draft
... von Neumann’s entropy is older than Shannon’s, and it reduces to the Shannon entropy for diagonal density matrices. But in general the von Neumann entropy is a subtler object than its classical counterpart. So is the quantum relative entropy, that depends on two density matrices that perhaps cannot ...
... von Neumann’s entropy is older than Shannon’s, and it reduces to the Shannon entropy for diagonal density matrices. But in general the von Neumann entropy is a subtler object than its classical counterpart. So is the quantum relative entropy, that depends on two density matrices that perhaps cannot ...
Quantum Computation: a Tutorial
... is a vector of norm 1. A basis is a pair of vectors u and v that can generates the whole space when linearly combined. The basis is orthonormal if u and v are normalized and orthogonal. For example, ( 10 ) and ( 01 ) form an orthonormal ...
... is a vector of norm 1. A basis is a pair of vectors u and v that can generates the whole space when linearly combined. The basis is orthonormal if u and v are normalized and orthogonal. For example, ( 10 ) and ( 01 ) form an orthonormal ...
New constructions for Quantum Money
... scheme with classical verification. His scheme makes use of a new quantum cryptographic idea, that of quantum retrieval games (QRGs) and its security is information theoretic. However, a clear drawback in contrast to Wiesner’s scheme was that the verification of a coin consists of multiple rounds be ...
... scheme with classical verification. His scheme makes use of a new quantum cryptographic idea, that of quantum retrieval games (QRGs) and its security is information theoretic. However, a clear drawback in contrast to Wiesner’s scheme was that the verification of a coin consists of multiple rounds be ...
Existential Contextuality and the Models of Meyer, Kent and Clifton
... both non-contextual and non-local. There do, of course, exist theories which have both these properties (Newtonian gravity, for example). However, in the framework of quantum mechanics the phenomena of contextuality and nonlocality are closely connected, as has been stressed by Mermin [6] (also see ...
... both non-contextual and non-local. There do, of course, exist theories which have both these properties (Newtonian gravity, for example). However, in the framework of quantum mechanics the phenomena of contextuality and nonlocality are closely connected, as has been stressed by Mermin [6] (also see ...
Compatibility in Multiparameter Quantum Metrology
... and h·i represents the average with respect to the probability distribution p(x|ϕ). The above inequality should be understood as a matrix inequality. In general, we can write Tr[G Cov(ϕ̃)] ≥ Tr(GF −1 (ϕ)) where G is some positive cost matrix, which allows us to asymmetrically prioritise the uncertai ...
... and h·i represents the average with respect to the probability distribution p(x|ϕ). The above inequality should be understood as a matrix inequality. In general, we can write Tr[G Cov(ϕ̃)] ≥ Tr(GF −1 (ϕ)) where G is some positive cost matrix, which allows us to asymmetrically prioritise the uncertai ...
The Light of Existence
... powers the electric field is like Peter paying Paul’s bill and Paul paying Peter’s bill. With such logic, I could borrow a Figure 3.5. Waves alter a surface million dollars today and never pay it back. Does current physics see light as an electro-magnetic Ponzi scheme? Ancient light, such as cosmic ...
... powers the electric field is like Peter paying Paul’s bill and Paul paying Peter’s bill. With such logic, I could borrow a Figure 3.5. Waves alter a surface million dollars today and never pay it back. Does current physics see light as an electro-magnetic Ponzi scheme? Ancient light, such as cosmic ...
Quantum Computing
... reasons. First, the connection of quantum mechanics with number theory was itself surprising. For cryptographers, the result was surprising because the diculty of factoring is the basis of the RSA cryptosystem [27], and nobody had anticipated the possibility of an attack via quantum physics. For ma ...
... reasons. First, the connection of quantum mechanics with number theory was itself surprising. For cryptographers, the result was surprising because the diculty of factoring is the basis of the RSA cryptosystem [27], and nobody had anticipated the possibility of an attack via quantum physics. For ma ...
The measure of existence of a quantum world and the Sleeping
... she will be richer (on average) placing bets on Tails. It might seem that the rules of the game are unfair: Beauty gets advantage for Tails since she plays twice and thus gets a double amount of money in the case of Tails. Let us correct this by asking Beauty to place her bets only in one of the Ta ...
... she will be richer (on average) placing bets on Tails. It might seem that the rules of the game are unfair: Beauty gets advantage for Tails since she plays twice and thus gets a double amount of money in the case of Tails. Let us correct this by asking Beauty to place her bets only in one of the Ta ...
Transport Theory
... Further, with spherical Fermi-surface (free electron like), τk roughly independent of k (Exercise: Show this) ne2 τ ...
... Further, with spherical Fermi-surface (free electron like), τk roughly independent of k (Exercise: Show this) ne2 τ ...
Theory of Nothing
... The instrument of death varies in each case, the probability values vary, it may be the speeding car, it may be the bolt of lightning out of the blue. However, every second of the day, there is some non-zero probability that we may die. Conversely, there is always some probability that we survive. T ...
... The instrument of death varies in each case, the probability values vary, it may be the speeding car, it may be the bolt of lightning out of the blue. However, every second of the day, there is some non-zero probability that we may die. Conversely, there is always some probability that we survive. T ...
Monday - AQIS 2016
... Figure 2: Experimental setup. Alice and Bob share entangled photon pairs which are generated via type-I SPDC. For Alice, cascade setup for sequentially measuring Ai and Ai+1 is used to test KCBS inequality. Whereas, to test CHSH inequality Bj is measured via standard polarization measurements using ...
... Figure 2: Experimental setup. Alice and Bob share entangled photon pairs which are generated via type-I SPDC. For Alice, cascade setup for sequentially measuring Ai and Ai+1 is used to test KCBS inequality. Whereas, to test CHSH inequality Bj is measured via standard polarization measurements using ...
MONABIPHOT_All_Courses_2016
... - Microscopic model of light-matter interaction: the elastically bound electrons and its implications. Radiating properties of an ensemble of oscillating dipoles with near-field and farfield emission. - Macroscopic level: the propagation of light in a dielectric medium, introduction to the index of ...
... - Microscopic model of light-matter interaction: the elastically bound electrons and its implications. Radiating properties of an ensemble of oscillating dipoles with near-field and farfield emission. - Macroscopic level: the propagation of light in a dielectric medium, introduction to the index of ...
How Many Query Superpositions Are Needed to Learn?
... corresponds a subset of Bn so-called consistent set and denoted by σqa . Functions in σqa are said to be consistent with tuple (q, a). In the learning game defined by protocol P , answer a to query q provides the information that the target function belongs to σqa . We also denote by Σq the set of ...
... corresponds a subset of Bn so-called consistent set and denoted by σqa . Functions in σqa are said to be consistent with tuple (q, a). In the learning game defined by protocol P , answer a to query q provides the information that the target function belongs to σqa . We also denote by Σq the set of ...
Max Born
Max Born (German: [bɔɐ̯n]; 11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s. Born won the 1954 Nobel Prize in Physics for his ""fundamental research in Quantum Mechanics, especially in the statistical interpretation of the wave function"".Born was born in 1882 in Breslau, then in Germany, now in Poland and known as Wrocław. He entered the University of Göttingen in 1904, where he found the three renowned mathematicians, Felix Klein, David Hilbert and Hermann Minkowski. He wrote his Ph.D. thesis on the subject of ""Stability of Elastica in a Plane and Space"", winning the University's Philosophy Faculty Prize. In 1905, he began researching special relativity with Minkowski, and subsequently wrote his habilitation thesis on the Thomson model of the atom. A chance meeting with Fritz Haber in Berlin in 1918 led to discussion of the manner in which an ionic compound is formed when a metal reacts with a halogen, which is today known as the Born–Haber cycle.In the First World War after originally being placed as a radio operator, due to his specialist knowledge he was moved to research duties regarding sound ranging. In 1921, Born returned to Göttingen, arranging another chair for his long-time friend and colleague James Franck. Under Born, Göttingen became one of the world's foremost centres for physics. In 1925, Born and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. The following year, he formulated the now-standard interpretation of the probability density function for ψ*ψ in the Schrödinger equation, for which he was awarded the Nobel Prize in 1954. His influence extended far beyond his own research. Max Delbrück, Siegfried Flügge, Friedrich Hund, Pascual Jordan, Maria Goeppert-Mayer, Lothar Wolfgang Nordheim, Robert Oppenheimer, and Victor Weisskopf all received their Ph.D. degrees under Born at Göttingen, and his assistants included Enrico Fermi, Werner Heisenberg, Gerhard Herzberg, Friedrich Hund, Pascual Jordan, Wolfgang Pauli, Léon Rosenfeld, Edward Teller, and Eugene Wigner.In January 1933, the Nazi Party came to power in Germany, and Born, who was Jewish, was suspended. He emigrated to Britain, where he took a job at St John's College, Cambridge, and wrote a popular science book, The Restless Universe, as well as Atomic Physics, which soon became a standard text book. In October 1936, he became the Tait Professor of Natural Philosophy at the University of Edinburgh, where, working with German-born assistants E. Walter Kellermann and Klaus Fuchs, he continued his research into physics. Max Born became a naturalised British subject on 31 August 1939, one day before World War II broke out in Europe. He remained at Edinburgh until 1952. He retired to Bad Pyrmont, in West Germany. He died in hospital in Göttingen on 5 January 1970.