2016 goals in review

It is widely accepted that 2016 was a terrible year. I agree, although it had its good moments, like Colombia finally signing a peace treaty to end the armed conflict with the FARC.

I had essentially no influence or control over the elections, deaths, and conflicts that have marked this last orbit around the sun, but I do have control over my own life. 2016 was the first year that I set myself quantitative goals, making it possible to look back and evaluate my performance with at least some degree of precision.  I set ambitious goals that I knew would be difficult to achieve: that’s the way to improve!

Below, I review these goals and my accomplishments in reaching them. I do this not only as a form of reflection, but also in the hope that it may inspire others to do something similar in the upcoming year  🙂

Goal #1: Obtain a total of 100 citations to my articles

As a young postdoc, I am in the stage of my scientific career where the stakes are high. Permanent positions are scarce and the competition is fierce: I have to perform at the highest level. At the end of 2015, I had 45 citations to my articles, so my goal was to essentially double that amount. Looking at my colleagues in quantum information who have been researchers longer than me, I have found that getting to ~1000 citations is a good indication of having reached the level of impact in a field that may merit a tenure-track position in respected research institutions. Hence, my goal is to aim at doubling my total citations every year until I reach that point: 50, 100, 200, 400, and so on. In that case, I would be on track to being competitive in my applications to permanent positions by the time I finish a second postdoc.

At the time of writing, I have a total of 81 citations to my papers, which is a non-negligible amount below my goal. Of course, I cannot really control how many times my papers are cited. All I can do is publish good research and work hard to make it visible to the community. Also, we should never forget that citations are not an accurate method of assessing scientific merit. However, it is important that I objectively analyze my competitiveness as I look to making important career decisions in the future.

Goal #2: Publish at least 5 papers.

What the community thinks of my work is ultimately not up to me, but it is in my power to be a productive scientist. As opposed to my days in grad school, as a postdoc I can work exclusively on research, most of which is related to topics that I have already mastered. This is truly the best time to shine as a researcher. I published six papers during the four years it took me to complete a PhD, so my goal was to effectively reach that level of productivity in only one year.

Indeed, I have accomplished this goal with five papers:

  1. Practical quantum retrieval games
  2. Covert quantum communication
  3. Quantum advantage on information leakage for equality
  4. Autonomous rotor heat engine
  5. Quantum money with nearly optimal error tolerance

However, I think it is fair to say that I have actually exceeded this goal, as I have an additional review paper on satellite quantum key distribution which is almost finished, and I have several projects which will be close to completion in the first month of 2017. Yey!

Goal #3: 150 sessions of exercise.

I have reached a point in my life when I have to work hard to maintain my health and well-being. My reasoning in setting 150 sessions as my goals was that I would have roughly three sessions per week. In fact, I was disciplined with exercise, which I have smoothly incorporated into my routine: gym on Tuesday and Thursday, table tennis on Friday. In 2016, I tallied a total of 116 sessions, and I am very satisfied with my body and strength.

So why only 116 sessions if I was disciplined? Well, it turns out that I exercised practically every time I could exercise, but there were too many moments when I could not: facility closures, travels, and sicknesses prevented me from going even when I wanted to. Overall, 150 hours was ambitious and I am satisfied with my progress towards this goal.

Goal #4: Play 5 complete songs in the guitar

I have been playing the guitar for many years now, but only as a very casual hobby. Music is something that I don’t want to do seriously — quite the contrary — it is a respite from everything that is serious in life. As such, when I would grab my guitar, I would play only excerpts of songs, not really putting in the effort to master them in their entirety. Again, this is fine, but I still wanted to at least have a small repertoire that I could play to completion. This was a relatively easy goal to achieve, and I can now fully play

  • Hey There Delilah – Plain White T’s
  • Lazy Eye – Silversun Pickups
  • Hotel California – The Eagles
  • Better Man – Robbie Williams
  • Sleepwalk – Johhny and Santo (this one is getting a bit rusty)
  • Good Riddance – Green Day

Goal #5: Read 5 books on investment

As a postdoc in Singapore I have finally reached the point in my life where, together with my wife Aleks, we earn more than we spend. As such, it is crucial to me to be responsible and knowledgeable about how to handle our savings, however modest. Throughout my life, I have received indirect advice from my parents and friends, but I am always more comfortable making decisions based on my own knowledge and understanding.

This year I read 3 books on finance, while deciding to stop there around the middle of the year. The reason is that I already learnt quite a lot from these books and I did not find any others than seemed to both interesting and different enough to merit a commitment to read. What I realize now is more useful is to read financial news and to start learning through practice and experience. The books I read are

  • A Random Walk Down Wall Street, Burton Malkiel
  • The Essays of Warren Buffet, Warren Buffet
  • Irrational Exuberance, Robert Schiller

Goal #6: Donate 1% of my income to charity

I don’t only care about improving my own life, but about making the entire world a better place. I try to do this with my actions every day, but another meaningful way of achieving this is to donate money directly to people who need it.

My only problem with donations is that I don’t have confidence in most charities making proper use of the donations they receive. That is why I love the approach of Raising for Effective Giving (REG), a meta-charity founded by professional poker players that works to allocate donations to the most effective charities. In their own words: “We rely on scientific thinking and cooperate with researchers, think tanks, and charity evaluators to find the interventions most effective at reducing suffering in the world and to provide members with the best information on the most effective giving opportunities.”

Even though it took me until the last month of the year, I have indeed donated 1% of my income to REG. I hope I can continue to increase this percentage for may years to come.

Happy 2017 everyone!



Anyone can understand quantum mechanics — Part 3

Before, we begin, HAVE YOU WATCHED THE VIDEO “ANYONE CAN QUANTUM”??? Paul Rudd, Keanu Reeves, Stephen Hawking, Quantum Chess, Quantum Physics for Babies, and even tardigrades: this video has it all!


Made by our colleagues from the Institute for Quantum Information and Matter in Caltech, this clip has masterfully shared with almost two million people all around the world the same message that I have been trying to spread with these blog posts: anyone can understand quantum mechanics! In their video, Keanu Reeves tells us that “Paul Rudd changed the world by showing the world that anyone can grapple with the concepts of quantum mechanics. It sparked an era of invention and ingenuity the likes of which humanity had never seen.” There is a lot of truth in that: when everyone believes they can understand nature at its most fundamental level, we can accomplish amazing things.

Of course, it’s one thing to claim that people can understand quantum mechanics, but it’s something else entirely to help people actually do it. That’s the job I started with my previous posts and that I am going to continue today. Let’s go!


In the previous installment of this series, we learnt the basic postulates of quantum mechanics. In other words, we learnt what quantum mechanics is. In this final part of the series, we are going to shift gears and study what quantum mechanics implies about our universe. What is possible in a quantum world that can’t be done in a classical one? What is new, what is different? These are important questions and today we’ll learn some of the answers!

My job, for instance, could be loosely described as studying the implications of quantum mechanics for communication, cryptography and thermodynamics. In particular, in this lesson we’ll learn about two important aspects of quantum mechanics that are not present in classical theories: Heisenberg’s uncertainty principle and entanglement.

Lesson 1: The uncertainty principle


The uncertainty principle of the Heisenberg on the right.

In our previous lesson, we used a quantum coin as an example of a quantum system, whose state could be |Heads\rangle, |Tails\rangle or any superposition of these two states. Today, we are going to be more general and instead we are going to think of a system with two possible configurations which we call |0\rangle and |1\rangle. Using this notation is great because it’s shorter to write (which is always appreciated) and because it is more general: we don’t really need to be talking about a quantum coin, it could be any system with two degrees of freedom. The word we use for such an object is a qubit, in analogy with a classical bit, which is any system that can be in states 0 or 1.

Remember that in quantum mechanics we can have superpositions, so we are also going to define two other important states of a qubit

|+\rangle=\frac{1}{\sqrt{2}}|0\rangle + \frac{1}{\sqrt{2}}|1\rangle

|-\rangle=\frac{1}{\sqrt{2}}|0\rangle - \frac{1}{\sqrt{2}}|1\rangle .

Notice that the states |+\rangle and |-\rangle are both an equal superposition of the states |0\rangle and |1\rangle . Notice also that the states |0\rangle and |1\rangle are equal superpositions of |+\rangle and |-\rangle since we can write

|0\rangle=\frac{1}{\sqrt{2}}|+\rangle + \frac{1}{\sqrt{2}}|-\rangle

|1\rangle=\frac{1}{\sqrt{2}}|+\rangle - \frac{1}{\sqrt{2}}|-\rangle .

Qubits come in many different kinds. This one is a superconducting qubit from the lab of John Martinis.


Do you remember how to define a measurement in quantum mechanics from the previous lesson? The only thing we have to do is to ask systems what states they are in. In this lesson, we are going to focus on two special measurements of a qubit. We’ll call the question

“Are you in state |0\rangle or |1\rangle ?”

 a Z measurement. Similarly, we’ll call the question

“Are you in state |+\rangle or |-\rangle ?”

an X measurement. Why do we call them that? Well, there’s a relatively complicated historical reason behind it, but this is the terminology that scientists use and I want you to be familiar with these terms.

Now let’s suppose that we have a qubit in the state |0\rangle and we want to measure it. If we make a Z measurement, we know for sure that the outcome will be “I’m in state |0\rangle”. However, because of the laws of quantum mechanics that we learnt last time, if we make an X measurement, half of the time we’ll obtain the outcome “I’m in state |+\rangle” and the other half we’ll get the outcome “I’m in state |-\rangle”. In other words, for this state, we don’t have any uncertainty about the outcome of a Z measurement, but we have maximum uncertainty about the outcome of an X measurement. See where I’m going?

What happens if instead we start with a qubit in the state |+\rangle? You guessed it, the situation is reversed! In this case, we don’t have any uncertainty about the outcome of an X measurement, but we have maximum uncertainty about the outcome of a Z measurement!  It turns out that no matter what state we start with, there will always be some uncertainty in at least one of these two measurements. That is Heisenberg’s uncertainty principle.

More precisely, the uncertainty principle states that for virtually any two measurements we can make on any system – let’s call them measurement A and measurement B – it holds that


In other words, no matter what state the system is in, there exist pairs of measurements whose outcomes cannot both be predicted perfectly. This never happens classically! In a classical world, if we know the state of a system perfectly, in principle we can predict everything about its future behaviour, including the results of any two measurements. But in a quantum world, there is a fundamental limitation to our ability to predict the outcomes of measurements: most of the time, there will always be some uncertainty about which outcomes we’ll see. The only exception to this rule occurs when both A and B are said to commute, but most pairs of measurements don’t have that property.

Many of you are probably thinking, “Wait, didn’t the uncertainty principle have something to do with the position and momentum of a particle?” Perhaps some of you have even heard this joke before:


Well, the uncertainty principle applies to measurements of position and momentum as well: we can never predict the outcome of both measurements perfectly. In other words, in our universe, for any measurement X of the position of a particle and any measurement P of its momentum, it holds that


The uncertainty principle tells us something very deep about our ability to obtain information from physical systems. In many ways, it sets a fundamental limit to our capability to make predictions and to perform precise measurements. This has HUGE implications. To name a few, the uncertainty principle is the reason why quantum states cannot be cloned, why empty space is not really empty, and why quantum cryptography is possible. That’s the beauty of our quantum world!

Before our next lesson, you can take a break and admire this picture that my wife took of the Gardens by the Bay in Singapore, the city where we now live.

Gardens by the bay

Futuristic nature

Lesson 2: Entanglement

So far in our discussion of quantum mechanics we have focused on single systems: a single quantum coin, a single quantum die, a single qubit. But what happens if we combine systems together? In particular, what happens if we have two qubits instead of one?

The first thing we have to understand is how to represent the states of two qubits. Turns out that all we have to do is to “stick them together”. If one qubit is in state |0\rangle and the other is in state |1\rangle, then we represent the joint state of both qubits as |0\rangle |1\rangle. Easy! Mathematicians call this operation “taking the tensor product”, I prefer to use the term “sticking them together”: it gets the point across.

Other examples of possible states of two qubits are

|1\rangle |0\rangle

|+\rangle |1\rangle

|-\rangle |+\rangle

(\frac{3}{5}|0\rangle +\frac{4}{5}|1\rangle) |0\rangle

You get the idea. Notice that in each of these examples, it is straightforward to identify what state each of the two individual qubits is in. For instance, for the state |-\rangle |+\rangle, it is clear that the first qubit is in state |-\rangle and the second qubit is in state |+\rangle.

Now comes the interesting part. Remember that in quantum mechanics we can have superpositions of different states. Hopefully many of you are already realizing that much of the magic of the quantum world comes solely from superposition: it is one of the defining properties that makes quantum mechanics such a beautiful and rich theory. For example, in quantum mechanics, a system of two qubits can be in the state

\frac{1}{\sqrt{2}}(|0\rangle |1\rangle + |1\rangle |0\rangle).

Does this state look special to you? If not, then let me ask you a couple of questions: what state is the first qubit in? What state is the second qubit in? Think about it for a while.


Seriously, think about it for a while.


Are you thinking about it? Because you really should…

So, what’s the answer? That’s right: they don’t have a definite state! In fact, if we perform any measurement in either of the two qubits, we will always get a completely random outcome.  Thus, this peculiar state has the intriguing property that even though we know the state of both qubits perfectly, we are completely ignorant of the state of each individual qubit. Mind-blowing isn’t it?



Any state that cannot be written in the form |state_1\rangle|state_2\rangle is called entangled, where |state_1\rangle is some state of the first qubit and |state_2\rangle is some state of the second qubit. You can check for yourself that indeed the state

\frac{1}{\sqrt{2}}(|0\rangle |1\rangle + |1\rangle |0\rangle) ,

which from now on we’ll call |\Psi\rangle, cannot be written in this form and is therefore an entangled state.

The Centre for Quantum Technologies, where I now work as a research fellow, organized a mini-competition last year to coin a new way of referring to entanglement to replace the popular “spooky action at a distance”, which I dislike (more on that in a few minutes). The winner entry was “Mutual existence”, which was chosen by writer George Musser and CQT professor Christian Kurtsiefer. You can read more about it and other entries here. In Musser’s words “I like ‘mutual existence’ because it captures the principle that entangled particles behave as a single unified system, with global properties that do not reside on either particle, or even derive from them.” Now you know what he means! The joint state of two entangled systems is perfectly defined, but in such a way that their individual states are not. Beautiful!

Now what happens if we measure one of the qubits in an entangled state? Well, we know we’ll get some outcome, but as you might have guessed, because the state of each individual qubit is not well defined, no matter what measurement we make, we’ll always obtain a random answer. If we measured the first qubit of state |\Psi\rangle by asking “are you in state |0\rangle or in state |1\rangle ?” we’ll obtain each possible answer with 50% probability. But notice something amazing: because quantum mechanics always gives consistent answers, if we then measure the second qubit we know what outcome we’ll obtain! If the outcome of the measurement of qubit 1 was “I’m in state |0\rangle” then for sure we’ll obtain outcome  “I’m in state |1\rangle” when we measure qubit 2, since |\Psi\rangle was an equal superposition of |0\rangle|1\rangle and |1\rangle|0\rangle . Moreover, this is true no matter how far apart the qubits are from each other.

Many people were frightened by this realization: the state of qubit 2 is initially not well-defined, but as soon as we measure qubit 1, we immediately know the state of qubit 2. This is what led Einstein to call this effect “spooky action at a distance”. But as you’ll see, it’s not spooky and it’s not action at a distance.

Following the argument of the great John Stewart Bell, imagine there is a person that always wears socks of different colours. In Bell’s case, this was his friend, Reinhold Bertlmann. On a given day, it was impossible to predict what sock he would wear on each foot. However, if you got a glimpse at one of his socks then you immediately knew that the other sock must be of a different colour. Sounds familiar?


The colour of Bertlmann’s socks is uncertain, but as soon as we see that one of them is pink, we immediately know the other isn’t.

So you see, there is nothing quantum about objects being correlated in this way: even if their states are uncertain, their shared properties may allow us to make inferences about one of them from knowledge of the other. Here’s what’s quantum about entangled states: this powerful correlation remains no matter what measurements we make!

Once again, in quantum mechanics, we have superpositions, so we can ask a richer class of questions. In the case of the entangled state |\Psi\rangle , we could ask the first qubit “Are you in state |+\rangle or in state |-\rangle.” You can check for yourselves (or trust me on this) that we can equivalently write |\Psi\rangle as |\Psi\rangle=\frac{1}{\sqrt{2}}(|+\rangle |+\rangle - |-\rangle |-\rangle) so now we know that the outcome of the same measurement on qubit 2 will always be the same as for qubit 1. This correlation between several different measurements is not possible to achieve classically: entangled states have much stronger correlations. That’s the reason that my personal entry for the mini competition was this:

Quantum correlations are stronger than classical ones and they lead to a myriad of applications, like randomness generation, quantum cryptography, and quantum teleportation. Perhaps most importantly, as shown by Bell in the 1970’s, the properties of entangled states have taught us that we cannot understand the world as being one in which the outcomes of all events have been pre-established and where signals cannot travel faster than light: at least one of these two principles does not hold in our universe.


I hope you have enjoyed this trip across the quantum world. My honest hope is to have given you an understanding of the basic concepts of quantum mechanics and, most importantly, to have ignited a desire to learn more about this most beautiful of theories.


Our Quantum World

I haven’t been blogging for a while, largely because I am busy trying to get a PhD, but also because I have re-directed my blogging efforts into helping create a new blog for the Institute for Quantum Computing! The blog is called “Our Quantum World” and if you haven’t seen it yet, I invite you to go check it out by visiting


We’ve had several great posts already by students, postdocs and faculty. The blog updates every two weeks and we have a lot of new content coming. I even wrote a post myself about academic publishing! Here is the link if you want to read it:


I feel a great sense of fulfillment to have taken part in this project and I genuinely hope that it will grow to be a window to share the brilliant ideas of researchers at IQC. Welcome to our quantum world! 🙂