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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Is there non-trivial multipartite entanglement not witnessed by the spectra of reduced states?

A lot of analysis of multipartite entanglement is based on examining the spectra of various reduced states. (E.g. area laws.) Of course one generally needs not just the $N$ local states of each ...
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State vector vs density operator

We formulate quantum mechanics using language of state vectors. One alternative formulation is possible using density operator or density matrix. Why we are doing this alternative approach? Is the ...
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Can Quantum Entanglement and Quantum Superposition be considered the same phenomenon?

Quantum entanglement is known to be the exchange of quantum information between two particles at a distance, while quantum superposition is known to be the uncertainty of a particle (or particles) ...
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Design a quantum circuit from a matrix

I have unitary matrix and I would find the quantum circuit associated. There are 3 qubits input so it's a 8x8 matrix but it's not a simple operation. The number of gates is not specified. Is there a ...
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Example of a state which is positive but its partial transpose is not positive

Could any one give me an example of a state whose density matrix is positive semidefinnite but partial transpose is not positive semidefinnite?
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124 views

Are there any known physical implementations of quantum gates?

I was wondering if there are any known implementations of a small number of quantum gates that can interact with each other. Certainly we don't have a "complete" set of quantum gates (where ...
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A universe of a finite but increasing number of states of motion?

A limitation of the geometric models of universe is that space locally is considered as a volume, whilst volume is a part of a selected system of inertia. Wouldn't it be more adequate to consider (the ...
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What is the entropy of a pure state?

Well, zero of course. Because $S = -\text{tr}(\rho \ln \rho)$ and $\rho$ for a pure state gives zero entropy. But... all quantum states are really pure states right? A mixed state just describes ...
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why non orthogonal states are indistinguishable?

I want to know what does it mean by distinguishable quantum state from Mathematics perspective I mean mathematically. As a non physics background student could any one explain me why non orthogonal ...
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Where does deleted information go?

I've heard that, in classical and quantum mechanics, the law of conservation of information holds. I always wonder where my deleted files and folders have gone on my computer. It must be somewhere I ...
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60 views

Is there a lower bound on energy needed to transfer one bit of information?

Let's say we want to transmit information between to stations (points in space). Is there a minimal energy required to transfer a single bit of information, assuming that we tolerate that the bit ...
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249 views

What is discrete phase space?

I've been reading a little about the usual, continuous Wigner functions and phase space quasi-distributions in general, and I believe I understand the idea behind them. The Wigner function arises when ...
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Uniqueness of representing POVM using projective measurement

$\newcommand\tr{\operatorname{tr}} \newcommand\ket[1]{\lvert#1\rangle} \newcommand\bra[1]{\langle#1\rvert} $[Skip to the conjecture for a self-contained mathematical formulation of the question.] ...
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Why do we believe in a “force” driven universe? [closed]

Why do we not believe in the potential for a "unified force field" universe, to the exclusion of the belief in the potential for a mechanical, gear driven universe, if the correct shape for the gear ...
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194 views

Why do we need non-trivial fibrations?

I am currently reading this paper. I understand how the Bloch sphere $S^2$ is presented as a geometric representation of the observables of a two-state system: $$ \alpha |0\rangle + \beta |1\rangle ...
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89 views

Second Qubit Not Flipped in Hadamard Gate

I'm very new to QM and Quantum Computing and I have a likely simple question, It may simply stem from my lack of knowledge of vector calculus. We have a 2-qubit quantum state: $$ \mid\psi\rangle = ...
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These two operators commute…but their eigenvectors aren't all the same. Why?

The Hamiltonian $$H = \left[ \begin{array}{cccc} a & 0 & 0 & -b \\ 0 & 0 & -b & 0\\ 0 & -b & 0 & 0\\ -b & 0 & 0 & -a \end{array} \right] $$ commutes ...
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Is it sensible to speak of the parity operator in 4 dimensional Hilbert space?

So I'm dealing with a system of two qubits, with the hamiltonian given by $$H = \left[ \begin{array}{cccc} a & 0 & -b & 0 \\ 0 & 0 & 0 & -b\\ -b & 0 & 0 & 0\\ 0 ...
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Do Category Theory and/or Quantum Logic add value in physics?

I know they have their adherents, but do more or less esoteric branches of mathematics such as Category Theory and/or Quantum Logic provide powerful tools for new theory development or are they just ...
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Local unitary transformation that maximizes overlap

Could anyone point me in the right direction (reference to papers would suffice) regarding the following: Given two quantum states $|\psi\rangle ,|\phi\rangle \in (\mathbb{C}^d)^{\otimes n}$, where ...
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280 views

Bra-ket notation, Bits, & Superposition

I am a quantum computing enthusiast, and recently I stumbled upon this the following two propositions: $$ \alpha|1\rangle + \beta|0\rangle$$ What does this mean? My understanding of this is that: ...
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Solution of dynamics of density matrix

Given the dynamics of the density matrix: $ \frac{d}{d t}\begin{pmatrix} \rho_{00} & \rho_{01} \\ \rho_{10} & \rho_{11} \end{pmatrix} = \begin{pmatrix} \lambda ...
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Is there a formalism for talking about diagonality/commutativity of operators with respect to an overcomplete basis?

Consider a density matrix of a free particle in non-relativistic quantum mechanics. Nice, quasi-classical particles will be well-approximated by a wavepacket or a mixture of wavepackets. The ...
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Finding the spectrum of a curious hamiltonian

I wish to analyse the following hamiltonian, i.e. find its eigenvalues and eigenstates. $$H = \frac{1}{2}\epsilon(\sigma _z \otimes \mathbb{1} + 1\otimes \sigma _z) - \Delta (\sigma _x \otimes \sigma ...
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Classical logic in concern with QM Mathematics

In no way am I a physicist, so please excuse improperly used terms. It is in my understanding that Quantum Physics does not obey Classical Logic, hence the existence of Quantum Logic. My questions ...
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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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Intuition on positive-operator valued measures (POVM)

I'm having a little trouble understanding what positive-operator valued measure (POVM) are- in particular why/how they are non-negative. For instance, if they just represent measurements, what about ...
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Split property for type III algebras entails practical separability

I am reading Halvorson's thesis (http://philsci-archive.pitt.edu/346/1/main-new.pdf), however I don't understand a proof at p.50 where he tries to explain why the split property allows a local agent ...
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Eigenvalue of the adiabatic Hamiltonian of Farhi's three qubit 2-SAT problem

I was trying to reproduce example 3.3 of Quantum Computation by Adiabatic Evolution by Edward Farhi et. al. This is an adiabatic algorithm to solve an instance of three qubits 2-SAT problem. I think ...
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Dimension of separable state

Please can you help me to understand how the dimension of the set of separable states is $\dim \cal H_1 + \dim \cal H_2$? This is the relevant passage: So far, we have assumed implicitly that the ...
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What are the “other” Hadamard matrices?

The Pauli matrices $$ X = \begin{pmatrix}0&1\\1&0\end{pmatrix}, Y=\begin{pmatrix}0&-i\\i &0\end{pmatrix},\,\text{and}\, Z=\begin{pmatrix}1&0\\0&-1\end{pmatrix} $$ can be used ...
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Are they the same thing: Wigner distribution in quantum Boltzmann equation and Wigner function in quantum optics?

We know that quantum Boltzmann equation (QBE) is an equation of motion for the interacting Green's function $G^<(\vec{x}_1,t_1;\vec{x}_2,t_2)\equiv\mathrm{i}\langle ...
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Information retrieval from a database

Consider a database $\cal D$ containing $N$ entries $A_0, A_1, ... A_{N-1}$, which are some fixed and unknown strings of $k$ bits; you can access this database sending a coherent superposition of ...
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What is a good book for quantum mechanics and quantum computation? [duplicate]

I am looking for a book in quantum computers for self-learning.The kind of book that teaches quantum-mechanics + quantum-computation. I have basic understanding in calculus , linear-algebra (like ...
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Dicke states, spin squeezing and quantum metrology

Dicke states are by definition simultaneous eigenstates of the $J_z$ and $J^2$ operator. What is the difference between these states and Dicke squeezed (DS) states? I know that these are "entangled" ...
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If distant observers never see a black hole form in finite time how can the information paradox be a problem?

So, at least as reported in the media, the physics community is still struggling with the problem of resolving the impossibility of retrieving information from beyond the event horizon of a black hole ...
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characterization of non-entangling gates

I suspect the following is true and "well-known" but I cannot find any reference for it. Can anyone help? Let $U$ be a unitary quantum gate acting on a pair of $d$-dimensional qudits. Suppose $U$ is ...
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If two quantum two-party states have the same entanglement, can they be transformed into each other by local unitary operation?

We know that local unitary operations will not change entanglement. But if two party state have the same entanglement in some measure, can they be related with local unitary operation?
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Is this theory about Universe and information true?

I recently saw this video about information and randomness. At some point, it states that a completely predictable universe would infringe the second law of thermodynamics, because it would imply that ...
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Simple Mach-Zehnder Interferometer with Polarizing Beam Splitters

I am wondering which state leaves the simple interferometer below. The beam splitters are polarizing beam splitters (PBS) which transmit vertical polarization and reflect horizontal polarization. Say ...
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Density matrix formalism and group representation

The postulates of quantum theory can be given in the density matrix formalism. States correspond to positive trace class operators with trace 1 on a Hilbert space $\mathcal{H}$. Composition is defined ...
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Measuring non-commuting observable at once

Given an Hilbert space $H$ (finite dimensional for sake of clarity), and two non-commuting operators $$A = \sum_a a |a\rangle\langle a|$$ and $$B=\sum_a b |b\rangle\langle b|,$$ is it possible to find ...
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Reduce density matrix for given eigenfunction [closed]

My question is about how to find reduce density matrix for partition of given eigenfunction. Full question is just in image.
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Can quantum vacuum carry entropy?

So, we know that the state of quantum vacuum does carry energy, as it was measured in the Casimir effect. This energy comes from particles almost instantaneous creation and annihilation. Even if they ...
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How to calculate resources taken up in quantum computation

Suppose I have $n$ qubits namely $\{|\psi_{1}\rangle,|\psi_{2}\rangle.....|\psi_{n}\rangle\}$. I apply a series of unitary operations $U_{1},U_{2}...U_{n}$ (applied in order) to these qubits. Each ...
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Time and particles [closed]

What it is in basic particles that make them propagate themselves through time or, basically, what brings that property known as Duration in a particle (wave)? I sense that this is somehow is based ...
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What kind of transformation can be applied to qubits?

I have a doubt on what kind of transformations can be applied to qubits. I understand that the transformations need to be reversible , but they also have to preserve the norm: that's why the ...
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QM interpretations

I don't fully appreciate what the discovery of the decoherence phenomenon adds to the Copenaghen interpretation of QM. I will be more precise: the Copenaghen interpretation, if I am not wrong, is ...
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How can I solve an equation involving partial trace?

I am unable to find the solution to the following equation: Tr$_{2}[U(|\psi\rangle \langle\psi|\otimes \rho)U^{\dagger}]=\rho$ Here $\psi$ is state vector representing a qubit and $\rho$ state of ...
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Proof involving tensor product

I am trying to prove when the following holds: $$|a\rangle |b\rangle \langle c|\langle d| = |a\rangle \langle c| \otimes |b\rangle \langle d|$$ where $\otimes$ stands for tensor product and the ...