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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Probability distribution of a pretty-good measurement

Let $\rho_{XE}$ be a classical-quantum state. That is, $$ \rho_{XE} = \sum_{x}\Pr[X=x] \cdot |x\rangle \langle x | \otimes \rho_{x} $$ where every $\rho_{x}$ is a density matrix with ...
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Unitarity of quantum evolution

In this paper by Charles Bennett, he says on page 25, I understand why U(XOR) gives the result it does but why is that a consequence of its unitary property? Thanks
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On $k$-extendability of bipartite states

Definition of $k$-extendability can be given as follows. Let $k\in \mathbb{N}$. A state $\rho_{AB}$ on a bipartite Hilbert space $\mathrm{A}\otimes\mathrm{B}$ is $k$-extendible with respect to ...
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Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...
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Are Feynman's Hamiltonian computers unitary?

In this paper, Feynman gave the idea of creating a time-independent Hamiltonian from a quantum circuit. Is there anyway to say that these Hamiltonians will always be Hermitian? Moreover, will these ...
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Difference between DMRG (density matrix renomalization group) and MPS (matrix product states)?

I am learning DMRG recently. I noticed there are many papers both in the DMRG approach and MPS (such as variational matrix product state (VMPS) by F.Verstraete and J.I.Cirac) approach. In my eyes, ...
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Rotations in Bloch Sphere about an arbitrary axis

I am trying to understand the following statement. "Suppose a single qubit has a state represented by the Bloch vector $\vec{\lambda}$. Then the effect of the rotation $R_{\hat{n}}(\theta)$ on the ...
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394 views

Kraus operator rank

All quantum operations $\mathcal{E}$ on a system of Hilbert space dimension $\mathcal{d}$ can be generated by an operator-sum representation containing at most $\mathcal{d^2}$ elements. Extending ...
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112 views

Clustered-Entanglement thermodynamics

I want to understand the tools required to do calculations in entanglement thermodynamics in general, but I'm considering first how to model entanglement mathematically in terms of many-body systems ...
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25 views

What does it mean to find a particle in a range at a given value?

Find the probability of finding the electron in the range $\Delta r = 0.02a_0$ at (a) $r = a_0$ and (b) $r = 2a_0$ for the state $n = 2$, $l = 0$, $m = 0$ in hydrogen. I don't understand the ...
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40 views

What is the easiest way to prepare a Glauber coherent state? [closed]

Without using a laser source. Can you, for example, create a coherent state by filtering another light source (incandescent light bulb, LED, etc)?
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95 views

Positive Partial Transposition in Fano form

Cite from "Geometry of Quantum States: An Introduction to Quantum Entanglement 1st Edition by Ingemar Bengtsson (Author), Karol Zyczkowski (Author)": "Partial transposition applied on a density ...
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How many states does a qubit have? [closed]

There is something I am trying to understand about qubits. If a qubit can exist in an infinite (is that even correct?) number of states prior to the measurement, then why can it only be measured in ...
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What is the current big question or motivation in quantum information? [closed]

As an prospective student, I am facing a crossing as many people did. I would love to know what is the current big question or motivation in the quantum information society? If anyone knows the answer ...
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Reference request: QFT and AdS/CFT for information theorists

There is a lot of buzz recently about connections between quantum information theory and quantum field theory/string theory. I would like to understand in particular how quantum information methods ...
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Questions regarding reversible processes, entanglement, and time reversal symmetry [closed]

Can we, a priori, state that a physical state is entangled with its environment? Its hard for me to come up with a reason for why we can't. For my next question, consider a physical state: ...
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1answer
50 views

How is the range of $x\cdot s$ in Simon's algorithm restricted to $\{0,1\}$?

The final critical step of Simon's algorithm (before setting up a simpler system of equations to solve) involves taking advantage of the fact that $$x\cdot s \in\{0,1 \}$$ but for $x,s \in ...
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Is Thermalization of a subsystem simply the result of Decoherence of its state?

I would appreciate answers that explain both the concepts in short to underline if there are any key differences between the two. Also, how does a localized state survive decoherence?
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Interpretation of position projection operator

Does the operator: $$\int_a^b \mathrm{d}x \, |x\rangle \langle x|$$ have physical meaning acting in a Hilbert space where it does not exactly correspond to the identity operator? Does it correspond ...
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95 views

Understanding the Mathematics of Wigner function [duplicate]

I fully understand that Wigner function provides the complete information of a state of a quantum system, i.e. quantum phase space, while not violating Uncertainty principle. But can anyone tell me ...
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1answer
68 views

Can a qubit have an imaginary component?

My knowledge of linear algebra is limited and my physics knowledge mostly comes from high school and Youtube so please bear with me. In the equation $$|x\rangle = a|0\rangle+b|1\rangle,$$ I read that ...
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120 views

How can all information be localized if local realism is dead?

I'm confused about whether quantum mechanics is local or not. The authors of a recent, much publicized experiment argue that their results "imply statistically significant rejection of the ...
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25 views

What is the difference between the atomic resonance frequency and the Rabi frequency?

I've been trying to work my way through the solution to the optical bloch equations for a two-level atom system which is being driven by a laser. One thing that has been confusing me is the difference ...
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49 views

Numerically finding the energy diagram of the hamiltonian

I'm looking at a collection of three two level systems (qubits) coupled to each other (with known bare state energies and couplings). The hamiltonian is given by ...
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mixture of maximally mixed and maximally entangled state

Consider the quantum system $\mathcal{B}(\mathbb{C}^d\otimes\mathbb{C}^d)$ and $|\psi\rangle=\frac{1}{\sqrt{d}}\sum_{i=0}^{d-1}|i,i\rangle$ be the (standard) maximally entangled state. Consider the ...
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What's so confusing about quantum physics? [closed]

Okay, just right off the bat, I want to make it clear that this is a stupid question. Check out this graph, from SMBC: Ignore the 'political discourse' part and replace it with 'talking about ...
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How is decoherence due to the environment compatible with the Copenhagen interpretation?

Let's say that "decoherence" is that transition from a pure quantum state to a mixed state due to interactions with the environment. (A reasonable definition?) How is that compatible with the ...
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What are some of the differences between (the fields of) quantum computation and quantum information theory? [closed]

I have just started self-learning quantum information theory, and have a sub-trivial question: what is the difference between that field of study and quantum computation? I have some understanding ...
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Is there something behind non-commuting observables?

Consider a quantum system described by the Hilbert space $\mathcal{H}$ and consider $A,B\in \mathcal{L}(\mathcal{H},\mathcal{H})$ to be observables. If those observables do not commute there's no ...
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Proof Reversible quantum gate is linear

Edit: to avoid confusion, this problem should start off my assuming the input bits and output bits are classical and just try all the possible combinations of constants to show linearity.
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Conservation of quantum coherence?

Is coherence conserved under unitary transformation? As we saw in the process of generating entanglement, coherence between states of the subsystem is transferred to quantum correlations (related to ...
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How does quantum superposition make calculation faster?

In every description of a quantum computer I've seen (that isn't extremely technical), they've been described as computers that use qubits, that use a superposition of 1 and 0 to make processing ...
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Electron jump into a transistor to read qubit state

Prof. Andrea Morello, a quantum physicist, in one of its quantum computer models uses the spin of the outermost electron in a phosphorus atom to represent a qubit. This atom is embedded to a ...
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Normal Ordering and Smearing

I read on Wikipedia two different descriptions of the "Husimi-Q representation." One is that it is the Wigner function convolved with a Gaussian, which in particular results in a positive definite ...
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How to represent a Liouville projection superoperator in Hilbert space?

Is there a general way to represent a Liouville projection operator in Hilbert space, or can they take on any form so long as they satisfy the required properties of a projector? e.g. The thermal ...
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Looking for an example of an operator that will not converge on maximally mixed state

Based on my former questions and the kind help from the answers (especially Norbert Schuch), it seems that the maximally mixed state is not that special as I thought. But still I have to admit that it ...
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An augmented version of the optimization problem

In my last question, I proposed the following problem: (1) Given a finite dimensional composite system AB whose initial state is a product state of A and B so that $\rho_{AB}=\rho_A\otimes \rho_B$. ...
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Holonomic and Topological Quantum Computing [closed]

In topological quantum computation, anyons are braided in spacetime, performing non-trivial evolutions of some degenerate groundstate. In holonomic quantum computation, the system is braided in ...
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Would the quantum state of a photon be disturbed if it were traveling through fiber optic cabling?

See here... https://en.wikipedia.org/wiki/Linear_optical_quantum_computing https://en.wikipedia.org/wiki/Optical_fiber_cable I'm just worried that upon reflection within the cable the photon's ...
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How to solve such a maximal entropy oriented optimization problem?

I am considering such a problem: (1) Given a finite dimensional composite system AB whose initial state is a product state of A and B so that $\rho_{AB}=\rho_A\otimes \rho_B$. (2) Assuming AB ...
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Is this correct? $Tr_{B}(U_{AB}(I_A\otimes \rho_B)U_{AB}^{+})=I_A$

A composite system AB, its initial state is a product state of A and B given by $(I_A\otimes \rho_B)$ (A in a completely mixed state). The composite system undergoes a unitary operation $U_{AB}$. My ...
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Finding the dependence of dephasing time on flux noise in Transmon Qubits

Before introducing some relevant concepts I'll begin by stating my question. What I am looking for is the connection between the noise the flux through the SQUID in my transmon qubit (related to the ...
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SPDC and single photon production

In Spatial Parametric Down Conversion, incoming photons are split into entangled photon pairs by passing through a non-linear optical medium. Since I get a photon pair as an output then how can I say ...
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Probability of obtaining the desired state in quantum linear regression

I was reading today the paper "Pattern classification with linear regression on a quantum computer" where the authors calculate in a final step the probability of success to measure the last qubit in ...
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Generating Single photons

How can single photons be generated by making a coherent state weaker by attenuating it?(For reference please see, Quantum Computation and Quantum Information by Nielsen and Chuang, 10th ...
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How is quantum superposition different from mixed state?

According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state. Now consider state ...
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Entanglement for Gaussian states

Let us consider the product Fock space $\Gamma(\mathbb{C}^m) \otimes \Gamma(\mathbb{C}^n)$ and consider Gaussian states in that space. While reading some literature on Gaussian state entanglement ...
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Partial trace question: how does this term become zero?

I have recently been introduced to the partial trace but I have a question about how my lecturer recognises 'zero' and 'non-zero' terms. Consider the state: $\psi_{AB} = c_{00}|00\rangle + ...
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Understanding the optimal approximate qubit cloning method

I'm trying to understand the operation used for optimal cloning of pure qubits states from the paper Optimal Cloning of Pure States by R. F. Werner. The paper describes the optimal cloning method ...
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Approximate cloning of a qubit, given multiple starting copies

Suppose I'm given several clones of a qubit in a pure unentangled state. That is to say, I'm given the state $(a \left|0\right\rangle + b \left|1\right\rangle)^{\otimes n}$. My goal is to make $d$ ...