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 spontaneous symmetry breaking in QUANTUM systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
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What do quantum theory and general relativity have in common? [closed]

What areas of commonality are there between quantum theory and general relativity? Is it even possible to use the the two when calculating the same physical behaviour? Is there a correlation between ...
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How does one compute the state of a quantum system following imperfect measurement?

Suppose I have a quantum system $S$ ("system") with Hamiltonian $H_S$ and initial density matrix $\rho_S(0)$. I allow $S$ to interact with another system $P$ ("probe"), which has Hamiltonian $H_P$ and ...
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Proof of inversion about the mean (Grover's) [closed]

I just have an probably trivial question, but i got stuck when deriving the inversion of the mean as used in Grover's search: I simply want to show that the application of $(2 \left| \psi ...
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Does this quote from my textbook imply that not all states are superpositions?

I read this at a book; The difference between bits and qubits is that a qubit can be in a state other than $|0\rangle$ or $|1\rangle$. It is also possible to form linear combinations of ...
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Intuition behind Hamiltonian

I am reading this paper by Das et al. which converts Deutsch's algorithm into an adiabatic quantum algorithm. I don't get the intuition behind the initial and final Hamiltonians. If defines the ...
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Bosonic qubits using BEC versus usual qubit implementations based on energy levels

All condensate atoms in a BEC (say like Rb, etc) effectively occupy the lowest energy-state. If it is that the case, then how are such bosons in a BEC encoded as a qubit? In particular, when Grover ...
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Seemingly a paradox on the eigenstate thermalization hypothesis (ETH)

In the research field of Many-body Localization (MBL), people are always talking about the eigenstate thermalization hypothesis (ETH). ETH asserts that for a isolated quantum system, all many-body ...
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Theoretically, how does quantum decoherence induce noise?

The decoherence process has allowed us to explain various (classical and decoherence) sources of measurement noise in quantum systems. I intuitively understand this physical concept of ...
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The definition of Gaussian State

Could you clarify to me what is a Gaussian state? I know what is a Gaussian function and Gaussian distribution, but I don't know how to respond to other when they ask me to provide the definition of a ...
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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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1answer
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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?