Tagged Questions
0
votes
1answer
42 views
Question about entangled states
I have a question about entangled state. Suppose I consider the entangled state $\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$. I saw an argument for how measurement of the first bit is affected by ...
4
votes
1answer
36 views
Limits of superdense coding
Holevo's theorem says that no more than n bits can be stored (and retrieved) in n qubits. Indeed, allowing error can't improve this either -- the probability of retrieving the correct information is ...
3
votes
2answers
68 views
Composition of squeeze operators?
I'm wondering if it exists a composition law for the squeezing operation ? I guess so for geometric reason, since they are (generalized, and the phase is annoying of course) hyperbolic rotations of ...
-1
votes
0answers
75 views
Quantum entanglement , time dilation , and information lose? [closed]
The question consist of two related parts:
1-What is the effect of time dilation -(resulted by a difference between the rate at which time flows for each particle)- on entangled particles ?
2-what ...
2
votes
0answers
26 views
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 ...
0
votes
0answers
39 views
Application of adiabatic quantum algorithm and quantum annealing algorithm [closed]
I am looking for a paper where the same problem is solved with both the adiabatic quantum algorithm and quantum annealing algorithm along with comparison between their performances. Any one with any ...
4
votes
2answers
72 views
How do you come up with a POVM?
This is a made-up example, just to understand a concept. If changing the probability values aids your explanation, that's fine by me.
Say you have a physical quantity $E$ that can take values 1, 2, 3 ...
2
votes
1answer
66 views
Trying to understand mixed states
I took a basic quantum chemistry course (McQuarrie's "Quantum Chemistry"), but it never dealt with mixed states -- only pure states (or if it did, we never got to it in class).
So I'm trying to ...
3
votes
2answers
76 views
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 ...
1
vote
2answers
95 views
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 ...
4
votes
2answers
104 views
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 ...
7
votes
1answer
118 views
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
$$
x_k = {\rm Tr}(\rho \sigma_k),
$$
...
7
votes
1answer
124 views
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 ...
3
votes
0answers
126 views
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 ...
0
votes
0answers
39 views
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.
1
vote
2answers
65 views
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 ...
0
votes
1answer
62 views
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!
0
votes
0answers
48 views
Constructing a Toffoli gate from CNOT and single-qubit gates [closed]
Toffoli gate in terms of CNOT and single-qubit gates.
Thanks much!
0
votes
2answers
70 views
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?
0
votes
0answers
58 views
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} ...
0
votes
1answer
32 views
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}{}
...
7
votes
2answers
261 views
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 ...
0
votes
0answers
27 views
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 ...
0
votes
0answers
43 views
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. ...
1
vote
1answer
165 views
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 ...
3
votes
1answer
130 views
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 ...
3
votes
4answers
245 views
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 ...
1
vote
4answers
134 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 ...
0
votes
1answer
74 views
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 ...
0
votes
1answer
61 views
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 ...
0
votes
0answers
42 views
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 ...
-2
votes
1answer
44 views
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 ...
1
vote
0answers
51 views
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 ...
2
votes
2answers
114 views
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 ...
1
vote
1answer
101 views
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 ...
9
votes
2answers
309 views
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 $\rho$ ...
-1
votes
1answer
80 views
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 ...
2
votes
2answers
102 views
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 ...
0
votes
2answers
106 views
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) ...
3
votes
1answer
66 views
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 ...
3
votes
0answers
93 views
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 ...
1
vote
3answers
182 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 ...
-1
votes
1answer
75 views
How is a Rydberg Blockade Radius defined?
Rydberg blockade is a phenomena in 3 or more level systems of Rydberg dressed atoms.
1
vote
1answer
67 views
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 ...
2
votes
2answers
528 views
How to apply a Hadamard gate?
How to apply a Hadamard gate to 3 qubits? by example how to apply $H$ to $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
4
votes
2answers
142 views
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 ...
0
votes
1answer
143 views
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 ...
2
votes
2answers
175 views
Constructing a Toffoli gate with 2-and 1-qubit gates?
I'm looking through Nielson's book on quantum computation and information and in part of it he says that any $C^2(U)$ gate can be constructed from two qubit and one qubit gates. I can't figure out how ...
7
votes
2answers
251 views
Should it be obvious that independent quantum states are composed by taking the tensor product?
My text introduces multi-quibt quantum states with the example of a state that can be "factored" into two (non-entangled) substates. It then goes on to suggest that it should be obvious1 that the ...
1
vote
1answer
131 views
Quantum Circuit, example of the Bernstein-Vazirani problem
This question is regarding the quantum circuit in the picture below.
Suppose we have the set up below, where U performs the operation $U:\mid x \rangle \mid y \rangle \rightarrow \mid x \rangle\mid y ...
