" Quantum gravity": an oxymoron
... scientist that definite reasons must be at the root of this failure. First of all, whereas “particles and fields exist within space-time, gravity is, in essence, space-time” [1]. This implies, in particular, that the physical meaning of the so-called critical (or “Planckian”) quantities M0 ≡ (~c/G)1 ...
... scientist that definite reasons must be at the root of this failure. First of all, whereas “particles and fields exist within space-time, gravity is, in essence, space-time” [1]. This implies, in particular, that the physical meaning of the so-called critical (or “Planckian”) quantities M0 ≡ (~c/G)1 ...
PowerPoint
... • Derivation of the key to Collapse Postulate from Axioms 1-3: explains why in general one cannot “find out” preexisting states. • Implies that observables are Hermitean (given an extra assumption that eigenvalues are real). • Proof similar to “no cloning theorem” -- information about preexisting st ...
... • Derivation of the key to Collapse Postulate from Axioms 1-3: explains why in general one cannot “find out” preexisting states. • Implies that observables are Hermitean (given an extra assumption that eigenvalues are real). • Proof similar to “no cloning theorem” -- information about preexisting st ...
First lecture, 7.10.03
... • This is one of the central features of quantum information which leads to secure (eavesdrop-proof) communications. • Crucial element: we must learn how to distinguish quantum states as well as possible -- and we must know how well a potential eavesdropper could do. If it gets through an H polarize ...
... • This is one of the central features of quantum information which leads to secure (eavesdrop-proof) communications. • Crucial element: we must learn how to distinguish quantum states as well as possible -- and we must know how well a potential eavesdropper could do. If it gets through an H polarize ...
8.4.2 Quantum process tomography 8.5 Limitations of the quantum
... z1 , z2 , , zm {1, 1} . Empirical average of these quantities, i zi / m , is an estimate for the true value of tr(Zρ). Central limit theorem ...
... z1 , z2 , , zm {1, 1} . Empirical average of these quantities, i zi / m , is an estimate for the true value of tr(Zρ). Central limit theorem ...
quantum channel capacity
... Alice wants to send qubits to Bob, via a noisy channel, e.g. a photon polarisation via an noisy optical fibre. Quantum Error Correction Codes can be used to reduce error (see Gottesman lectures). But this comes at a cost – each logical qubit is encoded in a larger number of physical qubits. The Comm ...
... Alice wants to send qubits to Bob, via a noisy channel, e.g. a photon polarisation via an noisy optical fibre. Quantum Error Correction Codes can be used to reduce error (see Gottesman lectures). But this comes at a cost – each logical qubit is encoded in a larger number of physical qubits. The Comm ...
Quantum Teleportation
... type. Both the sender and receiver keep only the qubits that were measured correctly, and they have now formed the key. If the bad guys intercept the transmission of photons, measure their polarizations, and then send them on to the receiver, they will inevitably introduce errors because they don't ...
... type. Both the sender and receiver keep only the qubits that were measured correctly, and they have now formed the key. If the bad guys intercept the transmission of photons, measure their polarizations, and then send them on to the receiver, they will inevitably introduce errors because they don't ...
A First Introduction to Quantum Behavior
... not imply lumpiness in space. To say as Feynman does that the particles “go everywhere” is not to picture them as trying out all the possibilities one at a time. Part of the essence of “being a particle”, namely its continuing existence at a succession of places and times, has been taken away. Waves ...
... not imply lumpiness in space. To say as Feynman does that the particles “go everywhere” is not to picture them as trying out all the possibilities one at a time. Part of the essence of “being a particle”, namely its continuing existence at a succession of places and times, has been taken away. Waves ...
What Could You Do With A Quantum Computer?
... program to follow out...and I'm not happy with all the analyses that go with just the classical theory, because nature isn’t classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem because it doesn't look so ea ...
... program to follow out...and I'm not happy with all the analyses that go with just the classical theory, because nature isn’t classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem because it doesn't look so ea ...
Document
... Imagine describing an electron in a superposition of up and down spin projection states and an electron spinning both up and down! Quantum mechanically it has a spin projection orthogonal (geometric) to being up or down. ...
... Imagine describing an electron in a superposition of up and down spin projection states and an electron spinning both up and down! Quantum mechanically it has a spin projection orthogonal (geometric) to being up or down. ...
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.