Questions tagged [quantum-information]

For questions about quantum information theory. In physics and computer science, quantum information is information that is held in the state of a quantum system. Quantum information is the basic entity of study in quantum information theory and can be manipulated using engineering techniques known as quantum information processing. (Wikipedia)

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4
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2answers
111 views

Image of a sum of positive operators contains the images of each individual operator?

In the proof of Proposition 2.52 of John Watrous' QI book, there is the statement that $\text{im}(\eta(a))\subset\text{im}(\rho)$, where $\rho=\sum_{i=1}^{N}\eta(i)$ is a sum of positive operators and ...
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1answer
324 views

Advances in Quantum Channel Capacity

I have been reading about the Quantum Channel Capacity and it seems to be an open problem to find such capacity in general. Quantum capacity is the highest rate at which quantum information can be ...
3
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1answer
80 views

Degradable channels and their quantum capacity

Note: I'm reposting this question as it was deleted by the original author, so that we do not lose out on the existing answer there, by Prof. Watrous. Further answers are obviously welcome. I have ...
2
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2answers
123 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 ...
3
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1answer
61 views

Could we use varying voltage with programmable gates?

One of the benefits I'm reading about qubits is that they can be in an infinite number of states. I'm aware of Holevo's bound (even though I don't fully understand it). However, it made me think of ...
3
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0answers
14 views

Counting channel uses of the lossy bosonic channel or definition of channel uses

The PLOB-bound ("Fundamental Limits of Repeaterless Quantum Communications") gives an asymptotic upper bound on the secret-key rate per used lossy bosonic channel. However, I'm not sure how to count ...
5
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1answer
58 views

Superoperator cannot increase relative entropy

Note: Cross-posted on Physics SE. So I have to show that a superoperator $\$$ cannot increase relative entropy using the monotonicity of relative entropy: $$S(\rho_A || \sigma_A) \leq S(\rho_{AB} || ...
3
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2answers
48 views

Proof of joint entropy theorem

From section 11.3.2 of Nielsen & Chuang: (4) let $\lambda_i^j$ and $\left|e_i^j\right>$ be the eigenvalues and corresponding eigenvectors of $\rho_i$. Observe that $p_i\lambda_i^j$ and $\...
3
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0answers
26 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 ...
5
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1answer
215 views

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 ...
3
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0answers
63 views

How to implement the mixed quantum state fidelity in a quantum circuit?

Suppose we use Uhlmann-Josza fidelity $F(\rho, \sigma):=(\mathrm{tr}\sqrt{\sqrt{\rho}\sigma\sqrt{\rho}})^2$, can we construct a quantum circuit that help us to calculate the fidelity of two mixed ...
2
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2answers
243 views

Can an isometry leave entropy invariant?

Consider two finite dimensional Hilbert spaces $A$ and $B$. If I have an isometry $V:A\rightarrow A\otimes B$, under what condition can I find a unitary $U:A\otimes B\to A\otimes B$ such that $$U\rho_{...
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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( \sum_{i=0}...
4
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1answer
133 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.,...
6
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2answers
97 views

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 ...
2
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1answer
122 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 ...
4
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2answers
469 views

How to show a density matrix is in a pure/mixed state?

Say we have a single qubit with some density matrix, for example lets say we have the density matrix $\rho=\begin{pmatrix}3/4&1/2\\1/2&1/2\end{pmatrix}$. I would like to know what is the ...
3
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18 views

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 ...
2
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1answer
48 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{...
9
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1answer
154 views

Proof of an Holevo information inequality

Suppose I have a classical-classical-quantum channel $W : \mathcal{X}\times\mathcal{Y} \rightarrow \mathcal{D}(\mathcal{H})$, where $\mathcal{X},\mathcal{Y}$ are finite sets and $\mathcal{D}(\mathcal{...
3
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1answer
146 views

How does the vectorization map relate to the Choi and Kraus representations of a channel?

I know that the Choi operator is a useful tool to construct the Kraus representation of a given map, and that the vectorization map plays an important role in such construction. How exactly does the ...
4
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1answer
248 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 ...
2
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0answers
29 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-...
4
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1answer
119 views

Classical vs. quantum channel capacities

The classical channel capacity ($C_{ea}$) and the quantum channel capacity ($Q$) as defined here (eqs. 1 and 2) are given by \begin{equation} C_{ea} = \text{sup}_{\rho} \Big[S(\rho) + S(\Phi_t \rho) -...
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Estimate/determine Bures separability probabilities making use of corresponding Hilbert-Schmidt probabilities

For two-qubit states, represented by a $4\times 4$ density matrix, the generic state is described by 15 real parameters. For ease of calculation, it can help to consider restricted families of states, ...
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31 views

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 ...
4
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1answer
1k views

How can quantum computing win 97% of times in coin flipping experiment?

I'm new to this field of science. I'm curious about how quantum computing can win 97% of times in a coin flipping experiment? Refer this link: Ted Talk by Shohini Ghose To give an idea about how ...
2
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1answer
255 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} ...
4
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1answer
78 views

How is the expression for the optimal entanglement witness derived?

In the Bertlmann 2009 paper in the Annals of Physics (here), an optimal witness operator for an entangled state $\rho$, given that the closest separable state to it is $\rho_0$ is given by: $$A_{\...
4
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1answer
147 views

What is an example of a measurement that is LOCC but not separable?

Could you give me an example of a measurement which is separable but not LOCC (Local Operations Classical Communication)? Given an ensable of states $\rho^{N}$, a separable measurement on it is a POVM ...
7
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2answers
208 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 ...
3
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0answers
45 views

Quantum Fisher information

I am reading paper Channel Identification and its Impact on Quantum LDPC Code Performance where the authors discuss the scenario where the decoder of a Quantum LDPC code uses an estimation of the ...
3
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1answer
112 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 ...
5
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1answer
95 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 ...
3
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1answer
93 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 ...
2
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0answers
35 views

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 $\...
3
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2answers
345 views

How is Bell’s Inequality converted to the CHSH inequality?

Bell’s inequality is $$S = P(a,b)-P(a,d)+P(c,b)+P(c,d) \leq 2,$$ which is calculated as $$S = ab – ad + cb + cd \leq 2.$$ The CHSH version is: $$E = \frac{N_{11} + N_{00} - N_{10} -N_{01}} {N_{11} + ...
5
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1answer
113 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 &...
4
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1answer
86 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 $x,y \in \{0, 1\}$ ...
8
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1answer
84 views

How would a Quantum Computer (network) perform loophole-free Bell tests?

In a simple form, Bell's theorem states that: No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics. Bell developed a series of inequalities ...
6
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2answers
70 views

Bell Inequality violations at large distances

Could anyone point to some references examining Bell inequality violations at large distances please? I see many times, in pop science articles and research literature alike, that the quantum ...
3
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1answer
51 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}{\...
4
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2answers
116 views

POVM three-qubit circuit for symmetric quantum states

I have been reading this paper but don't yet understand how to implement a circuit to determine in which state the qubit is not for a cyclic POVM. More specifically, I want to implement a cyclic POVM ...
4
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1answer
57 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) $...
2
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1answer
78 views

Concurrence for a two qubit state

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 ...
4
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1answer
69 views

Partial Transpose and Positive Operators

Question: For 2x2 and 2x3 systems, is the partial transpose the only positive but not completely positive operation that is possible? Why this came up: The criteria for detecting if a state $\rho$ is ...
2
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1answer
140 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?
31
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7answers
6k views

Why is it harder to build quantum computers than classical computers?

Is it because we don't know exactly how to create quantum computers (and how they must work), or do we know how to create it in theory, but don't have the tools to actually execute it in practice? Is ...
6
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0answers
98 views

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. ...
3
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0answers
58 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 $\rho_x^B$, ...