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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Entropy of Reeh-Schlieder correlations

Any state analytic in energy (which includes most physical states since they have bounded energy) contains non-local correlations described by the Reeh-Schlieder theorem in AQFT. It is further shown ...
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Proving two forms of atom-field interaction perturbation Hamiltonian are equivalent

In the presence of an electromagnetic field in the dipole-approximation (${\boldsymbol A} = {\boldsymbol A}(0,t)$) we have the two forms $$H_{{\boldsymbol d}\cdot {\boldsymbol E}} = - q {\boldsymbol ...
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Projection operators and their subspaces (of Hilbert space)

I've been watching Susskind's lectures on Quantum Entanglement, and something he said regarding (non-)commuting projection operators confused me. Consider two subspaces {$|a>$} and {$|b>$} of ...
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Quantum Cryptography Open Problems [closed]

I am a 3rd year Physics undergraduate interested in Quantum Cryptography. This summer , I want to work on a open problem in Quantum Cryptography. I have credited courses such as Quantum Computation ...
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Grover search algorithm for more than one marked elements [closed]

Grover search algorithm is a powerful tool for unstructured database search purposes. The two operations (Phase inversion and Inversion about the mean ) join hands to give the marked needle. I was ...
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Quantum entanglement [closed]

I've been reading articles about Quantum mechanics (for a sci-fi project of mine) - especially Quantum entanglement. The measurements of physical properties of the entangled particles are correlated, ...
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What is the probability of quantum tunneling occurring in this CPU?

You may have noticed over the last few years that Moore's law is no longer applying to the real world. This observation states that over the history of computing hardware, the number of transistors on ...
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52 views

How many states are there in the observable universe

If we took a single instant and considered all possible states of all energy and matter do we have any bounds on how much that would be? Would that number be related to information?
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Significance of 'chiral' form for a quibit?

Say I have a qubit with probability amplitude divided evenly among $|0>$ and $|1>$ $$\frac{1}{\sqrt 2}|0> + \frac{1}{\sqrt 2}|1>$$ So it seems that we have a, loosely speaking, ...
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Trace in non-orthogonal basis?

Physicists define the trace of an operator $\rho$ as the follows, $Tr(\rho)=\sum\limits_{|s\rangle \in B} \langle s| \rho |s\rangle$ where B is some orthonormal basis, and this quantity is ...
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Quantum Fourier Transform and Entropy

QFT is a nonlocal unitary transformation and so can generate entanglement in a system. It means a separable pure state can be converted into an entangled pure state. Now since the presence of ...
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Understanding of measurement in quantum mechanics?

I have a computer science background with basically zero physics background. I am trying to gain a 'high-level' understanding of quantum mechanics to aid me in some computer science work. Is my ...
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71 views

Entanglement entropy and area law

I am currently reading a review "Area law for the entanglement entropy" by Eisert, Cramer and Plenio (2010). From what I understand: In one dimension, for local gapped models, we have an area law ...
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Bragg's diffraction and Simon's problem

In Preskill's notes, John Preskill goes as If we scatter a photon off of a periodic array of needles , the photon is likely to be scattered in one of a set of preferred directions , where the ...
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Deriving Rabi rotation matrix

I want to understand where the matrix: $$ \left|\psi(t)\right> = \binom{a(t)}{b(t)} = \begin{bmatrix} cos(\Omega t/2)&-ie^{i\phi_L t}sin(\Omega t/2) \\ -ie^{-i\phi_L t}sin(\Omega t/2) & ...
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Advantage of taking qutrits in place of qubits

In general, all the quantum algorithms which I have read so far use qubits (so the space is $\mathbb{C}^2$) and the tensor products of the qubit spaces (space is ${\mathbb{C}^2}^{\otimes n}$). So my ...
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43 views

Physically realizable quantum circuits

How do we decide whether a quantum circuit can be realized physically or not ? I was wondering for physical realization of Shor's factoring algorithm using NMR ( I mean can we do it? ).
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Is there a handwavy way to explain what quantum correlation means?

Is there a simple way to explain the difference between a classical and truly quantum correlation to a non-quantum person who has basic understanding classical correlation? I mean without invoking ...
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52 views

A good book for Quantum Cryptography

I am interested in Quantum Information and Cryptography in particular. I have gone through Neilson's text and Preskill's notes . Can someone suggest me some good text for Quantum Cryptography ? I ...
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Positivity and Complete positivity of Simon Map [migrated]

Simon map in a specific basis is defined as $$ \left[ {\begin{array}{ccc} A & B & C \\ D & E & F \\ G & H & I \\ \end{array} } \right] \rightarrow \left[ ...
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32 views

Is the reduction map completely positive? [duplicate]

I am struggling with proving the complete positivity of a general map ( granted it is CP ). The reduction map is defined as $$ \rho \rightarrow \mathrm{Tr}(\rho)I - \rho $$ It is a trivial job to ...
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61 views

Design a quantum circuit from a matrix

I have unitary matrix and I would find the quantum circuit associated. There are 3 qubits input so it's a 8x8 matrix but it's not a simple operation. The number of gates is not specified. Is there a ...
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27 views

Quantum Key Distribution (QKD) Upper and Lower Bounds

Many papers on Quantum Key Distribution protocols discuss the protocols upper and lower bounds (on quantum bit error rate QBER). For example, BB84 has a lower bound of 11% and an upper bound of ...
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How can we show that a map is a completely positive map? [migrated]

I am doing a homework problem where I have to find whether the map $$ \rho ~\rightarrow~ {\rm tr}(\rho) I - \rho $$ is completely positive. If the map is not completely positive, a counter-example ...
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Physical consequences of non-trivial quantum states homology

The set of quantum states of a finite dimensional system is a complex projective space, whose homology groups are non-trivial http://en.wikipedia.org/wiki/Complex_projective_space#Homology. Has this ...
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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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Thought experiment using quantum entanglement in position and its effects

Consider we have two atoms $a$ and $b$. They are entangled with each other in position and momentum, with some wavefuction describing them in position space that is $\Psi(x_a, x_b)$. This ...
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Where does the requirement of prime number dimension figure in generating mutually unbiased bases (MUB)?

I have been studying this paper by S. Bandyopadhyay et al. - "A new proof for the existence of mutually unbiased bases". Here is the link. They explicitly construct MUB using generalized Pauli ...
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Information carried by single photon

In Quantum Information we can use photons for quantum bits (qubits). What i often read is that each photon can carry one unit of information, i.e. using the polarization state of a single photon. I ...
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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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134 views

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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Different implementation of Feynman's clock

In equation 7 of the paper, Feynman's clock, a new variational principle, and parallel-in-time quantum dynamics, the clock register is different from Feynman's original proposal. According to this ...
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What are the practical consequences of “approximate” quantum cloning with a stimulated emission cloning machine?

Say I build some stimulated emission-based cloning machine for photons (e.g. some active laser medium). Alternatively I could do cloning via interference, e.g. a linearly polarized photon could be ...
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Trace of an operator matrix (Quantum computation and quantum information)

I'm reading the book Quantum computation and quantum information by Mike & Ike and I'm stuck at 2.60/2.61. There, the author says that, given the operator $A|ψ⟩⟨ψ|$, its trace is: $${\rm ...
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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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Studying Physics [closed]

I'm preparing for entry into a Physics degree course, and was planning on a double major in Physics (with a specialization in Quantum Information later) but am now considering a minor in ...
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EPR paradox: instantaneous vs very fast?

An EPR quantum experiment can be explained by instantaneous collapse of the wave function regardless of the distance separating a pair of entangled particles. But do we have the certainty that the ...
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95 views

Are they the same thing: Wigner distribution in quantum Boltzmann equation and Wigner function in quantum optics?

We know that quantum Boltzmann equation (QBE) is an equation of motion for the interacting Green's function $G^<(\vec{x}_1,t_1;\vec{x}_2,t_2)\equiv\mathrm{i}\langle ...
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ER = EPR and Time Travel

In Maldacena-Susskind paper arXiv:1306.0533, they propose an idea of $$\text{ER = EPR}$$ the relation between the wormhole and the quantum entanglement. which ER means Einstein Rosen (ER) bridges, ...
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Entanglement in single particle state

Is it possible that we have entanglement in different degrees of freedom of a singe particle. like spin and linear momentum .
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Info request on studying QIT/QIS or QM with a Computer Science background [closed]

I've been considering a career change for a long time and recently discovered the Two-Slit Experiment, which, to put it frankly, blew my mind. I then started some hefty reading and investigation into ...
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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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Mutually unbiased bases

This question can be formulated in two ways. Let there be two $d$-dimensional orthonormal bases $B_{1}$ and $B_{2}$. I refer to the elements of $B_{1}$ by $\lvert\nu_{i}\rangle$ and to the elements of ...
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Tensor product of Hadamard Operators

The Hadamard Operator on one qubit is: \begin{align*} H = \tfrac{1}{\sqrt{2}}\left[\,\left(\color{darkgreen}{|0\rangle + |1\rangle}\right)\color{darkblue}{\langle ...
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relationship between Fredkin gate and the swap and I gates

I need to prove this relationship: $$G_{Fredkin} = I \otimes |0\rangle\langle 0| + G_{swap} \otimes |1\rangle\langle 1|$$ with $$G_{swap} = |00\rangle\langle 00| + |01\rangle\langle 10| + ...
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Quantum computing records (entangled qubits)

What is the current record number of entagled qubits and how has this number been increased? The latest result on stack exchange, which is 3 years old, reports 14 via this post: How many stabilised ...
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86 views

A tensor product of two spin-1 particles

I'm rather confused, and I was hoping if someone could help me figure out this (probably rather elementary) issue. I have two particles with spin 1, whose state I describe by $m_S$ and $m_I$ ...
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Time evolution in a static magnetic field of a 2-level system that is actually a 3 level system

What I want to do is describe the time evolution of only two states of a spin 1 particle on the bloch sphere. However, I'm running into trouble because I don't know how to construct the hamiltonian ...
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Physical Interpretation of the Bloch vector

In the expression of the density matrix of a (Electron-Spin) Qubit $$ \rho=\frac{1}{2}(I + x \sigma_x + y \sigma_y + z \sigma_z) $$ where $\tau=(x,y,z)$ is unit vector in the Bloch sphere, which is ...