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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Book recommendations on measures of entanglement

I am an undergrad. physics student writing my bachelor thesis at the moment. What book would you recommend that talks about measures of entanglement? It would be really cool if it gave different ...
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Qubits of higher dimension

In Quantum Computing, one usually looks at two-state-systems named qubits to perform a computation. One problem arises when the number of qubits is increased, because the whole system becomes in such ...
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One-body entropy?

In theoretical studies of Bose-Einstein condensates, it's common to look at the one-body density matrix: $$ n_{ab}=\langle\hat{c}_a^\dagger\hat{c}_b\rangle $$ where the $\hat{c}_j$ are annihilation ...
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Essential Reading on Quantum Information for Beginners [closed]

I am a first-year graduate student looking into research groups working in Quantum Metrology, Quantum cosmology and Quantum information science. Therefore, I was looking for good references in terms ...
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Do channels which do not affect a subsystem always have the form $\mathcal E=\mathcal T_{\mathcal A}\otimes\text{id}_B$?

consider a bipartite state on two Hilbert spaces $\rho_{AB}$. Usually, I think of a channel $\mathcal E$ as acting only on $A$ if $$\mathrm{Tr}_A(\mathcal E(\rho_{AB}))=\mathrm{Tr}_A(\rho_{AB}) \tag ...
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What are 'Quantum Coherences'?

In quantum mechanics there are many references to quantum coherences, but I am still unsure of what the precise definition of a coherence is in all cases. There is clearly a precise sense in which a ...
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Based Relay Quantum Communication

One of the methods to perform Quantum Communication in a long distance is to do it using quantum relays which is known by the relay based long-distance quantum communication. I'm looking for the ...
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1answer
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Can Wigner and his friend disagree on an ultimate measurement?

My understanding, roughly, is that the Wigner's Friend thought experiment involves a situation in which there are two isolated apparatuses that act on entangled particles (for example, polarized ...
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Optimal measurement for distinguishing states

Suppose we have $n$ identical spin-1/2 particles prepared by some machine. Depending on the setting of the machine, either all the particles are in state |$z_+$> or they are all in state |$x_+$ > (...
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Understanding Bennett's laws for quantum information

Charles Bennett's laws of quantum information are (see https://en.wikipedia.org/wiki/Bennett%27s_laws): 1 qubit $\succeq$ 1 bit 1 qubit $\succeq$ 1 ebit 1 ebit + 1 qubit $\succeq$ 2 bits 1 ebit + 2 ...
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Photon number for a multimode cavity

Let's assume I have a cavity with one main frequency and two different sideband frequencies characterized by the annihilation operators $a$, $a_1$ and $a_2$. If I want to calculate the number of ...
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Advice required on a self-study path [closed]

I am a student in the 3rd year of my BS-MS degree in Physics. Due to the recent Virus outbreak, my college is closed until further notice. Thus, I started watching some talks on YouTube about some ...
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How inelastic spin-exchange collisions works?

I'm studying for my bachelor thesis on Quantum Thermometry. The core of the procedure is motion-spin mapping onto quantum states of the probe, so inserting Caesium atoms in a ultra cold Rubidium gas ...
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Finite computational power of universe vs continuous nature of unbounded particles

I am not a physicist, but I've worked to make this an intelligible question for SE. What information is exactly and how it is stored in the universe is still being studied, but here Seth Lloyd gives ...
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How does einselection fit into quantum decoherence?

My understanding of decoherence is the following: There is a system state vector $|\Psi\rangle_s$ and the environment state vector $|\Psi\rangle_\epsilon$ which are combined to form $|\Psi\rangle_s \...
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How to prepare state |+⟩? [closed]

Is there a method how to prepare quantum pure state $|+⟩ = \frac{1}{\sqrt{2}}(|0⟩+|1⟩)$ ? Thanks a lot for concrete answer.
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Measuring overlap of two quantum states

I have a qubit state $|\psi\rangle = a|0\rangle + b|1\rangle$, and another qubit state $|\psi'\rangle = a'|0\rangle + b'| 1 \rangle$. I want, through quantum gates, to measure the overlap $|\langle \...
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Are entanglement witness operators together with delayed entanglement swapping a violation of the non-communication theorem?

An entanglement witness operator lets you measure a system (let us say two particles) and determine if it was entangled or not. A delayed entanglement swapping allows to delay the decision to entangle ...
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Generalised basis independent relationship between Von Neumann Entropy and Purity of a quantum state [duplicate]

I have been trying to find a generalized relationship between Von Neumann Entropy and Purity of a quantum state? In this post there is a discussion of a specific case for a qubit and a more general ...
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How can the universe have a finite information capacity yet be continuous? [closed]

The information capacity of the universe is proportional to its surface area, so the observable universe has a finite information capacity. But the universe is also usually thought to be infinitely ...
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What's quantum about quantum discord?

Quantum discord is a quantity that relates two subsystems of a quantum state. It reduces to the entanglement entropy for pure states, but it differs for mixed states; separable states have zero ...
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Schmidt decomposition for Matrix Product State in canonical form

During a lecture on comp. Quantum Phyiscs the concept of Matrix Product States (MPS) (with open boundry conditions) was introduced in the form $$\vert\psi\rangle = \sum_{i_1,\dots,i_n}\psi_{i_1\dots ...
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Compute the Schmidt Decomposition of a two-qubit state

I'm trying to compute the schmidt composition of $$ |A\rangle = \frac{1}{2 \sqrt{2}}(|00\rangle + \sqrt{3}|01\rangle + \sqrt3 |10\rangle + |11\rangle) $$ I've calculated the eigenvalues to be $$ 1+\...
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Can we obtain the same result as Deutsch algorithm using a XOR gate?

If I understand correctly, Deutsch's algorithm is useful to know if a function $f(x)$ is constant ($f(0)=f(1)$) or balanced ($f(0) \neq f(1)$). And the advantage is that it only requires the ...
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Understanding time evolution in Von Neumann's pre-measurement (Ozawa model)

I'm studying Quantum Information Theory as a non-physicist and so I'm struggling a bit with simple concepts. Let's say we have a system $\Psi$ composed of two sub-systems: $\Psi = \Gamma \cup \Xi$ ...
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Action of quantum fourier transform on two-fermion states

In section 2.2 of the paper https://arxiv.org/abs/1807.07112, there appears a Fourier transformation named $F_k^n$ that comes out of a matrix called $F_2$, $$ F_2 = \begin{pmatrix} 1 & 0 & 0 &...
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Quantum gate fSWAP acting on two-fermion states

When we have identical particles which are fermions, any exchange (swap) among 2 states introduces a minus sign. In the paper https://arxiv.org/abs/1807.07112, the Eq. (7) aims to represent that ...
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Deriving the Bloch Equation of qubit purification for any measurement angle

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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Non-diagonal matrix element in density matrix

Is it possible to determine non-diagonal element of density matrix? It will be cool, if somebody present few examples. What is meaning of such element?
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Microwave to optical photon conversion- relation with long distance communication

I am reading a paper on microwave to optical photon conversion (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.99.063830) and there the authors are saying- Long-distance communication using ...
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Does the degeneracy in dominant eigenvalues of MPS transfer matrix necessarily mean long-range correlation?

A short-range correlated MPS state generally has one non-degenerate dominant eigenvalue in its transfer matrix, and the degeneracy in transfer matrix generally leads to long-range correlation (I'm ...
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How is weak measurement operator formed?

I am new to the topic of weak measurement. While reading this paper ( the open Arxiv version is here ), the authors have just introduced the operators: $$\hat{P}(x)=\sqrt{\frac{1-\tanh(x)}{2}}\hat{P1}+...
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Is there an analog of the Solovay-Kitaev Theorem for approximating quantum states?

The Solovay-Kitaev theorem shows that we can approximate arbitrary unitary transformations with polynomially many quantum gates. Can we approximate the resulting state vectors in the same way by ...
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Error estimate for finite approximation of Hadamard gate from two rotations

I was teaching myself some fundamentals about quantum computing with qiskit while I stumbled upon a challenge I am not able to solve. One problem discusses how one can implement the Hadamard gate (in ...
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Quantum observables in nonstandard Hilbert space

Consider a Hermitian $(n \times n)$-matrix $A$, and a Hilbert space $\mathbb{C}^n$, foreseen with a nonstandard inner product. (An inner product $s(\cdot,\cdot)$ is standard if for any two vectors $x =...
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Can quantum computing solve the curse of dimensionality?

Edited version The curse of dimensionality is ubiquitous in machine learning (ML) modeling, stochastic control and reinforcement learning, arising in a probabilistic sense, with strong connections to ...
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Do distillable states necessarily violate the CHSH inequality?

Let $\rho$ be a bipartite quantum state. If $\rho$ is distillable will it necessarily violate the CHSH inequality ($|\langle A_0(B_0+B_1)+A_1(B_0-B_1)\rangle| \leq 2$)?
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Is there a measure similar to the Helstrom measurement which can distinguish between more than 2 pure quantum states?

My understanding is the Helstrom measurement distinguishes between 2 pure quantum states. Is there a measure similar to the Helstrom measurement which can distinguishes between more than 2 pure ...
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Relation between the Glauber correlation functions and statistical correlation

As stated in Wikipedia's page: Correlation or dependence is any statistical relationship, whether causal or not, between two random variables. Now in "The Quantum Theory of Optical Coherence" ...
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Find the normalized state and function such that the equation holds for arbitrary unitary matrix [closed]

I have been recently puzzled with a problem I do not know how to solve. Here is the setting and some of my thoughts on the problem. Given: Let us denote the set of all unitary $d \times d$ matrices ...
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Implementation of neural network quantum states of the anti-ferromagnetic Heisenberg model

I'm studying this Science paper "Solving the quantum many-body problem with artificial neural networks" and looking into the implementation of the Anti-ferromagnetic Heisenberg model. The Hamiltonian ...
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Is any energy converted to information when taking a photograph?

I am curious about the relationship between energy and information. I have only a beginner's knowledge, having read Shannon's original paper and a little about Landauer's limit which states that the ...
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Help interpret bra-ket notation, quantum measurement equation (neielsen chuang, postulate 3)

I'm reading Quantum Computation and Quantum Information by Nielsen and Chuang (http://mmrc.amss.cas.cn/tlb/201702/W020170224608149940643.pdf). Equation 2.92 on page 85 is a bit confusing to me if ...
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Why is the standard definition of fidelity unnecessarily complicated?

The (Uhlmann-Josza) fidelity of quantum states $\rho$ and $\sigma$ is defined to be $$F(\rho, \sigma) := \mathrm{tr} \left[\sqrt{\sqrt{\rho} \sigma \sqrt{\rho}} \right]^2.$$ Every article I've ever ...
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Prove that there exists a $d \times d$ unitary matrix $U$ which cannot be decomposed as a product of fewer than $d-1$ two-level unitary matrices

This is exercise 4.38 from Nielsen and Chuang: Prove that there exists a $d \times d$ unitary matrix $U$ which cannot be decomposed as a product of fewer than $d-1$ two-level unitary matrices. If ...
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Prove that any state can be generated from a maximally entangled state via LOCC

$\newcommand{\ket}[1]{|#1\rangle}$ I have proved that in a Hilbert space $\mathcal{H}=\mathbb{C}^2\otimes\mathbb{C}^2$, starting from the Bell state $\ket{\Phi^+}=\frac{\ket{00}+\ket{11}}{\sqrt{2}}$ ...
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Expressing the CHSH inequality in terms of probability

Let's say we have a distribution which gives the probabilities $\mathbb{P}(a,b|x,y)$, where $a,b$ are the outputs of a quantum channel for Alice and Bob respectively, and $x,y$ are the inputs (also ...
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Entanglement between what?

According to the standard definition of "Entropy of Entanglement" https://en.wikipedia.org/wiki/Entropy_of_entanglement one starts from the density matrix of a pure state $$ \rho=|\psi\rangle\...
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Why is the von Neumann entropy maximised when $p_n=1/N$?

For example, $\hat \rho=\sum_{\substack{n}} p_n |E_n \rangle \langle E_n|$ is a stationary mixed state of a given quantum system, where $|E_n \rangle$ are eigenstates of the Hamiltonian $\hat H$ with ...
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What operator do we use to measure at the end of a quantum search algorithm?

Perhaps an obvious question, but I do not have the answer to it, so I though I would still ask. In the below quantum search algorithm, also known as Grover's algorithm, what operator are we ...

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