Quantum information is the study of the informational content of quantum states. The most common object of study is the "qubit", the information in a two-state quantum system such as spin-1/2 or photon polarization.

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Second Qubit Not Flipped in Hadamard Gate

I'm very new to QM and Quantum Computing and I have a likely simple question, It may simply stem from my lack of knowledge of vector calculus. We have a 2-qubit quantum state: $$ \mid\psi\rangle = \...
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Split property for type III algebras entails practical separability

I am reading Halvorson's thesis (http://philsci-archive.pitt.edu/346/1/main-new.pdf), however I don't understand a proof at p.50 where he tries to explain why the split property allows a local agent ...
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Information retrieval from a database

Consider a database $\cal D$ containing $N$ entries $A_0, A_1, ... A_{N-1}$, which are some fixed and unknown strings of $k$ bits; you can access this database sending a coherent superposition of ...
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Density matrix formalism and group representation

The postulates of quantum theory can be given in the density matrix formalism. States correspond to positive trace class operators with trace 1 on a Hilbert space $\mathcal{H}$. Composition is defined ...
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Time and particles [closed]

What it is in basic particles that make them propagate themselves through time or, basically, what brings that property known as Duration in a particle (wave)? I sense that this is somehow is based ...
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What kind of transformation can be applied to qubits?

I have a doubt on what kind of transformations can be applied to qubits. I understand that the transformations need to be reversible , but they also have to preserve the norm: that's why the ...
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Taking photos without photons? [closed]

I was looking up some science news and I came across this! Blind quantum camera snaps photos of Schrödinger’s cat http://www.sciencenews.org/article/blind-quantum-camera-snaps-photos-schr%C3%B6dinger%...
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199 views

Are universally valid possibilistic theories possible?

This is a spin-off of the following question: Are Thomas Breuer's subjective decoherence and Scott Aaronson's freebits with knightian freedom the same things in essence? Given that Thomas ...
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How to prove that the ground state of the Hubbard model is not a Slater determinant?

Of course it is expected. But how to prove it analytically? Slater determinant is mentioned in almost every quantum mechanics textbook. But it is necessary to warn the undergraduate students that not ...
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Universality of Quantum Operations

Does an analog of the Solovay-Kitaev theorem exist for quantum operations, a generalization of quantum gates that also includes all completely positive maps?
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Most natural tensor structure for a quantum field

A quantum field is described by a Hilbert space. In many instances, the chosen tensor structure on this Hilbert space corresponds to that of space-like separated regions of space-time. The ...
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Continuous Variable Entanglement Measure for the Statistically Mixed State

Can anybody tell me, which is the best entanglement measure for the Continuous Variable Entanglement of a Statistically Mixed State ? I have read that Schmidt decomposition is not valid in this ...
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103 views

Entangled event horizons

Assuming it is possible in principle to entangle the degrees of freedom of the event horizons of two black holes, and that this is something that can be done, either after the black hole is formed, or ...
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142 views

Does nonlocal theory violate causality?

Let's talk about two kinds of nonlocal theories. The first one frequently derives from integrating out part of the degrees of freedom to obtain a kind of effective theory. Probably, we get an integral ...
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Spatial profile for a superconducting qubit's wavefunction

What is a spatial profile for a wavefunction of a superconducting qubit (such as say a flux qubit, charge qubit, or a transmon)? I am trying to calculate the energy shift of an superconducting qubit (...
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33 views

Quantum computing records (storage times)

Long storage times for qubits will be integral in the construction of a scalable quantum computer. This leads me to ask the current state of affairs in our ability to store qubits. Namely, what is the ...
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61 views

Applications of Quantum Walks [closed]

Can someone explain to me what real world applications could potentially benefit from the study of quantum random walks? I have researched a fair amount on how quantum walks operate and their ...
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154 views

leaving 2-norm propelled probability implications

I am curious about why there are no further generalized probability structures used in Physics. The great revolution was moving away from one-norm system to a two-norm system. What happens if we ...
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190 views

what is 't Hooft up to? [closed]

apart of the 't Hooft diagrams that you all love (and find all sort of dualities starting with them) one of the venues 't Hooft works nowadays is apparently some sort of "deterministic representation ...
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Qubit in Type 1.5 superconductor?

I'm interested in Type 1.5 superconductors, first proposed by Egor Babaev in 2002 and found in the laboratory in 2009 (magnesium dibromide). Such conductors favor small bundles of vortices. The most ...
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Can I usefully interpret a non-unital completely positive (CP) map as a cooling process?

Non-unital completely positive (CP) maps take a maximally mixed quantum state (aka a normalized identity matrix aka an infinite temperature state) and map it to something else. This necessarily ...
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Theoretical or experimental violations of the 2nd Law of Thermodynamics? [closed]

Theoretical challenges to the 2nd Law? What are some the theoretical challenges to the 2nd Law? (cf. Čápek, Vladislav, and Daniel P. Sheehan. Challenges to the Second Law of Thermodynamics: Theory ...
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How to obtain stabilizer's generators of a QEC code

The theory of QEC with stabilizer codes defines an alternative way to represent a quantum state in terms of operators. To understand better what I am concerning about, let's consider the 7-qubit ...
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What is known about the trace of two copies of a channel / four copies of an isometry

Let $\mathcal{E} : \mathcal{L}(A) \to \mathcal{L}(B)$ be a completely positive trace preserving map. By the Choi–Jamiołkowski isomorphism there is an isometry $J : A \to B \otimes C$ such that $\...
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Quantum annealing computing

What is Quantum Annealing and quantum annealing computing and what are its advantages and disadvantages with respect to quantum circuit quantum computing/computers?
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Definition of a 'tunneling lifetime'

I'm given a one-dimensional potential with two wells, one local minimum at some higher energy and one deep global minimum next to it, separated by a barrier of own shape and height (phase qubit). I ...
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586 views

Invariance of states under local unitary transformations [closed]

How can I show explicitly that the bell state $$|\psi^{-}>=\frac{1}{\sqrt{2}}(|0>|1>-|1>|0>)$$ is invariant under local unitary transformations $U_{1}\otimes U_{2}$ ?
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Do the states forming an orthonormal basis have the same amount of entanglement?

If $\{|\psi_{i}\rangle\}$ is an orthonormal basis for a bipartite system, will $E(|\psi_i\rangle) = E(|\psi_j\rangle)$ for all $i, j$, where $E$ is some entanglement measure?
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Spin Transition Energies

I am reading a paper: http://arxiv.org/ftp/arxiv/papers/1305/1305.2445.pdf On p. 22, the following Hamiltonian is given: $$ H = \mu_B g \mathbf{B} \cdot \mathbf{S} + D(S_Z^2+\frac{1}{3}S(S+1)) + E(...
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The role of state space composition in quantum computation

In a paper by Richard Josza and Noah Linden they argue that the way state spaces of composite systems are formed is a key aspect in the benefits of quantum computers. In (classical) phase space, two ...
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Creating matrix Hamiltonian for Feynman's CCNOT [closed]

I'm trying to read Quantum Mechanical Computer and to implement the CCNOT logical gate with Mathematica. Since i wish to use the SWITCH implementation of the CNOT [Fig.8] i've realized that i need to ...
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fiber optic second order PMD as an operator on the tensor product Hilbert space

Second order polarization mode dispersion (SOPMD) is a coupling mechanism between polarization and frequency. Take our photon to be the following tensor product: $\psi = \int \gamma_{\omega} | \...
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decoherence free subspace of a single photon

Take the state vector for a single photon as $\psi = \int \gamma_{\omega} | \omega \rangle \otimes (\alpha |H \rangle + \beta | V \rangle )d \omega$ $H, V, \omega$ are the horizontal polarization, ...
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Looking for description of Helstrom's measurement

I hope someone can help me find the page or chapter where Helstrom discusses his famous measurement for distinguishing between two mixtures in the textbook Quantum Detection and Estimation Theory. ...
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If distant observers never see a black hole form in finite time how can the information paradox be a problem?

So, at least as reported in the media, the physics community is still struggling with the problem of resolving the impossibility of retrieving information from beyond the event horizon of a black hole ...
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Entanglement, superposition, and propositional logic [duplicate]

From what I am understanding, there is entanglement in a system if there is a correlation between elements of that system. For an example that I found, If you have only two cards and know that one is ...
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What is the Reduced Density Matrix?

The difference between pure and mixed states is the difference in their density matrix structure. For density matrix $\rho$ of mixed state the trace of $\rho^{2}$ should be less than 1. For pure ...
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State vector vs density operator

We formulate quantum mechanics using language of state vectors. One alternative formulation is possible using density operator or density matrix. Why we are doing this alternative approach? Is the ...
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What are the practical applications of quantum foundations?

Many quantum foundation researchers keep emphasizing that For All Practical Purposes (FAPP), quantum foundations are irrelevant. They even invented an acronym for it! Does that mean that quantum ...
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285 views

Is a quantum system mandatory for generating true random sequence?

Is a quantum system necessary if we want to generate true random sequence? The mathematical framework used for classical mechanics doesn't involve any random value. But the mathematical framework of ...
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Why does replacing bra and ket basis vectors by their row and column representations give the wrong matrix representation in a non-orthogonal basis?

I have a Hermitian operator (for a 2D Hilbert space) given by $$H=|\psi\rangle \langle \psi|+|\phi\rangle \langle \phi|$$ where $|\psi\rangle$ and $|\phi\rangle$ are normalized but not necessarily ...
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193 views

A machine which copies any object with 100% accuracy?

Does physics allow for a machine that copies an object with 100% accuracy?
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421 views

Proof of Pauli group preservation by Clifford group conjugation?

A well know result is that Clifford group preserve the Pauli group under conjugation or, in other words: $C(P_{1} \otimes P_{2})C^{\dagger} = P_{3} \otimes P_{4}$, with $C \in$ Clifford group and $...
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161 views

Quantum violation of Newton's Third Law? [closed]

From this site: http://www.learning-mind.com/5-thought-provoking-quantum-experiments-showing-that-reality-is-an-illusion/ I gained the knowledge that a group of scientists, upon measuring a tiny ...
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336 views

How “fundamental” is quantum information/computation?

I am wondering how fundamental the study of quantum information theory and computation is, in the sense of contributing to our understanding of the basic laws of nature. Will quantum information ...
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290 views

Application of non maximally entangled state

In quantum information and quantum computation, we generally use Bell type states which are maximally entangled. I find that the set of entangled states as interesting objects from a mathematical ...
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419 views

Anybody have example of two-qubit non-Pauli and non-Clifford quantum gate?

A lot of known quantum gates are in the Pauli group (I,X,Z,Y) or in the Clifford group (H,P,Cnot). I need examples of the quantum gates that aren't in this groups. Also, are there are matlab functions ...
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Measuring polarization - problem with understanding

Let's assume that we have 2 polarizing filters. First with vertical (1) orientation and second with horizontal (0). I want to measure probability that photon passes through those 2 filters. I have: $...
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Holonomic and Topological Quantum Computing [closed]

In topological quantum computation, anyons are braided in spacetime, performing non-trivial evolutions of some degenerate groundstate. In holonomic quantum computation, the system is braided in ...
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Quantum computing, NP complexity [closed]

Hi I have a very limited knowledge of quantum physics and its bothering me trying to understand quantum computing. I want understand how a qubit can return usable data faster then a regular bit, how ...