Questions tagged [quantum-information]

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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Positivity of unitary evolution $u$

If we define $\mathcal{u}[.]=U[.]U^\dagger$ how could we show that $\mathcal(u)$ is positive? $U$ is unitary operator. $u$ is dynamical map.
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3 qubit maximally entangled state $\frac{1}{2}(|000\rangle + |110\rangle+ |011\rangle + |101\rangle)$

Is there any general criteria for maximal entanglement in 3 qubit system. I have encountered this problem-"Suppose you have a state $\frac{1}{2}(|000\rangle + |110\rangle+ |011\rangle + |101\...
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In what sense are spin coherent states “classical”?

Spin coherent states are often introduced as "the most classical states of a finite-dimensional system", or as the analogous of coherent states of light for finite-dimensional systems. See e....
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Does entanglement of a bipartite PPT state $\rho$ imply entanglement of $\rho + \rho^{\Gamma}$?

Consider an entangled bipartite quantum state $\rho \in \mathcal{M}_d(\mathbb{C}) \otimes \mathcal{M}_{d'}(\mathbb{C})$ which is positive under partial transposition, i.e., $\rho^\Gamma \geq 0$. As ...
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What's the solution of EPR paradox? [duplicate]

I know that Einstein said that if quantum entanglement is true, then the information of one particle state would be sent to the other particle faster than light which contradicts absolutely the ...
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Two CNOT gates on two Two qubits

Suppose we have two qubits in the state $(a|0⟩+b|1⟩)|0⟩ $, to which we apply the following circuit. Specify the state of each qubit after we applied the circuit to the state (a|0⟩+b|1⟩)|0⟩ . Let the ...
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How to prove Page's theorem?

Question Statement: Page's theorem in "Jerusalem Lectures on Black Holes and Quantum Information" is stated as (eq (5.12), page 51): For any bipartite Hilbert space $\mathcal{H}_A\otimes\...
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Is this possible to build a quantum network? [duplicate]

Since quantum entangled particles can transfer the data of their spin properties faster than the speed of light and without any problem of weak signal, can we use quantum entanglement to transfer ...
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Matrix representation of transformation defined on creation operators - Bogoliubov transform

In this paper by Alba Cervera-Lierta the following transformation is performed: $$ a_k=u_kc_k+iv_kc^\dagger_{-k} \\ a^\dagger_k=u_kc^\dagger_k-iv_kc_{-k} $$ where $c_k$ and $a_k$ represent ...
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What is the form of a many-body hamiltonian that are subject to the measurement of the position?

Suppose there is a $N$ body hamiltonian, suppose $N=2$ for simplicity: $$ H = - \frac{1}{2} \nabla_1^2 - \frac{1}{2} \nabla_2^2 + V(r_1,r_2) + \frac{1}{|r_1 - r_2|}. $$ If we make a measurement for ...
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Density operator of a system $S$ coupled to a bath $B$

In the second equation of section 8.1 in this MIT OCW lecture notes, I can't understand how they went from $$\rho_{S}(t)=Tr_{B}\{\rho_{SB}(t)\}=\sum_{k}\langle k|U_{SB}(\rho_{S}(0)\otimes|0\rangle\...
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Measuring qubit's state in a real experiment

In theory, it is fairly simple to measure a qubit's state. Let us consider a Ramsey experiment, where the qubit is in the ground state $|0\rangle$ initially. Then by applying a Hadamard gate the qubit ...
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Single-Qubit Density Matrix Evolution

In this paper general form of reduced single-qubit density matrix evolution interacting with bosonic reservoir can be cast in the following form: $$ \rho^s(t)=\begin{pmatrix} \rho^s_{11}(t) & \rho^...
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Grover's Algorithm — Quantum Oracles with different amplitudes

According to https://qiskit.org/textbook/ch-algorithms/grover.html, an oracle creates states like $|\psi⟩=\frac{1}{\sqrt2}|101⟩+|110⟩$, and picks out certain states with equal probability. But if I ...
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Is partial trace method valid for highly entangled state? [closed]

Suppose there are four wires of qubits and the state vector is highly entangled. I want to know the density matrix (or state vector) of wire-$1$ only. In this case, is it available to use partial ...
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What is an example of a system with non-vanishing topological entanglement entropy at finite temperatures?

In this paper: https://doi.org/10.1088/1367-2630/14/3/033044 it is show that for Kitaev toric code looses topological entanglement entropy over long times if it is thermally opened. What is an example ...
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How to specify a general quantum measurement?

I know that a general quantum measurement is described by a set of measurement operators $\{M_j\}$ satisfying the completeness relation $\sum_j M_j^\dagger M_j = 1$ and that the outcome j occurs with ...
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Quantum Entanglement and transfer of time information, is it possible? [duplicate]

If two particles are quantum entangled...let’s call them particle A and particle B. You measure the state of particle A. At this point, can you know the exact time at which the particle B goes from ...
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Is fidelity of teleportation a particular case of quantum correlations?

Fidelity is measure of distance between density operators. it is a measure of the "closeness" of two quantum states, the input state $\rho_{in}$ and the teleported state $\rho_{out}$. where ...
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Confusion regarding bra-ket notation and proof of a ket equation

My question is two-part. First, imagine a bipartite quantum state $|\Phi \rangle_{AB}$, made of $2n$-qubits, shared between Alice and Bob (with $n$-qubits each). Alice performs some unitary operation $...
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What is the physical intuition for Bloch Sphere? [duplicate]

I am very confused about how to think about the Bloch Sphere. How can we relate the concept of expectation value to the Bloch sphere? If my state lies in let's say $yz$ plane how can we say that ...
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1answer
54 views

Multiply phase of a qubit by $2^k$

Given a qubit in the state $|0\rangle+\exp(2πi/2^n)|1\rangle$, is there a quantum mechanical operator to multiply the phase of the qubit with $2^k$ (where $k \leq n$). Such that:- $$|0\rangle+\exp(...
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What exactly is the difference between entanglement and correlations?

Often when describing entanglement in an informal way, we talk about perfect correlation or anticorrelation of measurements of faraway particles, but I don't see how such correlation is particular to ...
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Can local projections on different parties give the same reduced state?

Suppose I have a bipartite pure state $\vert\psi\rangle_{AB}$. By the Schmidt decomposition, we know that the reduced states $\rho_A$ and $\rho_B$ have the same eigenvalues. I am now interested in ...
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Fubini Study metric from bra-ket notation

I know that the Fubini Study metric for the SU(2) coherent state is the metric on $CP^1$. The SU(2) un normalised coherent state is given by $$ \mid z\rangle=\sum_{m=-j}^{m=+j}\sqrt{\left( \begin{...
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How to tighten the Fuchs-Van de Graaff inequalities for pure and mixed states?

Defining the trace-distance as $D(\rho , \sigma) = \dfrac12 tr|\rho - \sigma|$ and the Fidelity between two quantum states as $F(\rho , \sigma) = tr\sqrt{\sqrt\rho\sigma\sqrt\rho}$ I need to show the ...
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Free evolution of a density matrix in position space

I have a density matrix $\rho$ in momentum representation at time $t=0$: \begin{equation} \langle p' |\rho(0) |p\rangle = \sum_{n=1}^{1000} p_n \Psi_n^*(p',0) \Psi_n(p,0) \end{equation} ...
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How to check if a qubit in a circuit is equal to another qubit?

If we have a set of qubits q1 ,q2 and q3 for example, $$ \vert{q_1}\rangle = a \vert{0}\rangle +b \vert{1}\rangle\\ \vert{q_2}\rangle=\vert{0}\rangle\\ \vert{q_3}\rangle=\vert{0}\rangle $$ the state ...
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How does the no-cloning theorem allow to replicate or copy any kind of information?

I am a recent undergraduate from India and currently studying quantum mechanics. I came across a result that quantum mechanics doesn't allow the cloning of even the smallest atoms because that would ...
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A simple question about hyper entanglement

Do we call hyper entanglement as a high-dimensional entangled state? Hyper entanglement is defined such as $$|ψ\rangle = \frac{1}{\sqrt{2}}(|HH\rangle_{ab}+|VV\rangle_{ab})\otimes\frac{1}{\sqrt{2}}(|...
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Is the probabilistic nature of QM simply just randomness (does it exclude causality)? [closed]

I have read this question: What is the reason that Quantum Mechanics is random? where Puk says in a comment: I see. I would call both "random", with the degree of "randomness" ...
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Hyper entanglement vs Maximally entangled bipartite state

Let's suppose we have hyper entanglement of two photons such as $$|ψ\rangle = \frac{1}{\sqrt{2}}(|HH\rangle_{ab}+|VV\rangle_{ab})\otimes\frac{1}{\sqrt{2}}(|SS\rangle_{ab}+|FF\rangle_{ab})$$ where $|H\...
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Is it possible for two observers to observe different wavefunctions for one electron?

Suppose there are 2 scientists who have decided to measure the location of an electron at a same fixed time. Is possible that while one observes the wavepacket localized at (position=x) while the ...
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How do we expand Bayes theorem to account for probability amplitudes?

The Bayes theorem simply states: $$ P(B | A) P(A) = P(A | B) P(B) $$ I wonder if there is something that can be meaningfully said as generalization of this relationship when the probabilities in ...
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Thermal Operations Characterization

In quantum thermodynamics, allowed operations (free transformations in the sense of resource theories) are usually defined via unitaries $U$ that leave the Gibbs state $e^{-\beta H}/Z$ ($Z=\text{Tr}\, ...
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Physical interpretation of a Hamiltonian [closed]

In natural basis $| 0 \rangle = \begin{pmatrix} 1 \\0 \end{pmatrix}$, $| 1 \rangle = \begin{pmatrix} 0 \\ 1 \end{pmatrix}$, what physical situation/model does the following Hamiltonian represent: $H = ...
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I'm confused about two aspects of quantum mechanics: 1.probabilistic nature of quantum 2.time evolution operator [duplicate]

first >> we know that quantum mechanics works with a probabilistic nature so that we can't say " what will happen? " but " what might happen? " second >> we can ask how ...
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What is the present state of research on quantum networks? [closed]

I recently came across the article The Quantum Internet Is Emerging, One Experiment at a Time in Scientific American where it was discussed how quantum networks could provide a level of privacy and ...
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1answer
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State of an entangled state after measurement

I have this general state $\lvert \psi \rangle_{AB} = \sum_{\alpha\beta}c_{\alpha\beta}\lvert\alpha \rangle \otimes \lvert \beta\rangle$ of two qbits. I want to write the state of the system after the ...
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Finding the effective drive on the emitter when driving the cavity in the jaynes-cummings model

I'm trying to figure out what the driving term in the Hamiltonian is when you drive an emitter (say a transmon qubit) through a coupled cavity (such as a CPW resonator). For this I am considering a ...
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Mutually un-biased bases [duplicate]

I was reading some lectures on quantum information theory and it came with the idea of " mutually unbiased bases" that I never heard about. But the definition is very simple: two basis $ B =...
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1answer
48 views

Time evolution of a tripartite quantum state

Question: How do we write the unitary evolution of a tripartite system in Hilbert Space $\mathcal{H}_A \otimes \mathcal{H}_B \otimes \mathcal{H}_C$ when it is subject to two unitary evolution ...
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Causality: Two definitions

The general definition of causality is that the principle of the 'effect never occuring before the cause', as in Wikipedia. The book 'Picturing Quantum Processes' (pg: 262) defines causality as states ...
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Matrix representation of beamsplitter, for numerical computation of output based on given photon number (Fock state) input

Question: Is it possible to express the effect of a simple 50% beamsplitter on photon number states using matrices, such that the output can be computed by matrix calculations rather than manual ...
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1answer
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How to recognize a tomographically complete set of operators?

What I understand... A tomographically complete set of operators is a set of operators such that measuring the probability distributions of an unknown quantum state over the spectrum of each of these ...
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2answers
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Is it possible to differentiate between pure states and mixed ones in the laboratory?

I am wondering if it is possible to differentiate between pure states and mixed ones in the laboratory? For example consider a quantum system define relative to the orthonormal basis {up,down}. We can ...
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Why can’t an elementary particle be forced to have a particular outcome in an entangled pair?

I read in a blog Quantum Entanglement: Slower Than Light that one can not force a particle from an EPR pair to have a not statistical outcome for the entanglement parameter. I can not understand why? ...
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45 views

Conditional density matrix

Let there be a composite system $\mathcal{H}=\mathcal{H}_{A}\otimes\mathcal{H}_{B}$, where $\mathcal{H}_{A}$ and $\mathcal{H}_{B}$ are Hilbert spaces of two subsystems of $A$ and $B$. Suppose the ...
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How to distinguish a quantum superposition from a mixed state (ensemble)? Does a single measurement provide any information? [closed]

I will measure an object that is either in a mixed state of $\vert A\rangle$ and $ \vert B \rangle$ or a superposition $\vert A\rangle + \vert B\rangle$, and I am trying to find out which. I have set ...
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Estimate time for a simple quantum evolution process

Consider the Hamiltonian given by the sum of two projectors $$H=-\gamma N P_s-P_w,$$ where $|s\rangle=\sum_{j=1}^N |j\rangle/\sqrt{N}$ is the uniform state on the $N$ orthonormal nodes $|j\rangle$, ...

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