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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What is meant by fermionic and bosonic “modes”?

The paper The Dirac quantum automaton: a short review (pdf) starts off by stating: The starting point for the construction of space–time and the physical laws therein is an unstructured, countably ...
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Why are simulated qubits less effective?

"We could map the whole Universe — all of the information that has existed since the Big Bang — onto 300 qubits" I've seen statements like this over the years coupled with the same explanation ...
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Reduced density operator of a maximally entangled state

Is the reduced density operator of a maximally entangled pure state always maximally mixed (trace being half)? I test it on 4 bell state and this claim is true. I wonder why and can the degree of ...
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Trace representation of density matrix question [closed]

System $A$ and system $B$ form a composite system. https://en.wikipedia.org/wiki/Partial_trace I wonder why $\rho_{AB}$ cannot be represented as $(\text{tr}_{B}(\rho))\otimes ...
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State evolution for Dot product of quantum states (Llyod et al. 2013) [closed]

I was reading the paper by Lloyd et al. which is concerned with quantum machine learning algorithms. In the algorithm they use the evolution of the following kind (i use a reduced formula, which is ...
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Issues with the proof of the no-cloning theorem

The no-cloning theorem states according to Wikipedia that it is impossible to create an identical copy of an arbitrary unknown quantum state. As far as I am aware the theorem is usually proofen ...
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Does Bekenstein bound imply that the number of possible states of a bounded system is finite?

Bekenstein bound limits the amount of information that can be stored in a system of bounded size and mass. Does that imply that the number of possible states is finite? Does that imply that the number ...
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The definition of entropy in quantum mechanics

I have seen entropy with several different definitions. Like Von Neumann entropy and Rényi entropy, etc. So I am curious why there are so many different definitions in quantum mechanics while only ...
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Generalized Born Rule for partial measurements

I'm looking for the mathematical formulation of this trait (from an introductory Quantum Computing course): How can I generalize this into higher dimensions? Or other observables? It does not seem ...
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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 ...
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Quantum Crypto infrastructure & hardware

To implement real quantum cryptography in the real world, does the physical link layer from Point A to Point B be an optical link for all parts? Is there any links or whitepaper containing prototypes ...
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Quantum entanglement and information transfer

I know it was stated many times that information transfer using entanglement is not possible and I am most probably wrong but I would be glad if you can at least point me to where I am mistaken. If ...
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Checking correctness of partial trace

I am doing some simulations that requires me to take partial trace over a three qubit density matrix $\rho_{ABC}$. I find the mixed state density matrix of one qubit by tracing out the other two, ...
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Which are some good books to learn about quantum states? [duplicate]

I am aware of the book Geometry of Quantum states: An introduction to Quantum Entanglement by Bengtsson & Zyczkowski. I have read the book Quantum Mechanics: A Modern Development by Ballentine.
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How does many possible futures not mean many possible pasts?

The following link implies that quantum mechanics only violates the "one future" aspect of information conservation: ...
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Local operation on bipartite quantum system [closed]

Suppose we have a state: $$ |\Psi_{1234}\rangle = \frac{1}{2}\left(|\Psi_{14}^+\rangle \otimes |\Psi_{23}^+ \rangle + |\Psi_{14}^-\rangle \otimes |\Psi_{23}^- \rangle - |\Phi_{14}^+\rangle \otimes ...
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How is Q superposition in Q information different from a classical dice?

Let's consider a dice with 1 or -1 on its faces, opposites faces adding up to 0. The point of this post is to relate the quantum coherence of a single qubit to something "weird", i.e., incapable of ...
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Measurability of multipartite entanglement

Consider an arbitrary quantum system of $N$ distinguishable channels, where each channel can be considered a beam ending in a photon counter for simplicity How completely can the multipartite ...
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How can we “exchange” particles, since they are “identical”?

Doubt 1: If two particles are identical, you can not distinguish between them. Then, I think, permutation operation is meaningless. Because you can not distinguish them, how can you tell if they are ...
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What's wrong with this experiment showing that either FTL communication is possible or complementarity doesn't hold?

The assumptions are: Alice and Bob have perfectly synchronized clocks Alice and Bob have successfully exchanged a pair of entangled photons The idea is simply to have Alice and Bob perform the ...
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What state is a qubit system in if it is measured by someone, but we do not know the measurement?

Suppose there is a qubit Q in the state $$ \lvert+\rangle = \frac{1}{\sqrt2}(\lvert 0\rangle+ \lvert 1\rangle) $$ Now somebody makes a computational basis measurement on Q, but we do not learn the ...
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Quantum Fourier transform question about the state after application of controlled-$R_{k}$ gate?

Quantum fourier transform "circuit" is this: Each of the $R_{k}$ is this: After the hadamard gate on first bit: The state is: I don't know why we can see after the controlled $R_{2}$ gate the ...
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In quantum Fourier transform, why can any controlled $R_{k}$ gate be formed by two controlled-Not gate?

Controlled $R_{k}$ gate is implemented in quantum Fourier transform like this: Each of the $R_{k}$ on a qubit is in this matrix form: My question is: Why each of these controlled $R_{k}$ gates, no ...
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Computational basis definition question

Whenever we express an operation in computational basis, do we assume the first qubit as the qubit in the topmost quantum wire in the circuit diagram? Let's just consider the case of two qubits ...
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What is the 'area law' in the context of matrix product states?

I am trying to get into the topic of matrix product states by reading this: A practical introduction to tensor networks: Matrix product states and projected entangled pair states. R. Orús. Ann. ...
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How to we measure quantum purity experimentally?

Quantum purity $\gamma$ of a general state $\rho$, where $\rho$ is a density matrix, is defined as $\gamma = \text{tr} (\rho^2)$. I'd like to understand how $\gamma$ can be measured experimentally. ...
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What is the significance of the imaginary unit in Deutsch gate?

What is the significance of the imaginary unit $i$ in Deutsch gate? Is this controlled $R_x(\pi\alpha)$ still universal without the imaginary unit $i$?
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A question on qbit

As layman I couldn't yet conceive how one could know that a given qbit, if it is said to have certain probability amplitudes alpha and beta, actually have (fairly accurately) these amplitude values, ...
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Nobel Prize challenge: Could neutrinos be used for quantum information processing?

We know that two scientists, Takaaki Kajita and Arthur B. McDonald, working on Neutrinos have just been awarded the 2015 Nobel Prize in Physics. My question as a Nobel Prize Challenge Question is: ...
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Is CNOT a one-qubit or two-qubit operation? [closed]

Is CNOT a one-qubit or two-qubit operation? It has inputs of two qubits and needs two quantum wires.
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Understanding measurement based quantum computing

I am currently reading M. A. Nielsen's review on Cluster-state Quantum Computation (Nielsen, Michael A. "Cluster-state quantum computation." Reports on Mathematical Physics 57.1 (2006): 147-161.). ...
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Geometric picture behind quantum expanders

A $(d,\lambda)$-quantum expander is a distribution $\nu$ over the unitary group $\mathcal{U}(d)$ with the property that: a) $|\mathrm{supp} \ \nu| =d$, b) $\Vert \mathbb{E}_{U \sim \nu} U \otimes ...
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Popular books on cutting-edge physics [closed]

I watched this video, in which different types of topics are discussed like Quantum Information, Quantum Computation, Universe as hologram, Hidden information, Quantum Entanglement, Black holes and ...
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Applying a NOT gate on an entangled qubit of equal amplitudes of $|1⟩$ and $|0⟩$

I am currently listening to lecture 11 (Superdense coding) of Michael Nielsen's Quantum Computation for the determined series. It starts off with 2 qubits, both in the $|0\rangle$ state. Then the ...
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If the discretized $x$ and $p$ are conjugate variables, why are there two $U$s in $U_{FFT}xU_{FFT}^{\dagger}=p $?

While studying some quantum mechanics from Nielsen's book on quantum computing, specifically the simulation of the single-particle Schrödinger equation using a quantum computer, I came across ...
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Constructing a Toffoli gate with 2-and 1-qubit gates?

I'm looking through Nielsen & Chuang's book on quantum computation and information and in part of it he says that any $C^2(U)$ gate can be constructed from two qubit and one qubit gates. I can't ...
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What is the actual meaning of the density operator?

I am not able to understand the definition of the density operator. I know that if $V$ is a vector space and if I have $k$ states belonging to this vector space, say $|\psi_{i}\rangle$ for $1\le i\le ...
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When is a unitary operator a quantum gate?

Quantum gates we use like X, Y, Z, H, CNOT, etc. are all unitary. When can an arbitrary unitary operator be considered as a quantum gate?
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A good book for Quantum Cryptography

I am interested in Quantum Information and Cryptography in particular. I have gone through Nielsen's text and Preskill's notes . Can someone suggest me some good text for Quantum Cryptography ? I ...
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Difference between operators used to represent quantum gates vs that to represent physical observables?

I have learnt that informations about a physical observable property is buried in the state vector of a quantum system. To get the possible value of a property all we need to do is multiply the state ...
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Indirect probing of entanglement measures

Entanglement is a purely quantum mechanical phenomena that e.q. increase precision of quantum interferometers, atomic clocks or have application in quantum computing. There are many "measures" of ...
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Measuring Qubits in Entangled State

If two people (Alice and Bob) are given a state $|\phi^+\rangle = \frac{1}{\sqrt2}(|00\rangle + |11\rangle)$ from a list of states, then Alice can read the first qubit, see if it is 0 or 1, and send ...
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Quantum teleportation of a macroscopic object

suppose that quantum teleportation of a macroscopic composite object, like say, a grain of rock, was physically and technologically possible The traditional teleportation scheme would have to prepare ...
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why shielding surfaces may not be continuous?

Books say that screening surfaces need not be continuous to work but my question is that counter electric field produced won't be less such as faraday cages is not countinuous then how it works??
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Definition of the “support” of the reduced density matrix

Some of the papers in condensed matter physics use the word "support" (space). For example, the following papers use the support especially for the reduced density matrix. ...
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Are coherent states of light 'classical' or 'quantum'?

Coherent states of light, defined as $$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle $$ for a given complex number $\alpha$ and where $|n\rangle$ is a ...
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Receiving Multiple Copies of a Qubit

Suppose you are given one of two non-orthogonal qubits randomly: either $|\phi\rangle$ or $|\psi\rangle$. Using a particular distinguishing procedure, you can guess which of the two qubits you were ...
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Is macroscopic causality an issue in the context of certain quantum experiments?

In order to formulate my question properly I need to explain a few things. Cramer_Herbert Zych_Brukner Reference 1. - John Cramer, Nick Herbert, "An Inquiry into the Possibility of Nonlocal Quantum ...
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Using LOCC Operations to Distinguish Bell States

Example taken from http://www.quantiki.org/wiki/LOCC_operations: Suppose I have two Bell states $|\phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$ and $|\psi^+\rangle = ...