Questions tagged [quantum-information]

NOTE: We are currently in the middle of removing this tag, so please don't use it! For questions about the quantum analogues of concepts in information theory, please use the information-theory tag.

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It seems computers cannot become conscious. But do you think consciousness can quantum compute? [closed]

We know this idea is as counter intuitive as the fundamental laws of quantum mechanics. Based on the views of Sir Roger Penrose (2020 Noble Laureate in Physics), it is the consciousness of observer ...
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Checking whether a state is almost orthogonal to permutation invariant states

Let us consider \begin{equation} |T\rangle = |\psi \rangle^{\otimes m} \end{equation} for an $n$-qubit quantum state $|\psi\rangle$. Let $\mathcal{V}$ be the space of all $(m + 1)$-partite states that ...
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Quantum relative entropy with respect to a pure state

I want to evalualte the quantum relative entropy $S(\rho|| \sigma)=-{\rm tr}(\rho {\rm log}(\sigma))-S(\rho)$, where $\sigma=|\Psi\rangle\langle\Psi|$ is a density matrix corresponding to a pure state ...
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Out-of-time-order correlation function in the interaction picture?

Recently there has been interest in understanding the out of time order correlation function (OTOC) $F$, which essentially compares the overlap of two operators $W$ and $V$ acting on a state in two ...
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231 views

What is an example of a measurement that is LOCC but not separable?

Could you give me an example of a measurement which is separable but not LOCC (Local Operations Classical Communication)? Given an ensable of states $\rho^{N}$, a separable measurement on it is a POVM ...
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332 views

Local operations and classical communication (LOCC) on quantum system

I'm currently busy learning about the basics of quantum information theory. Does anyone know how the measurement described in the wiki link LOCC is a measurement on the product space $\mathbb{C}^2 \...
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64 views

Find the local unitary that takes the bell state to a state phi that has an extractable bell state

I have a state $|p\rangle$ that has an extractable Bell state and I want to write it as a Bell state, $|b\rangle$, with a local unitary acting on one side. Basically I am trying to find a local ...
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1answer
234 views

Find the reduced density matrix for a four-qubit system

I have the state vector $|p\rangle$ made up of 4 qubits. Say system A is made up of the first and second qubits while system B is made up of qubits 3 and 4. I want to find the reduced density matrix ...
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67 views

Motivation for the definition of k-distillability

Definition of k-distillability For a bipartite state $\rho$, $H=H_A\otimes H_B$ and for an integer $k\geq 1$, $\rho$ is $k$-distillable if there exists a (non-normalized) state $|\psi\rangle\in H^{\...
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Geometric interpretation of 1-distillability

This is a sequel to Motivation for the definition of k-distillability Geometrical interpretation from the definition of 1-distillability The eigenstate $|\psi\rangle$ of the partially transposed $1$-...
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Connection between the definitions of concurrence for a two-qubit states

The concurrence for a state $\rho$ as defined here is \begin{equation} C(\rho) = {\rm max}\{0, \lambda_1-\lambda_2-\lambda_3-\lambda_4\}. \end{equation} Where $\lambda_i$ are the eigenvalues of matrix ...
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Semidefinite program for conditional min-entropy

I am trying to formulate the calculation of conditional min-entropy as a semidefinite program. However, so far I have not been able to do so. Different sources formulate it differently. For example, ...
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Are there Bell-like violations that can be observed without collecting statistics?

Observing the violation of Bell inequalities, be it in their original formulation, or in the nowadays more commonly used CHSH formulation, involves computing averages of specific experimentally ...
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424 views

import error :No module named 'qiskit_aqua'

I have an error when I use Quantum SVM kernel algorithm from Qiskit aqua. This is my code section with imports: ...
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What is the practical interest of superdense coding?

When you enter the field of quantum communications, you run at some point into the concept of superdense coding. Basically it is a way to encode classical bits on the qubits of a quantum channel, ...
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What are the real advantages of superdense coding?

In superdense coding, two qubits are prepared by Eve in an entangled state; one of them is sent to Alice and the other is sent to Bob. Alice is the one who wants to send (to Bob) two classical bits of ...
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148 views

Is there a lower bound on the average diamond norm of two uniformly random unitaries U1 and U1 of dimension D that are sampled from haar measure?

I could not find any lower bound on the diamond norm for two uniformly random unitaries of dimension D sampled from the haar measure.
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Defining entanglement for systems with more than two qubits

Introductory textbooks I've read define entanglement as when your product state cannot be factored into the tensor product of individual quantum states. But consider a three-qbit system: $$C_{2,0}H_2|...
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113 views

Aproximating unitaries with elements from a t-design

(This is basically a reference request) I am wondering if there are any results out there on to what accuracy a given unitary can be approximated with an element drawn from a t-design. To ...
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297 views

How is partial trace related to operator sum representation?

In Quantum Computation and Quantum Information by Nielsen and Chuang, the authors introduce operator sum representation in Section 8.2.3. They denote the evolution of a density matrix, when given an ...
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543 views

Simplest algorithm for intuitively demonstrating quantum speed-up?

What's the simplest algorithm (like Deutsch's algorithm and Grover's Algorithm) for intuitively demonstrating quantum speed-up? And can this algorithm be explained intuitively? Ideally this would be ...
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Prove that $\operatorname{Tr}_B(O_A M)=O_A\operatorname{Tr}_B(M)$

Can someone help me with the following question? Let $M$ be a general operator on the composite system $\mathcal{H}_A\otimes \mathcal{H}_B$ and let $O_A$ be an operator on $\mathcal{H}_A$. Using ...
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95 views

Can every process in nature be simulated by a Turing Machine or a quantum computer?

Given any initial condition or value A, A leads to B after a procedure of physics or nature P. Now is there any turing machine or quantum computer that can simulates P,converting A into B? In other ...
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What does it mean to take the Choi-Jamiolkowski of a quantum channel?

The Choi-Jamiolkowski of a channel $\newcommand{\on}[1]{\operatorname{#1}}\Lambda : \on{End}(\mathcal{H_A}) \xrightarrow{} \on{End}(\mathcal{H_B})$ is obtained through an isomorphism of the form: $$ ...
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67 views

How do I know in which state the qubit is in each step of the circuit for the simulator in qiskit?

I would like to know how to know in which state a qubit is (I am talking about single-qubit errors), because in order to apply a non unitary gate in the simulator I have to renormalize the state or ...
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Nielsen and Chuang ex 2.73

I've been trying to solve exercise 2.73 (p.g 105), and I'm not sure if i'v been overthinking it and the answer is as simple as i've described below or if I am missing something, or i'm just wrong! Ex ...
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Understanding Quantum Channel and Choi Jamiolkowski Notation [closed]

I am given the following $\newcommand{\on}[1]{{\operatorname{#1}}}$ Let $|i\rangle$, $1 \leq i \leq \on{dim}\,\mathcal{H_A}, |s\rangle$, $1 \leq s \leq \on{dim}\,\mathcal{H_B}$ be unitary bases. ...
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1answer
145 views

How is data encoded in a quantum neural network?

I am a newbie to quantum machine learning. I am trying to build a quantum neural network (QNN). What I studied so far about QNN is that input would be qubits and hidden layer parameter can be set ...
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1answer
62 views

Continuity bounds on $D_{\max}(\rho_{AB}\|\rho_A\otimes\rho_B)$

The max-relative entropy between two states is defined as $$D_{\max }(\rho \| \sigma):=\log \min \{\lambda: \rho \leq \lambda \sigma\},$$ where $\rho\leq \sigma$ should be read as $\sigma - \rho$ is ...
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1answer
31 views

Error parameters from Qiskit backends

In order to build a custom noise model in Qiskit Aer, I requested the error parameters from different backends and got 3 (9) parameters for each single-qubit (two-qubit) gate as output. However, I ...
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1answer
52 views

It two unitaries are delta apart in trace norm, then what is the trace norm of outputs states when the same input state is applied to two unitaries?

Suppose we are given two unitary matrices $U$ and $V$, with the following guarantee, $$||U - V||_1 \geqslant \delta$$ for some $\delta \geqslant 0$. We apply an input density state $\rho$ ...
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1answer
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Questions on the max-relative entropy $D_{\max}(\rho||\sigma)$

The max-relative entropy between two states is defined as $$D_{\max }(\rho \| \sigma):=\log \min \{\lambda: \rho \leq \lambda \sigma\},$$ where $\rho\leq \sigma$ should be read as $\sigma - \rho$ is ...
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2answers
52 views

More than one Schmidt coefficient implies entanglement?

I'm studying Quantum Information Theory by Mark M. Wilde, and I got stuck in solving the exercise 3.8.2 in page 100. The exercise is to show that a pure bipartite state is entangled if and only if it ...
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Constructing and Measuring in an Arbitrary 3-qubit basis

As part of a Quantum Theory project I have "constructed" an arbitrary 3-qubit basis: $\left|B_0\right> =\left|000\right>$ $\left|B_1\right> = \frac{1}{\sqrt{2}}\cos(x)(\left|100\right> +...
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1answer
39 views

Questions about the Hamiltonian of a decay

In paper Simulating quantum systems on a quantum computer the author mention in section 3, simulating a decay to obtain the ground state, and give the Hamiltonian for that: $$H=H_1+H_2 + H_{1I}\otimes ...
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2answers
233 views

How to define a quantum channel for the partial trace?

I understand that the partial trace is a linear map, a completely positive map and a trace-preserving map. However, I have no idea how to define a quantum channel with the partial trace because ...
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1answer
69 views

Is there a systematic way to build quantum circuits?

The question is quite straightforward. In classical computation, there exists several ways to build logical circuits based on thruth tables and Karnaugh maps. Is there anything equivalent for quantum ...
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1answer
110 views

How does the teleportation circuit work after the initial entanglement?

I'm trying to understand why we do what we do when we teleport a state from Alice's first qubit to Bob's qubit. I understand the initial entanglement, but could use help walking through the program. ...
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1answer
149 views

Is back in time (classical) information transfer possible (based on delayed choice entanglement swapping)?

Delayed choice entanglement swapping. Two pairs of entangled photons are produced, and one photon from each pair is sent to a party called Victor. Of the two remaining photons, one photon is sent to ...
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1answer
161 views

Compute the output of the quantum teleportation circuit

Sender and receiver use the teleportation protocol, where the sender teleports a quantum state $\left| \varphi \right>=\alpha\left| 0 \right> + \beta \left|1\right>$ to the receiver. I want ...
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1answer
37 views

Half of Standard Basis Measurement

I know that we can measure a state in standard basis (Z) where the post measurement state is either $|0\rangle$ or $|1\rangle$. But can you do a 'half-Z' basis measurement? I mean, you only measure ...
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64 views

How does Quantum Teleportation works? [duplicate]

I've started learning Quantum Computing from the Qiskit Textbook and was able to easily understand or work out everything until it came to the working of Quantum Teleportation I can understand the ...
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20 views

Deriving Bloch vector $dr$ from master equation

I am trying to derive the Bloch vector $dr$ for a measurement of a observable in any arbitrary direction $\theta$. For context this is the setup and derivation I have for continuous measurement along ...
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Information content of qubits

I have two question concerning information content of qubit. Question 1: How many classical bits are needed to represent a qubit: A qubit can be represented by a vector $q = \begin{pmatrix}\alpha \\\...
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Is quantum deletion via a partial randomization procedure possible?

The paper, Quantum deletion is possible via a partial randomization procedure claims that it is possible to bypass the no-deleting theorem by a procedure called R-deletion. But this seems to go ...
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Graphs are represented using oracle, where oracle is the adjacency matrix. Is there any simple example of this?

I have been reading papers on graph theory in quantum computing. Mostly, papers explain that they use adjacency matrix to represent the graph. But I could't find the practical simple example to ...
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1answer
55 views

Guide for Quantum Information and Computing Internships and Learning Opportunities

I know this perhaps not a suitable topic for this SE - after all, this is about QC knowledge sharing - but I am wondering if this could be a resource for people who are interested in the field, are ...
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138 views

Convert a quantum Phase Oracle into a Probability Oracle

Suppose we have an oracle $O_f$ that given an initial state $|x\rangle$ maps it into the following state: $$ O_f : |x\rangle \mapsto e^{if(x)} |x\rangle $$ Now, assuming that $f(x) \in [0,1]$, is it ...
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22 views

Measurements of entropy

I am starting on quantum computing and I got to entropy measurements, but that has me stuck, because there seems to be a lack of resources for newcomers on those concepts and their utility. Anyone ...
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1answer
76 views

How to calculate the Von Neuman entropy on qiskit with the module quantum_info?

I am trying to wrap my head around he quantum_info module on qiskit, since most of the functions on qiskit.tools are going to be ...

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