Questions tagged [quantum-information]

NOTE: We are currently in the middle of removing this tag, so please don't use it! For questions about the quantum analogues of concepts in information theory, please use the information-theory tag.

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2
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1answer
58 views

Perform quantum gate operations using state vectors and matrices

I am getting confused as to how to perform gate operations using matrices and am hoping someone will help me walk through this example. Say I want to perform a Pauli-X gate on the 3rd qubit in a 3-...
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1answer
161 views

Simultaneous eigenstate of commuting observables and their tensor product

So this is about something from Preskill's notes on Quantum Computation and Information, Chapter 4, page 3. Imagine we have a maximally entangled state (Bell state). We can identify the Bell state by ...
4
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1answer
278 views

CTCs and information time travel — what non-trivial insights do they lead to?

Context: In quantum complexity theory and quantum information, there are several papers which study the implications of closed timelike curves (CTCs). In 2008, Aaronson and Watrous published their ...
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1answer
144 views

Trace distance of two classical-quantum states

I have these two classical-quantum states: $$\rho = \sum_{a} \lvert a\rangle \langle a\lvert \otimes q^a \\ \mu = \sum_{a} \lvert a\rangle \langle a\lvert \otimes r^a $$ Where $a$ are the classical ...
2
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1answer
148 views

Direct derivation of the Kraus representation from the natural representation, using SVD

$\newcommand{\Y}{\mathcal{Y}}\newcommand{\X}{\mathcal{X}}\newcommand{\rmL}{\mathrm{L}}$As explained for example in Watrous' book (chapter 2, p. 79), given an arbitrary linear map $\Phi\in\rmL(\rmL( \X)...
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1answer
97 views

Proving the inequality $|\mathrm{tr}(AU)|\le \mathrm{tr}|A|$ in Uhlmann's theorem

In Nielsen and Chuang, in the Fidelity section, (Lemma 9.5, page 410 in the 2002 edition), they prove the following. $$ \mathrm{tr}(AU) = |\mathrm{tr}(|A|VU)| = |\mathrm{tr}(|A|^{1/2}|A|^{1/2}VU)| $$ ...
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1answer
62 views

Explicit 16⨯16 matrix representations of two-qudit entanglement witnesses

I have a set of $16 \times 16$ two-qudit density matrices. I would like to study the bound-entanglement for this set, making use of entanglement witnesses for which explicit matrix representations are ...
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32 views

Complexity analysis of separability in the multipartite case

It's well known that determining whether a bipartite mixed state is separable or entangled is a $\mathsf{NP}$-hard problem under some accuracy estimates (cf. this TCS SE discussion). Now I'm curious ...
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What does “bipartite” mean?

This is a really easy question, but my mother language is not English and I get confused quite a lot reading Preskill notes. What does a bipartite system mean? Is this just that it "lives" in a ...
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Is there a two-qudit Choi entanglement witness $W^{(+)}$?

Example 2 in arXiv:1811.09896 states that the "Choi EW (entanglement witness) $W^{(+)}$ obtained from the Choi map in $d=3$ $\ldots$ is given by \begin{equation} W^{(+)} = \frac{1}{6} \left( \...
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2answers
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How should we interpret these quantum logic gates as physical observables?

In quantum mechanics each operator corresponds to some physical observable, but say we have the operators $X,Y,Z,H, \operatorname{CNOT}$. I understand how these gates act on qubits, but what do they ...
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2k views

What's the difference between Kraus operators and measurement operators?

It is said in a lecture note[1] by John Preskill that, Equivalently, we may imagine measuring system $B$ in the basis $\{|a\rangle\}$, but failing to record the measurement outcome, so we are ...
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Finding separable decompositions of bipartite X-states using the methodology of Li and Qiao

Two recent papers of Jun-Li Li and Cong-Feng Qiao (arXiv:1607.03364 and arXiv:1708.05336) present "practical schemes for the decomposition of a bipartite mixed state into a sum of direct products of ...
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1answer
59 views

What are the ranges of the four $q$ parameters in the magic simplex of Bell states formula?

Equation (7) in the 2012 paper, "Complementarity Reveals Bound Entanglement of Two Twisted Photons" of B. C. Hiesmayr and W. Löffler for a state $\rho_d$ in the "magic simplex" of Bell states \begin{...
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247 views

How does the probability of measurement turn out to be negative?

c) Compute $$\text{Prob}(\uparrow_\hat{n}\uparrow_\hat{m}) \equiv \text{tr}(\pmb{E}_A(\hat{n})\pmb{E}_B(\hat{n})\pmb{p}(\lambda)), \tag{4.164}$$ where $\pmb{E}_A(\hat{n})$ is the projection of Alice's ...
5
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1answer
268 views

Understanding this description of teleportation

In the context of quantum teleportation, my lecturer writes the following (note that I assume the reader is familiar with the circuit): If the measurement of the first qubit is 0 and the measurement ...
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36 views

What proportions of certain sets of PPT-two-retrit states are bound entangled or separable?

For two particular (twelve-and thirteen-dimensional) sets of two-retrit states (corresponding to 9 x 9 density matrices with real off-diagonal entries), I have been able to calculate the Hilbert-...
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Are X-state separability and PPT- probabilities the same for the two-qubit, qubit-qutrit, two-qutrit, etc. states?

On p. 3 of "Separability Probability Formulas and Their Proofs for Generalized Two-Qubit X-Matrices Endowed with Hilbert-Schmidt and Induced Measures" (https://arxiv.org/abs/1501.02289), it is ...
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3k views

Will quantum computers be able to solve the game of chess?

Will it be possible to use quantum computing to one day solve the game of chess? If so, any estimate as to how many qubits it would require? The game of checkers has already been solved through back ...
2
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1answer
765 views

What is a complementary map?

I have a quantum map described by the following Kraus operators $$A_0 = c_0 \begin{pmatrix} 1 & 0\\ 0 & 1 \end{pmatrix}, \qquad A_1 = c_1 \begin{pmatrix} ...
5
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1answer
110 views

Quantum teleportation of a state, from one of two bases

I'm watching Christian Schaffner's talk on quantum position-based cryptography (link here) and have a question about a particular application of teleportation. At about the 16:40 mark, he seems to ...
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1answer
434 views

Understanding quantum circuit diagrams: a circuit that compares two states $|YX\rangle$ and $|AB\rangle$

I have a quantum circuit which I would like to understand, which compares two standard basis states $|YX\rangle$ and $|AB\rangle$. It operates on the corresponding bits in each of the two states: i.e.,...
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Application of improved compatibility

Note: Cross-posted on Physics SE. It's a standard piece of quantum information theory that noise can be helpful in augmenting compatibility of quantum observables. For example given a qubit state $\...
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1answer
156 views

How does quantum memory work using atoms?

I was trying to learn quantum memory and went through some papers, websites, etc. The current understanding I have (which I'm not sure is right) is this: Two photons are prepared together which are ...
3
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1answer
68 views

EPR states with permuted qubits

Suppose I prepare following state consisting of (for example) three EPR pairs: $$\lvert\Psi\rangle = \frac{\lvert00\rangle+\lvert11\rangle}{\sqrt{2}}\otimes\frac{\lvert00\rangle+\lvert11\rangle}{\...
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1answer
89 views

Convex Combination of Separable States

The state $$ \frac{1}{2}\left(| \phi^+ \rangle \langle \phi^+ | + | \psi^+ \rangle \langle \psi^+ | \right) $$ where $$ | \phi^+ \rangle = \frac{1}{\sqrt2} \left(|00 \rangle + | 11 \rangle \right) $...
4
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1answer
342 views

Connection between the definitions of concurrence for a two-qubit states

The concurrence for a state $\rho$ as defined here is \begin{equation} C(\rho) = {\rm max}\{0, \lambda_1-\lambda_2-\lambda_3-\lambda_4\}. \end{equation} Where $\lambda_i$ are the eigenvalues of matrix ...
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1answer
586 views

Can we teleport a human or send information faster than light using quantum teleportation?

What does quantum teleportation mean? Is it something that will allow us to send information faster than the light? Can we teleport a human with it?
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Quantum teleportation with moving Alice and Bob

I have questions regarding quantum teleportation, which keep confusing me. Suppose Alice and Bob are in the same inertial frame $K$, and at time $t$ (in $K$) Alice teleports a quantum state to Bob. ...
4
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1answer
160 views

Why is $P(1,2)_{\text{same}} = \frac{1}{4}$ and not $\frac{1}{2}$ in Preskill's Bell experiment?

Context: Three coins on the table. Each is either heads or tails. You can uncover any one of the three coins, revealing whether it is heads or tails but then you choose two the other two coins ...
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51 views

Can “experimental data from a quantum computer” be used to test separability probability conjectures?

An article entitled "Experimental data from a quantum computer verifies the generalize Pauli exclusion principle" by Scott E. Smart, David I. Schuster, and David A. Mazziotti has just appeared In the ...
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1answer
59 views

Transmission of information over long distances

I am reading that entangled particles can share information across long distances and the speed is usually faster than the speed of light...so am I right in assuming that future communications in the ...
4
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2answers
273 views

Non-uniqueness of pure states ensemble decomposition

Apparently, the decomposition of a state into an ensemble of pure states is not unique. I can't understand why, as if I understood correctly a "pure state ensemble decomposition" is just the ...
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119 views

Real-life examples of classical-quantum channels

In quantum information theory, classical-quantum channels are considered to be channels whose input is the realizations $x\in\mathcal{X}$ of a classical random variable to a quantum state $\rho_x^B$, ...
4
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2answers
185 views

Defining entanglement for systems with more than two qubits

Introductory textbooks I've read define entanglement as when your product state cannot be factored into the tensor product of individual quantum states. But consider a three-qbit system: $$C_{2,0}H_2|...
5
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1answer
261 views

Is the set of classical-quantum states convex?

I read about the classical-quantum states in the textbook by Mark Wilde and there is an exercise that asks to show the set of classical-quantum states is not a convex set. But I have an argument to ...
2
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1answer
84 views

How to formulate the master equation for three systems?

I have a three composite system of the form $H_{\text{tot}}=H_{ab}\otimes H_c$ where the system $C$ is behaving as the dissipator or the environment (I can model it as a thermal bath). And it is ...
5
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2answers
419 views

How many Kraus operators are required to characterise a channel with different start and end dimensions?

If we have a quantum channel mapping from a $d$-dimensional state to a $d$-dimensional state, it can be described by at most $d^2$ Kraus operators. Suppose our channel maps instead from a $d_1$-...
3
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284 views

Dephasing channels

I'm taking a quantum information course and one of my exercises says to find $p,p'$, for which there is a channel $\tilde\Lambda(\Lambda(\rho))=\Lambda'(\rho)$, where $\Lambda$ and $\Lambda'$ are ...
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1answer
68 views

Shared entanglement to copy orthogonal states

Assume that Alice and Bob are allowed to share entanglement and are spatially separated. Alice is given an unknown state and asked to measure this in the computational basis to obtain $\vert 0\rangle$ ...
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70 views

Isometric Extension of an Erasure Channel

Show that an isometric extension of the erasure channel is $$U^N_{A\to BE} =\sqrt{1−\epsilon}\left(|0\rangle_B \langle 0|_A +|1\rangle_B \langle 1|_A \right)\otimes|e\rangle_E+ \sqrt{\epsilon}|e\...
3
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1answer
125 views

Convention for expressing measurement in non-standard basis

If we're measuring in common bases like $|0\rangle$, $|1\rangle$ or $|+\rangle$, $|-\rangle$ we express this by saying we're measuring with $\sigma_z$ or $\sigma_x$, or measuring in the computational ...
4
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1answer
108 views

Determining whether $P(ab|xy)$ factorizes in Bell experiments

Continuing from my previous (1, 2) questions on Brunner et al.'s paper on Bell nonlocality. Again, we have the following standard Bell experiment setup: where independent inputs $x,y \in \{0, 1\}$ ...
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1answer
111 views

Comprehension questions on quantum cryptography especially BB84

I have recently read a lot about the BB84 protocol, I have used three primary sources, the original work, a QK book, and a diploma thesis. My questions refer to the photons sent by Alice, the base of ...
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81 views

Quantum channel Holevo information additivity: proof approach

I have an interesting idea for a proof approach that someone might find useful. Here it is. Suppose we are given a quantum qubit channel $N$ (for example the amplitude damping channel) whose Holevo ...
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75 views

Three sender quantum simultaneous decoder conjecture

Recently I have started to read about network quantum information theory, where network problems are studied under the classical-quantum channel. For example, capacities of the cq-MAC, cq-broadcast or ...
4
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53 views

What is the quantum bandwidth of a planar array of noisy qubits, assuming free classical communication?

A common task to perform during quantum computation on the surface code is moving qubits from one place to another. There are standard ways to do this within the surface code, but I was wondering what ...
2
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1answer
203 views

Are the eigenvalues of an observable always -1 and 1?

What are the necessary & sufficient conditions for a matrix to be an observable, and what is the proof that any such matrix has eigenvalues -1 and 1 (if indeed that is the case)? I ask because in ...
3
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1answer
209 views

How to transfer non maximally entangled state to maximally entangled?

Let a three-qubit state shared between Alice, Bob and Charlie stationed at distant laboratories be $$\psi_{ABC}=\frac{\sqrt{2}}{\sqrt{3}}|000\rangle+\frac{1}{\sqrt{3}}|111\rangle.$$ How to evaluate ...
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1answer
151 views

Definition of locality in Bell experiments

Continuing from my previous question on Brunner et al.'s paper; so given a standard Bell experimental setup: where independent inputs $x,y \in \{0, 1\}$ decide the measurement performed by Alice &...