0
votes
0answers
22 views

Matrix forms to understand a state transition operator

Given an equilibrium of two states.$\left| 00 \right> \rightleftharpoons \left| 11 \right>$. And introduce a map $\mathcal{B}(\mathbb{C}^2\otimes \mathbb{C}^2) \rightarrow ...
1
vote
0answers
15 views

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 ...
0
votes
0answers
26 views

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 ...
0
votes
0answers
26 views

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 ...
0
votes
0answers
16 views

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 ...
0
votes
1answer
71 views

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, ...
3
votes
0answers
46 views

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 ...
0
votes
1answer
36 views

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, ...
1
vote
2answers
112 views

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 ...
2
votes
1answer
69 views

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 ...
0
votes
2answers
65 views

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 ...
2
votes
0answers
72 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 ...
0
votes
0answers
24 views

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 ...
3
votes
3answers
115 views

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 ...
0
votes
1answer
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? ).
5
votes
1answer
97 views

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 ...
2
votes
1answer
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 ...
1
vote
0answers
28 views

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[ ...
1
vote
0answers
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 ...
0
votes
1answer
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 ...
1
vote
1answer
28 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 ...
0
votes
0answers
32 views

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 ...
2
votes
0answers
43 views

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 ...
1
vote
0answers
60 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 ...
2
votes
0answers
43 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 ...
4
votes
1answer
124 views

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 ...
2
votes
0answers
16 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 ...
1
vote
5answers
92 views

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 ...
2
votes
1answer
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 ...
2
votes
2answers
73 views

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 .
1
vote
1answer
48 views

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 ...
2
votes
0answers
38 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 ...
2
votes
0answers
63 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 ...
3
votes
1answer
52 views

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 ...
0
votes
0answers
19 views

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| + ...
9
votes
0answers
178 views

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 ...
0
votes
1answer
45 views

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 ...
1
vote
1answer
58 views

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 ...
3
votes
1answer
81 views

Couder-Fort Oil Bath Experiments and Quantum Entanglement Phenomena

The oil bath experiments of Couder and Fort have been able to reproduce various "pilot wave like" quantum behavior on a macroscopic scale. Particularly striking is the fact that the double-slit ...
2
votes
2answers
174 views

What's wrong with this faster-than-light gedankenexperiment?

It is common wisdom - and mathematically proven - that quantum entanglement cannot be used to bypass the relativistic speed limit and transfer information faster than light. So there must be something ...
3
votes
1answer
88 views

Rotation about the $z$-axis on the Bloch sphere

I'm having some trouble with successfully working out a rotation about the $z$-axis on the Bloch sphere. Now, I know how this is performed, in principle. A rotation of the Bloch-sphere around an ...
1
vote
2answers
96 views

Writing down an entanglement in bra-ket notation

I have a relatively complex (for me anyhow) situation which I would like to capture in bra-ket notation, rather than in words. However, I've not been able to find a source which will help me ...
1
vote
0answers
41 views

POVM positive density matrix decomposition

I have to prove that given a density matrix $\rho$ in a finite d-dimensional Hilbert space $\mathcal{H}_d$, it always exists at least one informationally complete POVM measure $\{E_i\}_{i=1}^{d^2}$ ...
2
votes
1answer
67 views

Integration over the state space

I came across the concept of average fidelity $\int f(\psi)d\,\psi$ where the integration is with respect to the uniform Haar measure on pure states. I've only seen Haar measures in connection with ...
3
votes
1answer
177 views

Bra-ket notation, Bits, & Superposition

I am a quantum computing enthusiast, and recently I stumbled upon this the following two propositions: $$ \alpha|1\rangle + \beta|0\rangle$$ What does this mean? My understanding of this is that: ...
3
votes
0answers
65 views

Finding the ground state of the toric code Hamiltonian

How do I write by proof, the ground state of the toric code (by Kitaev) Hamiltonian $ H=-\sum_{v}A(v)-\sum_{p}B(p) $ where $A(v)=\sigma_{v,1}^{x}\sigma_{v,2}^{x}\sigma_{v,3}^{x}\sigma_{v,4}^{x}$ and ...
0
votes
2answers
169 views

Can you read and write a quantum state to a particle without collapsing its probability field?

I know the main problem with a quantum computer is that you can't read and write data from it until after it has run though all of its calculations. But would reading and writing quantum data to ...
3
votes
0answers
96 views

Does natural unit of information and entropy, nat, play special role in the freebit picture?

Please refer this question to understand why I consider the freebit picture important. In short, it is conjectured, that for certain real systems the most complete physical description possible ...
0
votes
1answer
35 views

Are Feynman's Hamiltonian computers unitary?

In this paper, Feynman gave the idea of creating a time-independent Hamiltonian from a quantum circuit. Is there anyway to say that these Hamiltonians will always be Hermitian? Moreover, will these ...
1
vote
0answers
121 views

How do I write the Hamiltonian for a 3-level system?

I came across following types of three-level systems like V-system, Λ-system and 2-photon absorption It seems that their Hamiltonians can be written intuitively by checking out the coupled levels ...