quantum
... Malus and Furry An EPR Experiment measures the correlated polarizations of a pair of entangled photons, obeying Malus’ Law [P(qrel) = Cos2qrel] The measurement gives the same result as if both filters were in the same arm. Furry proposed to place both photons in the same random polarization state. T ...
... Malus and Furry An EPR Experiment measures the correlated polarizations of a pair of entangled photons, obeying Malus’ Law [P(qrel) = Cos2qrel] The measurement gives the same result as if both filters were in the same arm. Furry proposed to place both photons in the same random polarization state. T ...
Lundeen PRL 102, 020..
... rotation. In this experiment, we reduce this disturbance by rotating the photon’s polarization by only 20 , reducing g fourfold, and thereby performing a weak measurement. The trade-off is that it is now impossible to know through which arm a particular detected photon went. Instead, we measure the ...
... rotation. In this experiment, we reduce this disturbance by rotating the photon’s polarization by only 20 , reducing g fourfold, and thereby performing a weak measurement. The trade-off is that it is now impossible to know through which arm a particular detected photon went. Instead, we measure the ...
As we know, the measurement of a static (specific
... some detail. As we know, the measurement of a static (specific) property M such as mass always returns the same results. This fact is unproblematic, and if all observables exhibited this characteristic, as far as value determinism is concerned standard quantum mechanics would be on a par with classi ...
... some detail. As we know, the measurement of a static (specific) property M such as mass always returns the same results. This fact is unproblematic, and if all observables exhibited this characteristic, as far as value determinism is concerned standard quantum mechanics would be on a par with classi ...
Lecture02
... • The hypothesis is that it is equally probable (equally likely) that the system is in ANY ONE of it’s accessible states. • This postulate is reasonable & doesn’t contradict any laws of mechanics (classical or quantum). Is it correct? • That can only be confirmed by checking theoretical predictions ...
... • The hypothesis is that it is equally probable (equally likely) that the system is in ANY ONE of it’s accessible states. • This postulate is reasonable & doesn’t contradict any laws of mechanics (classical or quantum). Is it correct? • That can only be confirmed by checking theoretical predictions ...
Error Free Quantum Reading by Quasi Bell State of Entangled
... speed of several hundred Mbit/sec under very small energy. If proposals of quantum technologies can provide a potential in principle such performances, these may deserve to investigate. Here, we are concerned with investigation on a potential of quantum reading from digital memories. The classical r ...
... speed of several hundred Mbit/sec under very small energy. If proposals of quantum technologies can provide a potential in principle such performances, these may deserve to investigate. Here, we are concerned with investigation on a potential of quantum reading from digital memories. The classical r ...
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... If one calls a commutant of a set A the special set of bounded operators on L(H) which commute with all elements in A, then this second condition implies that the commutant of the commutant of A is again the set A. On the other hand, a von Neumann algebra A inherits a unital subalgebra from L(H), an ...
... If one calls a commutant of a set A the special set of bounded operators on L(H) which commute with all elements in A, then this second condition implies that the commutant of the commutant of A is again the set A. On the other hand, a von Neumann algebra A inherits a unital subalgebra from L(H), an ...
Simple alternative model of the dual nature of light
... single or starved photon regime, even if a particle-like behavior would be in agreement with the herein described model where photons and light quanta are considered as different objects. For now, reversing Dirac’s famous statement is just a hypothesis that could clarify some apparent paradoxes, par ...
... single or starved photon regime, even if a particle-like behavior would be in agreement with the herein described model where photons and light quanta are considered as different objects. For now, reversing Dirac’s famous statement is just a hypothesis that could clarify some apparent paradoxes, par ...
March meeting 2006 on non-abelian statistics
... model. The degrees of freedom are an Ising spin on the links of a square lattice. The potential is chosen to require that in the ground state, there must be an even number of spins up touching each vertex. ...
... model. The degrees of freedom are an Ising spin on the links of a square lattice. The potential is chosen to require that in the ground state, there must be an even number of spins up touching each vertex. ...
6 Compact quantum spaces: “fuzzy spaces”
... However, up to now there is no consistent quantum theory of all fundamental interactions including gravity. There are many reasons to expect some sort of quantum structure of space-time at very short distances, notably at the Planck scale. We will discuss a possible mathematical realization of such ...
... However, up to now there is no consistent quantum theory of all fundamental interactions including gravity. There are many reasons to expect some sort of quantum structure of space-time at very short distances, notably at the Planck scale. We will discuss a possible mathematical realization of such ...
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.