# Tagged Questions

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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### Is it possible to use quantum mechanics for an effective time based encryption?

This is for an application in cryptography. There is a concept called "time based cryptography", where a message can be decrypted only after a certain time, Say "12/12/2060, 12:30 GMT". There are some ...
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### Grover algorithm $R_D$ Circuit

I need sketch two circuits to understand Grover algorithm. The first is the operator $R_f$ and another is the operator $R_D = H^{\otimes n}(2|0\rangle\langle0|-I)H^{\otimes n}$. I get the first ...
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### Why does quantum cryptography give us uncrackable codes?

Why does quantum cryptography give us uncrackable codes? What makes it 'uncrackable'? Articles in for example pop science magazines always claim QC produces uncrackable coded, however I highly doubt ...
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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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### Positivity in the Pauli/Bloch/coherence vector representation

Suppose $\rho$ is an $n$-qubit state and $\vec{x}$ is a vector of coefficients in the Pauli representation (also called the Bloch or coherence vector). That is $$x_k = {\rm Tr}(\rho \sigma_k),$$ ...
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### Creating matrix Hamiltonian for Feynman's CNOT

I'm trying to read Quantum Mechanical Computer and to implement the CNOT logical gate with some analytical software. Since i wish to use the SWITCH implementation of the CNOT [Fig.8] i've realized ...
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### How are qubits better than classical bit?

WHAT I KNOW: classical computers store information in bits which can either be 0 or 1, but in quantum computer the qubit can store 0 , 1 or a state that is the superposition of these two states. Now ...
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### projective measurement & POVM

Let us consider the following completely positive map $\mathcal{B}(\mathbb{C}^n)\ni\rho\mapsto L\rho L^\dagger$, where $L\in\mathcal{B}(\mathbb{C}^n)$ is any arbitrary operator (and can have rank ...
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### Deutsch-Jozsa algorithm [closed]

How many calls are required to determine is the function balanced or not on the classical computer with probability of error < 50%. Ref: Deutsch-Jozsa algorithm.
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### Qubit projections

Given the qubit: $$\frac{|0\rangle+i|1\rangle}{\sqrt{2}}$$ What is the corresponding point on the extended complex plane and Bloch sphere? How to perform calculations and get the point representing ...
1answer
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### Two qubits problem [closed]

Given the 2 qubit state: (a/b) |00> + (c/b) |01> + (c/b) |10> + (d/b) |11> What is the probability that 2 qubits are equal? Thanks much!
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### Constructing a Toffoli gate from CNOT and single-qubit gates [closed]

Toffoli gate in terms of CNOT and single-qubit gates. Thanks much!
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### Purpose of Grover's algorithm?

How is the output of Grover's algorithm useful if the result is required to use the oracle? If we already know the desired state, what's the point of using the algorithm?
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### Hamiltonian matrix propertu

A professor made an statement to prove the variational theorem: Because the Hamiltonian (H operator of quantum physics) is diagonal in its own eigenfunction, the terms in \$\left \langle \Phi _{m} ...
1answer
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### Violation of the Normalization Constraint?

Say we have two qubits $|a\rangle$ and $|b\rangle$ both initialized to $|0\rangle$. We then apply the rotation gate $R_{x}(\frac{\pi}{2})$ of matrix representation \$\left( \begin{array}{} ...
1answer
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### Entangled or unentangled?

I got a little puzzled when thinking about two entangled fermions. Say that we have a Hilbert space in which we have two fermionic orbitals $a$ and $b$. Then the Hilbert space $H$'s dimension is just ...
1answer
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### Question on hadamard gate and cnot gate circuit tables

I'm trying to solve this problem for homework: Now show that if the CNOT gate is applied in the Hadamard basis - i.e. apply the Hadamard gate to the inputs and outputs of the CNOT gate - then ...
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### What does the sum of two qubits tell about their correlations?

How much can I learn about correlations between two quits by measuring the sum of their values? What is the best way to formalize such a question? Below is my original, longer formulation of ...
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### Circuit identities HTH [closed]

Using this circuit indetities $HXH=Z, HYH=-Y, HZH = X$ prove $HTH=R_x(\pi/4)$. here $H$ is Hadamard matrix, $X,Y$ and $Z$ are Pauli matrix, $R_x$ is a rotation matrix and \$T=\left[ \begin{array}{cc} 1 ...
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### Partial Measure Probability

Let be a $$|\psi\rangle = \dfrac{3}{5\sqrt{2}}|00 \rangle- \dfrac{3i}{5\sqrt{2}}|01 \rangle+ \dfrac{2\sqrt{2}}{5}|10 \rangle - \dfrac{2\sqrt{2} i}{5}|11 \rangle$$ state with two qubits. ...
1answer
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### I am interested in learning Quantum Computing what should I do? [closed]

I wish to learn about quantum computing which seems to be a topic of hot research and overall just intrigues me. I have a strong background in discrete mathematics and number theory. And am a pretty ...
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### Is it ever necessary to extend an analysis of Grover's algorithm beyond $k/N = 1/2$?

Is it ever necessary to extend an analysis of Grover's algorithm beyond $k/N = 1/2$, where $k$ is the number of "hits" in a total of $N$ possible values for $|\,x\rangle$? If we know $k$, and know ...
1answer
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### Bloch sphere representation

Suppose you know that a qubit is either is in state $|+\rangle$ with probability $p$ or in state $|-\rangle$ with probability $1-p$. If this is the best you know about the qubit's state, where in the ...
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### Is this statement about quantum mechanics valid?

In Philosophy of Language by William G. Lycan, there are the lines: Even apparent truths of logic, such as truths of the form "Either P or not P", might be abandoned in light of suitably weird ...
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### 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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### 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 ...
1answer
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### Information bearing degrees of freedom of a quantum simple harmonic oscillator

I am trying to make sense of arXiv:physics/0210005. I am confused with the concept of information bearing degrees of freedom of a system mentioned at the very beginning. To verify the arguments of the ...
1answer
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### Landauer's principle vs Wien's displacement law

Can we argue based on Landauer's principle that if one bit information is changed inside a blackbody, the total radiated energy should be at least or in order of kTln2? If it is so, can we also argue ...
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### Landauer's principle vs Rayleigh–Jeans law

Can we argue based on Landauer's principle that if one bit information is changed inside a blackbody, the total radiated energy should be at least or in order of $kTln2$? If it is so, can we also ...
1answer
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### 2 following gates, inverse circuit

I have a circuit that has 4 wires and 2 following each other Toffoli gates. The first Toffoli gate occupies 3 wires from above, the following Toffoli gate occupies 3 wires from below. What will look ...
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### How large must the Quantum teleportation fidelity have to be in order for it to be useful?

This question relates and stems from my original question. Please read this one and the comments before answering this question. Quantum Teleportation Fidelity I know that for discrete variables ...
2answers
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### How is the energy/eigenvalue gap plot drawn for adiabatic quantum computation?

I was going through arXiv:quant-ph/0001106v1, the first paper by Farhi on adiabatic quantum computation. Equation 2.24 says, $$\tilde{H}(s) = (1-s)H_B + sH_P$$ which means the adiabatic evolution ...
1answer
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### 2 following gates, permutation matrix

I have a circuit that has 4 wires and 2 following each other Toffoli gates. I have permutation matrix for each Toffoli gate (A and B). Do I have to multiply that 2 matrices to get the entire ...
2answers
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### Entropy of a state subject to the action of a set of random unitaries

Suppose that we have a known set of unitaries $U_1,...,U_n$ randomly selected from the Haar measure and suppose that each unitary is applied with probability $\frac{1}{n}$ to some input state $\rho$ ...
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### QFT in Quantum Computing and Control Theory?

Is QFT being applied to quantum computing and control theory? I took yesteryear a basic course on quantum computing and if I remember correctly we didn't touch on any QFT (though I think that if it ...
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### Quantum gates Hadamard before a toffoli gate

After applying a Hadamard gate so that the state splits into either $|1\rangle+|0\rangle$ or $|0\rangle-|1\rangle$ what happens when applying a ccnot (toffoli) gate, this flips a third qbit if the ...
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### How to measure a qubit in a random basis

Let a two dimensional system be in the state $\phi=|0\rangle\langle0|$, for any basis $M$ spanned by the orthogonal vectors $|\psi_0\rangle,|\psi_1\rangle$, we can measure $\phi$ in basis $M$ and ...
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### Quantum gate: Phase shift

I dont undestand how to apply a phase shift gate to a qubit. By example how to map $|\psi_0\rangle = \cos (30^\circ) |0\rangle + \sin (30^\circ) |1\rangle$ to \$|\psi_1\rangle = \cos(-15^\circ) ...
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### mixture of maximally mixed and maximally entangled state

Consider the quantum system $\mathcal{B}(\mathbb{C}^d\otimes\mathbb{C}^d)$ and $|\psi\rangle=\frac{1}{\sqrt{d}}\sum_{i=0}^{d-1}|i,i\rangle$ be the (standard) maximally entangled state. Consider the ...
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### POVM advantage in state discrimination

Suppose we are given the task of discriminating, with minimum error, between a set of states $\{|\psi_1\rangle,|\psi_2\rangle,\ldots,|\psi_N\rangle\}$. In other words, we are given an unknown state ...
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### 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 ...
1answer
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### How is a Rydberg Blockade Radius defined?

Rydberg blockade is a phenomena in 3 or more level systems of Rydberg dressed atoms.
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### Quantum circuit simulation software [closed]

Would anyone be able to recommend some software that you can use to simulate a quantum circuit? Something someone created to easily be able to create nice looking quantum circuits and quickly ...
1answer
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### Which similar properties must objects have to sustain quantum entanglement?

Quantum entanglement occurs when particles such as photons, electrons, molecules as large as buckyballs, and even small diamonds interact physically and then become separated; the type of ...
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### Toric Code and Random Bond Ising Model

It was established by Dennis, Kitaev et al. that the 2D Toric Code can be mapped to a 2D Random Bond Ising Model. The original derivation was given in the paper "Topological quantum memory" which ...
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### How to apply a Hadamard gate?

How to apply a Hadamard gate to 3 qubits? by example how to apply $H$ to $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
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### Dealing with environment in a CHSH game

I am reading arxiv:1209.0448. I understand that my questions could be highly trivial. I would appreciate if anyone helps me to resolve my confusions. In a CHSH game, Alice and Bob cannot have ...
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### Quantum Teleportation Fidelity

I understand that quantum teleportation fidelity is the overlap of the initial quantum state with the teleported quantum state. If the teleportation is perfect, then the fidelity would equal 1 or 100% ...
1answer
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### Two Qubit problem

A two-qubit system was originally in the state $\frac{3}{4}|00\rangle-\frac{\sqrt{5}}{4}|01\rangle+\frac{1}{4}|10\rangle-\frac{1}{4}|11\rangle$ , and then we measured the first qubit to ...
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### Reversible gates

Is it possible to make any gate reversible merely by retaining the input bits in the output and introducing ancilla bits as necessary? That is, given an irreversible gate with $k$ inputs and $l$ ...
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