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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Statistical sum of physical quantities in a quantum system

Let $C = A + B$ (statistical sum, so $\mathbb{E}[C] = \mathbb{E}[A] + \mathbb{E}[B]$), and let $p(A = a) = 1$. Are the following true? $\mathbb{E}[C^2] = a^2 + 2a\mathbb{E}[B] + \mathbb{E}[B^2]$ ...
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365 views

Types of photon qubit encoding

How many types of qubit encoding on photons exist nowadays? I know only two: Encoding on polarization: $$ \lvert \Psi \rangle = \alpha \lvert H \rangle + \beta \lvert V \rangle $$ $$ \lvert H ...
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Where is noncommutativity in the state-effect formalism of quantum mechanics?

In quantum information theory, one can adopt the basic formalism where every system is given by an operator algebra, state preparation procedures correspond to linear functionals on that algebra ...
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knowledge of an internal observer

I would like to discuss the consequences of the concept of an internal observer in quantum theory. If we assume that we have a universe that evolves unitarily at a global scale and an observer is ...
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Unknown quantum state with promise of classical data

I am trying to solve a problem in the measurement and identification of quantum states with a promise as to what states it could be. Here is the problem. Imagine a system that produces qubits in ...
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155 views

Shor's Algorithm: Why throw away the f(x)?

I'm having a little trouble understanding Shor's algorithm - namely, why do we throw away the result f(x) that we get after applying the F gate? Isn't that the answer we need? My notation: ...
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What is the significance of being equivalent up to local isometry?

Background : I am reading the paper device independent outlook on quantum mechanics. The author mentions the concept of two pure states being equivalent up local isometry. From what I understood two ...
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37 views

Measuring quantum entanglement in paper by Ma et al [duplicate]

Looking at the links below, could somebody please explain how entanglement between Alice and Bob particles is established/deduced from Victor's choice/measurement? I understand that Alice and Bob can ...
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22 views

Mermin Inequality

Suppose I want to calculate the maximum of Bell inequality for three parties system. In this case I will have 6 measurement directions (unit vectors). It has been done in the paper PHYSICAL REVIEW A ...
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How asymptotically efficient is quantum state tomography of a flat qubit?

Suppose you receive $n$ copies of a qubit rotated by an unknown angle. That is to say, you're given the state: $$T(\theta) = \left(\sin(\theta) \left|0\right\rangle + \cos(\theta) ...
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58 views

Toric Code and the String-Net Model

What, exactly, makes the toric code a quantum error-correcting code as opposed to any other string-net model? What makes it special? The way I understand it, it's a normal string-net model on a torus, ...
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45 views

How does a Bell measurement physically look like?

I do know how Bell states look like. They can be distinguished by doing a Bell measurement. A measurement has 4 possible outcomes (as there are 4 states, which form orthonormal basis). However I have ...
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Geometric measure of entanglement for fermions or bosons?

For a system consisting of multiple components, say, a spin chain consisting of $N\geq 3 $ spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner ...
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Is there a simple expression for the coherent information of a Pauli channel?

The coherent information of a channel $\Lambda$, with complementary channel $\Lambda_c$ is defined as: $I(\Lambda)=max_{\rho} \{ S(\Lambda[\rho])-S(\Lambda_c[\rho])\}$ I have noticed that it seems ...
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43 views

commutation relations for operators in projected subspaces

I am looking for a consistent re-definition of commutators for certain operators when I work in a projected subspace. Basically, I have a spin defined in terms of 4 Majorana operators $b_{x}$, ...
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Can single maximal fraction be increased by one-party local operation?

For a quantum channel $\Lambda$, the corresponding bipartite state is $\rho=(I\otimes\Lambda)(|\Phi\rangle\langle\Phi|)$, where $|\Phi\rangle=\frac{1}{\sqrt{n}}\sum_{i}|ii\rangle$. The maximal ...
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Verifying quantum states

Suppose Alice creates a secret n-qubit state $\lvert \psi \rangle$ from a description $d$, and gives the states to Bob. (Bob doesn't know $d$ ) Bob who doesn't trust the channel, wants to verify if ...
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explaining qubits to beginning CS students

&I have 15 minutes as a guest lecturer to explain the notion of quantum computing to CS students in a Theory of Computation class. There is a lot of information on the web, e.g., ...
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The implications of Gödel's Second Incompleteness Theorem on Theoretical Physics models

Does Gödel's Second Incompleteness Theorem imply that no Theoretical Physics model of reality can be proved to be consistent using the laws of physics? I work partially in Quantum Information Theory ...
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31 views

Local unitary transformation that maximizes overlap

Could anyone point me in the right direction (reference to papers would suffice) regarding the following: Given two quantum states $|\psi\rangle ,|\phi\rangle \in (\mathbb{C}^d)^{\otimes n}$, where ...
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Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...
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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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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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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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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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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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82 views

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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27 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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50 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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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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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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Double slit experiment and entanglement

Just wondering, what would happen in this experiment. In the experiment you would first have two entangled particles. Then you fire one of the particles, lets say "Particle A", at a double slit ...
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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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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)) + ...
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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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Is the translational information all that matters, or do we need to take into account internal states?

For anyone in this community that's familiar with quantum teleportation, I need desperate help. I am currently working on my senior thesis and my goal is to teleport a molecule. Background: So in ...