Questions tagged [quantum-information]

For questions about quantum information theory. In physics and computer science, quantum information is information that is held in the state of a quantum system. Quantum information is the basic entity of study in quantum information theory and can be manipulated using engineering techniques known as quantum information processing. (Wikipedia)

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

I have a state |p> that has an extractable Bell state and I want to write it as a Bell state, |b>, with a local unitary acting on one side. Basically I am trying to find a local unitary U that ...
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What is the correspondence between a quantum gate and the interference pattern generated?

Assuming the quantum gate model, I'm trying to understand the correspondence between a quantum gate acting on qubits in superposition and the probability amplitude associated with each state of ...
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Information and entropy [on hold]

Since the entropy of the universe always increases. And in quantum information, we define information in terms of entropy, in such a way that more the entropy, more is the information. Does it mean ...
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What are the Main Classes of Quantum Error-Correcting Codes?

Classically, we have the Hamming Code, Turbo Code, Reed-Solomon Code, etc. I am interested in knowing the classes of quantum error-correcting codes. They don't have to be analogous to classical codes, ...
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Why cant i open any of the guides? [closed]

Why cant i open any of the guides? The page just keeps working and never opening. Are the guides located somewhere else? Or is my machine just that slow.
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Non maximally entangled states for QKD

Why aren't non maximally entangled states produced and used in quantum key distribution schemes? What would be the advantage/disadvantage to use such states rather than maximally entangled ones?
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Can the Kraus decomposition always be chosen to be a statistical mixture of unitary evolutions?

If $\mathcal{E}$ is a CPTP map between hermitian operators on two Hilbert spaces, then we can find a set of operators $\{K_j\}_j$ such that $$\mathcal{E}(\rho)=\sum_j K_j\rho K_j^\dagger $$ in the ...
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Why is the resource theory approach used in quantum information processing?

What are the advantages and applications of using the resource theory approach in QIP ? What specific problems can be solved using in particular this approach ?
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Density Evolution to Optimize QLDPC code design

Density Evolution is a simulative tool that models the behaviour of SPA (sum-product) decoders. It is useful because it enables the optimization of code designs so that extensive simulations can be ...
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The merit of quantum error correction codes

We know that word error rate (WER) rather than qubit error rate (QER) is used to evaluate the performance of quantum Turbo codes and quantum LDPC codes. In classical coding theory, when we are ...
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1answer
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How to integrate Simulaqron on ProjectQ

I am trying to simulate quantum teleportation on ProjectQ using simulaqron (enabling me to use quantum internet for teleportation) however I am not sure if my approach is right. In the working paper ...
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The most important quantum question , how to force a superposition qubit to collapses to an exact value? [closed]

Note: forcing a superposition qubit to collapses to 1, means cancel the other value 0 to get 1 appear Question details step by step: ...
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What is $\mathbb{Z}_2$ symmetry?

I encountered the notion of $\mathbb{Z}_2$ symmetry in an article. Can someone give a definition?
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Find probability of a single qubit's measurement results from a 5 qubit state

I have a tensor product of a 5 qubit state |h>. From this I want to calculate the probability of the 2nd qubit being in state |1>. Can someone show me how I can do this? I know I can use the Born rule ...
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IBM Quantum experience

What is this Dedicated use of IBMq_16_melbourne? I am trying to run a simulation but it is not running. Is there any way to run the simulations? When is the backend coming online again for normal ...
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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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Measuring Coherence Length for T1 and T2 values with IBMQ Experience

So I'm currently working on a little program to measure how long the coherence time of a qubit is. Basically the idea is to initialise a qubit with a X or H gate then stick in a varying amount of ...
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1answer
58 views

Taking the two qubit reduced density matrix on a 5 qubit system

I am wanting to find the two qubit reduced density matrix on a 5 qubit system. I have the 5 qubit state in the form of a tensor product and I want to find the reduced density matrix of qubits 1 and 3. ...
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1answer
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What is the intuition of using Hadamard gate in quantum fourier transform?

According to this answer by rrtucci, I still cannot catch the spirit of QFT algorithm. So I would like to ask why are we using the Hadamard gate when computing the Fourier Transform? Moreover, what ...
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Does entanglement allow communication of user specified information or not?

At first when I heard about entanglement, I thought "Neat, so we can make a manipulation on our quantum computer here in such a way that can be interpreted as a binary output somewhere else, and have ...
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How to implement NM Algorithm for Variational Quantum Eigensolver?

First of all: thanks for reading again. I appreciate the feedback I have gotten from this community the past weeks as I started to feel ready to ask questions about quantum computing topics. I am ...
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Does the Choi-Jamiolkowski isomorphism really establish a connection between kinematics and dynamics?

I understand the mathematical construction of the Choi-Jamiolkowski isomorphism aka channel-state duality. It all makes sense formally, yet I still struggle to grasp its physical (or quantum-...
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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 ...
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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 ...
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Bell State 11 not working for parity curve

I am currently writing a script to automate the creation of parity curves for a 2 qubit bell state and then calculate fidelity and proving entanglement from that (inspired by this paper). It was going ...
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1answer
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How to prove the following bosonic entanglement expression?

Based on the article given by J. L. Ball, I. Fuentes-Schuller, and F. P. Schuller, Phys. Lett. A 359, 550 (2006) had used the following expression of von-Neumann entropy \begin{equation} S = - \...
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1answer
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How to find a common eigenstate of commuting operators?

I have multiple different operators in matrix form and I need to find their common eigenstates. The challenge is that the common eigenstate is in a superposition of multiple states and isn't just a ...
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What is the motivation for Weyl matrices in quantum information theory?

Quantum Entanglement and Geometry — Andreas Gabriel (2010) — Sec: 2.3.4 ~p. 11 Another basis for $d\times d$-dimensional matrices that has proven to be quite useful in quantum information theory is ...
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Quantum fidelity simplified formula while both of the density matrices are single qubit states

I have a question while reading the quantum fidelity definition in Wikipedia Fidelity of quantum states, at the end of the Definition section of quantum fidelity formula, it says Explicit expression ...
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1answer
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Perform quantum gate operations using state vectors and matrices

I am getting confused as to how to perform gate operations using matrices and am hoping someone will help me walk through this example. Say I want to perform a Pauli-X gate on the 3rd qubit in a 3-...
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1answer
44 views

What is Landauer’s principle?

How does the act of erasing information increase the total entropy of the system? This goes by the name Landauer's principle. Some details are here. Can anyone shed more light on this?
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What are nontrivial examples of $n$-sharable bipartite states?

A bipartite state $\newcommand{\ket}[1]{\lvert #1\rangle}\rho_{AB}$ is said to be $n$-sharable when it is possible to find an extended state $\rho_{AB_1\cdots B_n}$ such that partial tracing over any ...
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Simultaneous eigenstate of commuting observables and their tensor product

So this is about something from Preskill's notes on Quantum Computation and Information, Chapter 4, page 3. Imagine we have a maximally entangled state (Bell state). We can identify the Bell state by ...
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What property ensures that von Neumann entropy is conserved?

So I always had this idea in my mind that unitary evolution in quantum mechanics conserves information (or in other words von Neumann entropy) because unitary evolution preserves the trace. But this ...
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Twirling Quantum Channels: Pauli and Clifford Twirling

I am currently working through some papers related with approximations of more general quantum channels such as amplitude and phase damping channels to Pauli channels. The reason to do so is so that ...
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Structural Physical Approximation of Partial Transpose

To make the partial transpose a complete positive and therefore physical map, one has to mix it with enough of the maximally mixed state to offset the negative eigenvalues. The most negative ...
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CTCs and information time travel — what non-trivial insights do they lead to?

Context: In quantum complexity theory and quantum information, there are several papers which study the implications of closed timelike curves (CTCs). In 2008, Aaronson and Watrous published their ...
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Does the dilation in Naimark's theorem produce a state?

A POVM, as defined for example in (Peres and Wooters 1991), is defined by a set of positive operators $\mu(a)$ satisfying $\sum_a \mu(a)=\mathbb 1$. We do not require the $\mu(a)$ to be projectors, ...
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Trace distance of two classical-quantum states

I have these two classical-quantum states: $$\rho = \sum_{a} \lvert a\rangle \langle a\lvert \otimes q^a \\ \mu = \sum_{a} \lvert a\rangle \langle a\lvert \otimes r^a $$ Where $a$ are the classical ...
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How to understand the Haar measure from a quantum information perspective?

I found it a little difficult to understand it using Wikipedia and some mathematical documents. How to understand the Haar measure from a quantum information theory perspective? Are there any ...
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Are there disadvantages in using the inner product between states instead of the fidelity?

Would there be any disadvantages of using inner product, that is, $\mathrm{Tr}(A^{\dagger}B)$ (say making it, $\mathrm{Tr}(\sqrt A \sqrt B)$ to normalise) to quantify how far two quantum states are ...
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How does a map being “only” positive reflect on its Choi representation?

We know that a map $\Phi\in\mathrm T(\mathcal X,\mathcal Y)$ being completely positive is equivalent to its Choi representation being positive: $J(\Phi)\in\operatorname{Pos}(\mathcal Y\otimes\mathcal ...
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Direct derivation of the Kraus representation from the natural representation, using SVD

$\newcommand{\Y}{\mathcal{Y}}\newcommand{\X}{\mathcal{X}}\newcommand{\rmL}{\mathrm{L}}$As explained for example in Watrous' book (chapter 2, p. 79), given an arbitrary linear map $\Phi\in\rmL(\rmL( \X)...
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261 views

How are witness operators physically implemented?

Let's take an example of an entanglement witness of the form $W = | \phi \rangle \langle \phi | ^{T_2}$ where $ | \phi \rangle $ is some pure entangled state. If I wanted to test some state $\rho$, I ...
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Proving the inequality $|\mathrm{tr}(AU)|\le \mathrm{tr}|A|$ in Uhlmann's theorem

In Nielsen and Chuang, in the Fidelity section, (Lemma 9.5, page 410 in the 2002 edition), they prove the following. $$ \mathrm{tr}(AU) = |\mathrm{tr}(|A|VU)| = |\mathrm{tr}(|A|^{1/2}|A|^{1/2}VU)| $$ ...
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Explicit 16⨯16 matrix representations of two-qudit entanglement witnesses

I have a set of $16 \times 16$ two-qudit density matrices. I would like to study the bound-entanglement for this set, making use of entanglement witnesses for which explicit matrix representations are ...
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Are entanglement witnesses of this form optimal?

One can make an entanglement witness by taking the partial transpose of any pure entangled state. Consider $|\phi \rangle $ as any pure entangled state. Then $W = | \phi \rangle \langle \phi |^{T_2} ...
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Degradable channels and their quantum capacity

Note: I'm reposting this question as it was deleted by the original author, so that we do not lose out on the existing answer there, by Prof. Watrous. Further answers are obviously welcome. I have ...
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Quantum channel cannot increase Holevo information of an ensemble

I need to prove the fact that a quantum channel (a superoperator) cannot increase the Holevo information of an ensemble $\epsilon = \{\rho_x, p_x\}$. Mathematically expressed I need to prove $$\begin{...
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Counting channel uses of the lossy bosonic channel or definition of channel uses

The PLOB-bound ("Fundamental Limits of Repeaterless Quantum Communications") gives an asymptotic upper bound on the secret-key rate per used lossy bosonic channel. However, I'm not sure how to count ...