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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Does the Choi-Jamiolkowski isomorphism really establish a connection between kinematics and dynamics?

I understand the mathematical construction of the Choi-Jamiolkowski isomorphism aka channel-state duality. It all makes sense formally, yet I still struggle to grasp its physical (or quantum-...
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IBM Q [Grover's Algorithm] [on hold]

How to design the grover's algorithm by using n=5?
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1answer
26 views

How to prove the following bosonic entanglement expression?

Based on the article given by J. L. Ball, I. Fuentes-Schuller, and F. P. Schuller, Phys. Lett. A 359, 550 (2006) had used the following expression of von-Neumann entropy \begin{equation} S = - \...
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35 views

Bell State 11 not working for parity curve

I am currently writing a script to automate the creation of parity curves for a 2 qubit bell state and then calculate fidelity and proving entanglement from that (inspired by this paper). It was going ...
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22 views

What if I say computing without a (computer), no device? or unit or machine [on hold]

Natural 100% adding up what computers were invented for. Ourselves a processor, autonomously. Thru neural supremacy. Individual person with the right timing and thought process in his brain whom will ...
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26 views

Motivation for the definition of k-distillability

Definition of k-distillability For a bipartite state $\rho$, $H=H_A\otimes H_B$ and for an integer $k\geq 1$, $\rho$ is $k$-distillable if there exists a (non-normalized) state $|\psi\rangle\in ...
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Geometric interpretation of 1-distillability

This is a sequel to Motivation for the definition of k-distillability Geometrical interpretation from the definition of 1-distillability The eigenstate $|\psi\rangle$ of the partially ...
4
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1answer
57 views

How to find a common eigenstate of commuting operators?

I have multiple different operators in matrix form and I need to find their common eigenstates. The challenge is that the common eigenstate is in a superposition of multiple states and isn't just a ...
4
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1answer
30 views

Quantum fidelity simplified formula while both of the density matrices are single qubit states

I have a question while reading the quantum fidelity definition in Wikipedia Fidelity of quantum states, at the end of the Definition section of quantum fidelity formula, it says Explicit expression ...
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37 views

What is the motivation for Weyl matrices in quantum information theory?

Quantum Entanglement and Geometry — Andreas Gabriel (2010) — Sec: 2.3.4 ~p. 11 Another basis for $d\times d$-dimensional matrices that has proven to be quite useful in quantum information theory is ...
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1answer
28 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-...
2
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1answer
36 views

What is Landauer’s principle?

How does the act of erasing information increase the total entropy of the system? This goes by the name Landauer's principle. Some details are here. Can anyone shed more light on this?
3
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1answer
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What are nontrivial examples of $n$-sharable bipartite states?

A bipartite state $\newcommand{\ket}[1]{\lvert #1\rangle}\rho_{AB}$ is said to be $n$-sharable when it is possible to find an extended state $\rho_{AB_1\cdots B_n}$ such that partial tracing over any ...
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1answer
2k views

What exactly is an oracle?

What exactly is an "oracle"? Wikipedia says that an oracle is a "blackbox", but I'm not sure what that means. For example, in the Deutsch–Jozsa algorithm,$\hspace{85px}$,is the oracle just the box ...
3
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1answer
41 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 ...
2
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1answer
36 views

What property ensures that von Neumann entropy is conserved?

So I always had this idea in my mind that unitary evolution in quantum mechanics conserves information (or in other words von Neumann entropy) because unitary evolution preserves the trace. But this ...
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42 views

Twirling Quantum Channels: Pauli and Clifford Twirling

I am currently working through some papers related with approximations of more general quantum channels such as amplitude and phase damping channels to Pauli channels. The reason to do so is so that ...
2
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1answer
55 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
150 views

How to understand the Haar measure from a quantum information perspective?

I found it a little difficult to understand it using Wikipedia and some mathematical documents. How to understand the Haar measure from a quantum information theory perspective? Are there any ...
4
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1answer
50 views

Structural Physical Approximation of Partial Transpose

To make the partial transpose a complete positive and therefore physical map, one has to mix it with enough of the maximally mixed state to offset the negative eigenvalues. The most negative ...
4
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1answer
168 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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2answers
415 views

How can quantum decoherence be managed?

I've stumbled myself upon this article on Wikipedia, which says: Decoherence can be viewed as the loss of information from a system into the environment (often modeled as a heat bath), since every ...
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1answer
42 views

Does the dilation in Naimark's theorem produce a state?

A POVM, as defined for example in (Peres and Wooters 1991), is defined by a set of positive operators $\mu(a)$ satisfying $\sum_a \mu(a)=\mathbb 1$. We do not require the $\mu(a)$ to be projectors, ...
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1answer
56 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 ...
3
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1answer
51 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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2answers
84 views

Are there disadvantages in using the inner product between states instead of the fidelity?

Would there be any disadvantages of using inner product, that is, $\mathrm{Tr}(A^{\dagger}B)$ (say making it, $\mathrm{Tr}(\sqrt A \sqrt B)$ to normalise) to quantify how far two quantum states are ...
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0answers
28 views

How does a map being “only” positive reflect on its Choi representation?

We know that a map $\Phi\in\mathrm T(\mathcal X,\mathcal Y)$ being completely positive is equivalent to its Choi representation being positive: $J(\Phi)\in\operatorname{Pos}(\mathcal Y\otimes\mathcal ...
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2answers
132 views

Is the Kraus representation of a quantum channel equivalent to a unitary evolution in an enlarged space?

I understand that there are two ways to think about 'general quantum operators'. Way 1 We can think of them as trace-preserving completely positive operators. These can be written in the form $$\...
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1answer
42 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
252 views

How are witness operators physically implemented?

Let's take an example of an entanglement witness of the form $W = | \phi \rangle \langle \phi | ^{T_2}$ where $ | \phi \rangle $ is some pure entangled state. If I wanted to test some state $\rho$, I ...
16
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1answer
428 views

Purpose of using Fidelity in Randomised Benchmarking

Often, when comparing two density matrices, $\rho$ and $\sigma$ (such as when $\rho$ is an experimental implementation of an ideal $\sigma$), the closeness of these two states is given by the quantum ...
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2answers
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What is quantum gate teleportation?

Quantum state teleportation is the quantum information protocol where a qubit is transferred between two parties using an initial shared entangled state, Bell measurement, classical communication and ...
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2answers
283 views

Convexity and conditional von Neumann Entropy

I have read somewhere / heard that the set of all states that have non-negative conditional Von Neumann entropy forms a convex set. Is this true? Is there a proof for it? Can anything be said about ...
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1answer
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Quantum channel cannot increase Holevo information of an ensemble

I need to prove the fact that a quantum channel (a superoperator) cannot increase the Holevo information of an ensemble $\epsilon = \{\rho_x, p_x\}$. Mathematically expressed I need to prove $$\begin{...
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1answer
149 views

Are entanglement witnesses of this form optimal?

One can make an entanglement witness by taking the partial transpose of any pure entangled state. Consider $|\phi \rangle $ as any pure entangled state. Then $W = | \phi \rangle \langle \phi |^{T_2} ...
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1answer
92 views

Is there a relation between the factorisation of the joint conditional probability distribution and Bell inequality?

[I'm sorry, I've already posted the same question in the physics community, but I haven't received an answer yet.] I'm approaching the study of Bell's inequalities and I understood the reasoning ...
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
309 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
75 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 ...
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2answers
115 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
60 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 ...
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0answers
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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 ...
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1answer
57 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} || ...
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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 $\...
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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 ...
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1answer
213 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 ...
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57 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 ...
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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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0answers
22 views

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}...
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1answer
129 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.,...